=========================================================
Computing overlaps from file examples/lneed/lneed_commute.inp
---------------------------------------------------------
=========================================================
Recognized function symbols in input:

  name                arity   strict-pos  binder-arity        
  ----                -----   -----       -----               
  \                   1       []          [1]                 
  app                 2       [1]         [0,0]               

=========================================================

---------------------------------------------------------
================================================================================
Critical Pair:

  (
     A#9[(app (\ X#5.S#7) T#11[(letrec {E#1} in (letrec {E#2} in S#3))])]
    ,
     A#9[(letrec {X#5=T#11[(letrec {E#1;E#2} in S#3)]} in S#7)]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#11[(letrec {E#1;E#2} in S#3)],(\ X#5.[.])),
             (T#11[(letrec {E#1;E#2} in S#3)],(letrec {X#5=[.]} in S#7))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (\ X#5.S#7) T#11)],
           T#10  |->  (app (\ X#5.S#7) T#11),
           S#6   |->  T#11[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  A#9[(app (\ X#5.S#7) T#11[(letrec {E#1;E#2} in S#3)])]
    -llet-in1->                   A#9[(app (\ X#5.S#7) T#11[(letrec {E#1} in (letrec {E#2} in S#3))])]
    ................................................................................
                                  A#9[(app (\ X#5.S#7) T#11[(letrec {E#1;E#2} in S#3)])]
    -SR,lbeta1->                  A#9[(letrec {X#5=T#11[(letrec {E#1;E#2} in S#3)]} in S#7)]
    

================================================================================
Critical Pair:

  (
     A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(letrec {E#1} in (letrec {E#2} in S#3))])]
    ,
     A#9[(app A#10[(letrec {X#5=S#6} in S#7)] T#11[(letrec {E#1;E#2} in S#3)])]
  )

where

   Delta1 = {A#8,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7))}


and found solution:

    Sol = {T#4  |->  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11)],
           A#8  |->  A#9[(app A#10 T#11[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(letrec {E#1;E#2} in S#3)])]
    -llet-in1->                   A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(letrec {E#1} in (letrec {E#2} in S#3))])]
    ................................................................................
                                  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(letrec {E#1;E#2} in S#3)])]
    -SR,lbeta1->                  A#9[(app A#10[(letrec {X#5=S#6} in S#7)] T#11[(letrec {E#1;E#2} in S#3)])]
    

================================================================================
Critical Pair:

  (
     (app (\ X#5.S#7) T#9[(letrec {E#1} in (letrec {E#2} in S#3))])
    ,
     (letrec {X#5=T#9[(letrec {E#1;E#2} in S#3)]} in S#7)
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#9[(letrec {E#1;E#2} in S#3)],(\ X#5.[.])),
             (T#9[(letrec {E#1;E#2} in S#3)],(letrec {X#5=[.]} in S#7))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7))}


and found solution:

    Sol = {A#8  |->  [.],
           T#4  |->  (app (\ X#5.S#7) T#9),
           S#6  |->  T#9[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (app (\ X#5.S#7) T#9[(letrec {E#1;E#2} in S#3)])
    -llet-in1->                   (app (\ X#5.S#7) T#9[(letrec {E#1} in (letrec {E#2} in S#3))])
    ................................................................................
                                  (app (\ X#5.S#7) T#9[(letrec {E#1;E#2} in S#3)])
    -SR,lbeta1->                  (letrec {X#5=T#9[(letrec {E#1;E#2} in S#3)]} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#11[(app (\ X#5.S#8) T#13[(letrec {E#1} in (letrec {E#2} in S#3))])]
     )
    ,
     (letrec {E#6} in A#11[(letrec {X#5=T#13[(letrec {E#1;E#2} in S#3)]} in S#8)])
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#13[(letrec {E#1;E#2} in S#3)],(\ X#5.[.])),
             (T#13[(letrec {E#1;E#2} in S#3)],(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (\ X#5.S#8) T#13)],
           T#12  |->  (app (\ X#5.S#8) T#13),
           S#7   |->  T#13[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(letrec {E#1;E#2} in S#3)])])
    -llet-in1->                   (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(letrec {E#1} in (letrec {E#2} in S#3))])])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(letrec {E#1;E#2} in S#3)])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=T#13[(letrec {E#1;E#2} in S#3)]} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(letrec {E#1} in (letrec {E#2} in S#3))])]
     )
    ,
     (letrec
        E#6
     in
        A#11[(app A#12[(letrec {X#5=S#7} in S#8)] T#13[(letrec {E#1;E#2} in S#3)])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)]),
           T#10  |->  A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(letrec {E#1;E#2} in S#3)])])
    -llet-in1->                   (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(letrec {E#1} in (letrec {E#2} in S#3))])])
    ................................................................................
                                  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(letrec {E#1;E#2} in S#3)])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(app A#12[(letrec {X#5=S#7} in S#8)] T#13[(letrec {E#1;E#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        (app (\ X#5.S#8) T#11[(letrec {E#1} in (letrec {E#2} in S#3))])
     )
    ,
     (letrec {E#6} in (letrec {X#5=T#11[(letrec {E#1;E#2} in S#3)]} in S#8))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#11[(letrec {E#1;E#2} in S#3)],(\ X#5.[.])),
             (T#11[(letrec {E#1;E#2} in S#3)],(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in (app (\ X#5.S#8) T#11)),
           A#9   |->  [.],
           T#10  |->  (app (\ X#5.S#8) T#11),
           S#7   |->  T#11[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {E#6} in (app (\ X#5.S#8) T#11[(letrec {E#1;E#2} in S#3)]))
    -llet-in1->                   (letrec {E#6} in (app (\ X#5.S#8) T#11[(letrec {E#1} in (letrec {E#2} in S#3))]))
    ................................................................................
                                  (letrec {E#6} in (app (\ X#5.S#8) T#11[(letrec {E#1;E#2} in S#3)]))
    -SR,lbeta2->                  (letrec {E#6} in (letrec {X#5=T#11[(letrec {E#1;E#2} in S#3)]} in S#8))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(letrec {E#1} in (letrec {E#2} in S#3))]
       ;E#13
     in
        A#9[(app (\ X#5.S#8) S#7)]
     )
    ,
     (letrec
        X#11= T#10[(letrec {E#1;E#2} in S#3)]
       ;E#13
     in
        A#9[(letrec {X#5=S#7} in S#8)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;E#13} in A#9[(app (\ X#5.S#8) S#7)]),
           E#6   |->  {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    -llet-in1->                   (letrec {X#11=T#10[(letrec {E#1} in (letrec {E#2} in S#3))];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13} in A#9[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#1} in (letrec {E#2} in A#9[(app (\ X#5.S#8) S#7)]))
    ,
     (letrec {E#1;E#2} in A#9[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#9[(app (\ X#5.S#8) S#7)],
           E#6  |->  {E#1;E#2}}

and instantiated rules:

                                  (letrec {E#1;E#2} in A#9[(app (\ X#5.S#8) S#7)])
    -llet-in1->                   (letrec {E#1} in (letrec {E#2} in A#9[(app (\ X#5.S#8) S#7)]))
    ................................................................................
                                  (letrec {E#1;E#2} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#1;E#2} in A#9[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in (letrec {E#2} in S#3))])]
     )
    ,
     (letrec
        E#7
       ;EE#11[X#5,(letrec {X#6=S#8} in S#9)]
     in
        A#13[(app A#14[(var X#5)] T#15[(letrec {E#1;E#2} in S#3)])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {E#1;E#2} in S#3)])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {E#1;E#2} in S#3)])])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#5)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1;E#2} in S#3)])])
    -llet-in1->                   (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in (letrec {E#2} in S#3))])])
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1;E#2} in S#3)])])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1;E#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {E#1} in (letrec {E#2} in S#3))]
       ;E#15
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {E#1;E#2} in S#3)]
       ;E#15
       ;EE#11[X#5,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           E#7   |->  {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15},
           E#14  |->  {E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#13=T#12[(letrec {E#1} in (letrec {E#2} in S#3))];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (\ X#6.S#9) T#18[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {X#6=T#18[(letrec {E#1;E#2} in S#3)]} in S#9)]
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#18[(letrec {E#1;E#2} in S#3)],(\ X#6.[.])),
             (T#18[(letrec {E#1;E#2} in S#3)],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18)];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (\ X#6.S#9) T#18)],
           T#17         |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(letrec {E#1;E#2} in S#3)])];E#7} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(letrec {E#1} in (letrec {E#2} in S#3))])];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(letrec {E#1;E#2} in S#3)])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=T#18[(letrec {E#1;E#2} in S#3)]} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(app A#17[(letrec {X#6=S#8} in S#9)] T#18[(letrec {E#1;E#2} in S#3)])]
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[(letrec {E#1;E#2} in S#3)])]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           T#12         |->  A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(letrec {E#1;E#2} in S#3)])];E#7} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(letrec {E#1} in (letrec {E#2} in S#3))])];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(letrec {E#1;E#2} in S#3)])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(app A#17[(letrec {X#6=S#8} in S#9)] T#18[(letrec {E#1;E#2} in S#3)])];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (\ X#6.S#9) T#16[(letrec {E#1} in (letrec {E#2} in S#3))])
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {X#6=T#16[(letrec {E#1;E#2} in S#3)]} in S#9)
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#16[(letrec {E#1;E#2} in S#3)],(\ X#6.[.])),
             (T#16[(letrec {E#1;E#2} in S#3)],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (\ X#6.S#9) T#16);E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  [.],
           T#12         |->  (app (\ X#6.S#9) T#16),
           S#8          |->  T#16[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=(app (\ X#6.S#9) T#16[(letrec {E#1;E#2} in S#3)]);E#7} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#5=(app (\ X#6.S#9) T#16[(letrec {E#1} in (letrec {E#2} in S#3))]);E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (\ X#6.S#9) T#16[(letrec {E#1;E#2} in S#3)]);E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=(letrec {X#6=T#16[(letrec {E#1;E#2} in S#3)]} in S#9);E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#7
       ;EE#17[X#16,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])]
       ;E#7
       ;EE#17[X#16,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (letrec {E#2} in S#3))])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];E#7;EE#17[X#16,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (letrec {E#2} in S#3))])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (\ X#6.S#9) T#20[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=T#20[(letrec {E#1;E#2} in S#3)]} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#20[(letrec {E#1;E#2} in S#3)],(\ X#6.[.])),
             (T#20[(letrec {E#1;E#2} in S#3)],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (\ X#6.S#9) T#20)],
           T#19         |->  (app (\ X#6.S#9) T#20),
           S#8          |->  T#20[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[(letrec {E#1;E#2} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[(letrec {E#1} in (letrec {E#2} in S#3))])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[(letrec {E#1;E#2} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=T#20[(letrec {E#1;E#2} in S#3)]} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[(letrec {E#1;E#2} in S#3)])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[(letrec {E#1;E#2} in S#3)])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           T#12         |->  A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(letrec {E#1;E#2} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(letrec {E#1} in (letrec {E#2} in S#3))])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(letrec {E#1;E#2} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[(letrec {E#1;E#2} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (\ X#6.S#9) T#18[(letrec {E#1} in (letrec {E#2} in S#3))])
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#6=T#18[(letrec {E#1;E#2} in S#3)]} in S#9)
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#18[(letrec {E#1;E#2} in S#3)],(\ X#6.[.])),
             (T#18[(letrec {E#1;E#2} in S#3)],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (\ X#6.S#9) T#18);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=(app (\ X#6.S#9) T#18[(letrec {E#1;E#2} in S#3)]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#16=(app (\ X#6.S#9) T#18[(letrec {E#1} in (letrec {E#2} in S#3))]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (\ X#6.S#9) T#18[(letrec {E#1;E#2} in S#3)]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=(letrec {X#6=T#18[(letrec {E#1;E#2} in S#3)]} in S#9);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#14;E#15} in (letrec {E#12;E#13} in A#10[(var X#5)]))
    ,
     (letrec {E#13;E#15;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#12,E#14}
   Delta3 = {[{E#14;E#15},(letrec {E#12;E#13} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {
             {E#12;E#14} =?= {EE#11[X#5,(app (\ X#6.S#9) S#8)]}}

from overlapping -llet-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#10[(var X#5)],
           E#7  |->  {E#13;E#15},
           E#1  |->  {E#14;E#15},
           E#2  |->  {E#12;E#13}}

and instantiated rules:

                                  (letrec {E#12;E#13;E#14;E#15} in A#10[(var X#5)])
    -llet-in1->                   (letrec {E#14;E#15} in (letrec {E#12;E#13} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {E#13;E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#13;E#15;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
        ............................
    Delta4:
    {E#12;E#14} =?= {EE#11[X#5,(app (\ X#6.S#9) S#8)]}

================================================================================
Critical Pair:

  (
     (letrec {E#14;E#15} in (letrec {E#12;E#13} in A#10[(var X#5)]))
    ,
     (letrec {E#13;E#15;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#12,E#15}
   Delta3 = {[{E#14;E#15},(letrec {E#12;E#13} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {
             {E#12;E#14} =?= {EE#11[X#5,(app (\ X#6.S#9) S#8)]}}

from overlapping -llet-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#10[(var X#5)],
           E#7  |->  {E#13;E#15},
           E#1  |->  {E#14;E#15},
           E#2  |->  {E#12;E#13}}

and instantiated rules:

                                  (letrec {E#12;E#13;E#14;E#15} in A#10[(var X#5)])
    -llet-in1->                   (letrec {E#14;E#15} in (letrec {E#12;E#13} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {E#13;E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#13;E#15;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
        ............................
    Delta4:
    {E#12;E#14} =?= {EE#11[X#5,(app (\ X#6.S#9) S#8)]}

================================================================================
Critical Pair:

  (
     (letrec {E#14;E#15} in (letrec {E#12;E#13} in A#10[(var X#5)]))
    ,
     (letrec {E#13;E#15;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#13,E#14}
   Delta3 = {[{E#14;E#15},(letrec {E#12;E#13} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {
             {E#12;E#14} =?= {EE#11[X#5,(app (\ X#6.S#9) S#8)]}}

from overlapping -llet-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#10[(var X#5)],
           E#7  |->  {E#13;E#15},
           E#1  |->  {E#14;E#15},
           E#2  |->  {E#12;E#13}}

and instantiated rules:

                                  (letrec {E#12;E#13;E#14;E#15} in A#10[(var X#5)])
    -llet-in1->                   (letrec {E#14;E#15} in (letrec {E#12;E#13} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {E#13;E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#13;E#15;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
        ............................
    Delta4:
    {E#12;E#14} =?= {EE#11[X#5,(app (\ X#6.S#9) S#8)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#8)
       ;E#7
     in
        A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in (letrec {E#2} in S#3))])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#8)
       ;E#7
     in
        A#11[(app A#12[(\ X#6.S#8)] T#13[(letrec {E#1;E#2} in S#3)])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#11[(app A#12[[.]] T#13[(letrec {E#1;E#2} in S#3)])])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)]),
           T#10  |->  A#11[(app A#12[(var X#5)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1;E#2} in S#3)])])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in (letrec {E#2} in S#3))])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1;E#2} in S#3)])])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(\ X#6.S#8)] T#13[(letrec {E#1;E#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(letrec {E#1} in (letrec {E#2} in S#3))]
       ;X#5= (\ X#6.S#8)
       ;E#13
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#11= T#10[(letrec {E#1;E#2} in S#3)]
       ;X#5= (\ X#6.S#8)
       ;E#13
     in
        A#9[(\ X#6.S#8)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)]),
           E#7   |->  {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13},
           E#12  |->  {X#5=(\ X#6.S#8);E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    -llet-in1->                   (letrec {X#11=T#10[(letrec {E#1} in (letrec {E#2} in S#3))];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#8);E#13} in A#9[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#1} in (letrec {X#5=(\ X#6.S#8);E#10} in A#9[(var X#5)]))
    ,
     (letrec {X#5=(\ X#6.S#8);E#1;E#10} in A#9[(\ X#6.S#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {X#5=(\ X#6.S#8);E#10} in [.])],
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#9[(var X#5)],
           E#2  |->  {X#5=(\ X#6.S#8);E#10},
           E#7  |->  {E#1;E#10}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#1;E#10} in A#9[(var X#5)])
    -llet-in1->                   (letrec {E#1} in (letrec {X#5=(\ X#6.S#8);E#10} in A#9[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#1;E#10} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#1;E#10} in A#9[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(\ X#6.S#8);E#10} in (letrec {E#2} in A#9[(var X#5)]))
    ,
     (letrec {X#5=(\ X#6.S#8);E#10;E#2} in A#9[(\ X#6.S#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2}
   Delta3 = {[{X#5=(\ X#6.S#8);E#10},(letrec {E#2} in [.])],
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#9[(var X#5)],
           E#1  |->  {X#5=(\ X#6.S#8);E#10},
           E#7  |->  {E#10;E#2}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#10;E#2} in A#9[(var X#5)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#8);E#10} in (letrec {E#2} in A#9[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#10;E#2} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#10;E#2} in A#9[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(app A#14[(var X#7)] T#15[(letrec {E#1} in (letrec {E#2} in S#3))])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(app A#14[(\ X#6.S#9)] T#15[(letrec {E#1;E#2} in S#3)])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#13[(app A#14[[.]] T#15[(letrec {E#1;E#2} in S#3)])]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#7)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[(letrec {E#1;E#2} in S#3)])])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[(letrec {E#1} in (letrec {E#2} in S#3))])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[(letrec {E#1;E#2} in S#3)])])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(\ X#6.S#9)] T#15[(letrec {E#1;E#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {E#1} in (letrec {E#2} in S#3))]
       ;X#5= (\ X#6.S#9)
       ;E#15
       ;VV#11|X#7,(var X#5)|
     in
        A#10[(var X#7)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {E#1;E#2} in S#3)]
       ;X#5= (\ X#6.S#9)
       ;E#15
       ;VV#11|X#7,(var X#5)|
     in
        A#10[(\ X#6.S#9)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)]),
           E#8   |->  {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15},
           E#14  |->  {X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -llet-in1->                   (letrec {X#13=T#12[(letrec {E#1} in (letrec {E#2} in S#3))];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#15;E#16} in (letrec {X#5=(\ X#6.S#9);E#13;E#14} in A#10[(var X#7)]))
    ,
     (letrec {X#5=(\ X#6.S#9);E#14;E#16;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#13,E#16}
   Delta3 = {[{E#15;E#16},(letrec {X#5=(\ X#6.S#9);E#13;E#14} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {
             {E#13;E#15} =?= {VV#11|X#7,(var X#5)|}}

from overlapping -llet-in1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#4   |->  [.],
           S#3   |->  A#10[(var X#7)],
           E#2   |->  {X#5=(\ X#6.S#9);E#13;E#14},
           E#8   |->  {E#14;E#16},
           E#1   |->  {E#15;E#16},
           E#12  |->  {E#13;E#14}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#13;E#14;E#15;E#16} in A#10[(var X#7)])
    -llet-in1->                   (letrec {E#15;E#16} in (letrec {X#5=(\ X#6.S#9);E#13;E#14} in A#10[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#14;E#16;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#14;E#16;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
        ............................
    Delta4:
    {E#13;E#15} =?= {VV#11|X#7,(var X#5)|}

================================================================================
Critical Pair:

  (
     (letrec {X#5=(\ X#6.S#9);E#13;E#14} in (letrec {E#15;E#16} in A#10[(var X#7)]))
    ,
     (letrec {X#5=(\ X#6.S#9);E#14;E#16;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#13,E#16}
   Delta3 = {[{X#5=(\ X#6.S#9);E#13;E#14},(letrec {E#15;E#16} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {
             {E#13;E#15} =?= {VV#11|X#7,(var X#5)|}}

from overlapping -llet-in1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#4   |->  [.],
           S#3   |->  A#10[(var X#7)],
           E#1   |->  {X#5=(\ X#6.S#9);E#13;E#14},
           E#8   |->  {E#14;E#16},
           E#2   |->  {E#15;E#16},
           E#12  |->  {E#13;E#14}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#13;E#14;E#15;E#16} in A#10[(var X#7)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#9);E#13;E#14} in (letrec {E#15;E#16} in A#10[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#14;E#16;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#14;E#16;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
        ............................
    Delta4:
    {E#13;E#15} =?= {VV#11|X#7,(var X#5)|}

================================================================================
Critical Pair:

  (
     (letrec {X#5=(\ X#6.S#9);E#13;E#14} in (letrec {E#15;E#16} in A#10[(var X#7)]))
    ,
     (letrec {X#5=(\ X#6.S#9);E#14;E#16;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#15}
   Delta3 = {[{X#5=(\ X#6.S#9);E#13;E#14},(letrec {E#15;E#16} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {
             {E#13;E#15} =?= {VV#11|X#7,(var X#5)|}}

from overlapping -llet-in1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#4   |->  [.],
           S#3   |->  A#10[(var X#7)],
           E#1   |->  {X#5=(\ X#6.S#9);E#13;E#14},
           E#8   |->  {E#14;E#16},
           E#2   |->  {E#15;E#16},
           E#12  |->  {E#13;E#14}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#13;E#14;E#15;E#16} in A#10[(var X#7)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#9);E#13;E#14} in (letrec {E#15;E#16} in A#10[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#14;E#16;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#14;E#16;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
        ............................
    Delta4:
    {E#13;E#15} =?= {VV#11|X#7,(var X#5)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#14[(app A#15[(var X#7)] T#16[(letrec {E#1} in (letrec {E#2} in S#3))])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#14[(app A#15[(var X#7)] T#16[(letrec {E#1;E#2} in S#3)])]
     )
  )

where

   Delta1 = {A#11,T#13,T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#14[(app A#15[[.]] T#16[(letrec {E#1;E#2} in S#3)])]),
             ((var X#7),A#14[(app A#15[[.]] T#16[(letrec {E#1;E#2} in S#3)])])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#7)] T#16)],
           A#11  |->  A#14[(app A#15 T#16[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[(letrec {E#1;E#2} in S#3)])])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[(letrec {E#1} in (letrec {E#2} in S#3))])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[(letrec {E#1;E#2} in S#3)])])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[(app A#15[(var X#7)] T#16[(letrec {E#1;E#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {E#1} in (letrec {E#2} in S#3))]
       ;X#5= (\ X#6.S#9)
       ;E#16
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {E#1;E#2} in S#3)]
       ;X#5= (\ X#6.S#9)
       ;E#16
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#14=T#13;X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)]),
           E#8   |->  {X#14=T#13[(letrec {E#1;E#2} in S#3)];E#16},
           E#15  |->  {X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -llet-in1->                   (letrec {X#14=T#13[(letrec {E#1} in (letrec {E#2} in S#3))];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#14=T#13[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[(var X#5)] T#21[(letrec {E#1} in (letrec {E#2} in S#3))])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {E#1;E#2} in S#3)])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#18,A#16,T#13,T#4,A#10,A#17}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#19[(app A#20[[.]] T#21[(letrec {E#1;E#2} in S#3)])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21)]];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[A#19[(app A#20[(var X#5)] T#21)]],
           T#18         |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[(letrec {E#1;E#2} in S#3)])]];E#8} in A#11[(var X#7)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[(letrec {E#1} in (letrec {E#2} in S#3))])]];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[(letrec {E#1;E#2} in S#3)])]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {E#1;E#2} in S#3)])]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[A#10[(var X#5)]] T#19[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[A#10[(\ X#6.S#9)]] T#19[(letrec {E#1;E#2} in S#3)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19)];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] T#19[(letrec {E#1;E#2} in S#3)])]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  A#17[(app A#18[A#10[(var X#5)]] T#19)],
           A#16         |->  A#17[(app A#18 T#19[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[(letrec {E#1;E#2} in S#3)])];E#8} in A#11[(var X#7)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[(letrec {E#1} in (letrec {E#2} in S#3))])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[(letrec {E#1;E#2} in S#3)])];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(\ X#6.S#9)]] T#19[(letrec {E#1;E#2} in S#3)])];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[(var X#5)] T#19[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[(\ X#6.S#9)] T#19[(letrec {E#1;E#2} in S#3)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#17[(app A#18[[.]] T#19[(letrec {E#1;E#2} in S#3)])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19)];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  [.],
           T#13         |->  A#17[(app A#18[(var X#5)] T#19)],
           A#10         |->  A#17[(app A#18 T#19[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[(letrec {E#1;E#2} in S#3)])];E#8} in A#11[(var X#7)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[(letrec {E#1} in (letrec {E#2} in S#3))])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[(letrec {E#1;E#2} in S#3)])];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(\ X#6.S#9)] T#19[(letrec {E#1;E#2} in S#3)])];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(app A#20[(var X#17)] T#21[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#8
       ;EE#18[X#17,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(app A#20[(var X#17)] T#21[(letrec {E#1;E#2} in S#3)])]
       ;E#8
       ;EE#18[X#17,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21)];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] T#21[(letrec {E#1;E#2} in S#3)])];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#17,A#10[(var X#5)]]},
           T#13         |->  A#19[(app A#20[(var X#17)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#1;E#2} in S#3)])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#1} in (letrec {E#2} in S#3))])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#1;E#2} in S#3)])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#1;E#2} in S#3)])];E#8;EE#18[X#17,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {E#1;E#2} in S#3)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#1;E#2} in S#3)])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]},
           T#13         |->  A#21[(app A#22[(var X#18)] T#23)],
           A#16         |->  A#21[(app A#22 T#23[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -llet-in1->                   (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#1} in (letrec {E#2} in S#3))])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[A#21[(app A#22[(var X#5)] T#23[(letrec {E#1} in (letrec {E#2} in S#3))])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[(letrec {E#1;E#2} in S#3)])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#16,T#13,T#4,A#10,A#19}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#21[(app A#22[[.]] T#23[(letrec {E#1;E#2} in S#3)])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[A#21[(app A#22[(var X#5)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#5)] T#23)],
           A#10         |->  A#21[(app A#22 T#23[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[(letrec {E#1;E#2} in S#3)])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -llet-in1->                   (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[(letrec {E#1} in (letrec {E#2} in S#3))])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[(letrec {E#1;E#2} in S#3)])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[(letrec {E#1;E#2} in S#3)])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[A#10[(var X#5)]] T#21[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[(letrec {E#1;E#2} in S#3)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] T#21[(letrec {E#1;E#2} in S#3)])];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  A#19[(app A#20[A#10[(var X#5)]] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -llet-in1->                   (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[(letrec {E#1} in (letrec {E#2} in S#3))])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[(var X#5)] T#21[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {E#1;E#2} in S#3)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#19[(app A#20[[.]] T#21[(letrec {E#1;E#2} in S#3)])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -llet-in1->                   (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[(letrec {E#1} in (letrec {E#2} in S#3))])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#16;E#17} in (letrec {X#5=(\ X#6.S#9);E#14;E#15} in A#11[(var X#7)]))
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#15
       ;E#17
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#10}
   Delta2 = {E#1,E#2,E#14,E#17}
   Delta3 = {[{E#16;E#17},(letrec {X#5=(\ X#6.S#9);E#14;E#15} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {
             {E#14;E#16} =?= {EE#12[X#7,A#10[(var X#5)]]}}

from overlapping -llet-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           S#3   |->  A#11[(var X#7)],
           E#2   |->  {X#5=(\ X#6.S#9);E#14;E#15},
           E#8   |->  {E#15;E#17},
           E#1   |->  {E#16;E#17},
           E#13  |->  {E#14;E#15}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#14;E#15;E#16;E#17} in A#11[(var X#7)])
    -llet-in1->                   (letrec {E#16;E#17} in (letrec {X#5=(\ X#6.S#9);E#14;E#15} in A#11[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#15;E#17;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#15;E#17;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
        ............................
    Delta4:
    {E#14;E#16} =?= {EE#12[X#7,A#10[(var X#5)]]}

================================================================================
Critical Pair:

  (
     (letrec {X#5=(\ X#6.S#9);E#14;E#15} in (letrec {E#16;E#17} in A#11[(var X#7)]))
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#15
       ;E#17
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#10}
   Delta2 = {E#1,E#2,E#14,E#17}
   Delta3 = {[{X#5=(\ X#6.S#9);E#14;E#15},(letrec {E#16;E#17} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {
             {E#14;E#16} =?= {EE#12[X#7,A#10[(var X#5)]]}}

from overlapping -llet-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           S#3   |->  A#11[(var X#7)],
           E#1   |->  {X#5=(\ X#6.S#9);E#14;E#15},
           E#8   |->  {E#15;E#17},
           E#2   |->  {E#16;E#17},
           E#13  |->  {E#14;E#15}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#14;E#15;E#16;E#17} in A#11[(var X#7)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#9);E#14;E#15} in (letrec {E#16;E#17} in A#11[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#15;E#17;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#15;E#17;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
        ............................
    Delta4:
    {E#14;E#16} =?= {EE#12[X#7,A#10[(var X#5)]]}

================================================================================
Critical Pair:

  (
     (letrec {X#5=(\ X#6.S#9);E#14;E#15} in (letrec {E#16;E#17} in A#11[(var X#7)]))
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#15
       ;E#17
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#10}
   Delta2 = {E#1,E#2,E#16}
   Delta3 = {[{X#5=(\ X#6.S#9);E#14;E#15},(letrec {E#16;E#17} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {
             {E#14;E#16} =?= {EE#12[X#7,A#10[(var X#5)]]}}

from overlapping -llet-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           S#3   |->  A#11[(var X#7)],
           E#1   |->  {X#5=(\ X#6.S#9);E#14;E#15},
           E#8   |->  {E#15;E#17},
           E#2   |->  {E#16;E#17},
           E#13  |->  {E#14;E#15}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#14;E#15;E#16;E#17} in A#11[(var X#7)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#9);E#14;E#15} in (letrec {E#16;E#17} in A#11[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#15;E#17;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#15;E#17;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
        ............................
    Delta4:
    {E#14;E#16} =?= {EE#12[X#7,A#10[(var X#5)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(app A#17[(var X#7)] T#18[(letrec {E#1} in (letrec {E#2} in S#3))])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(app A#17[(var X#7)] T#18[(letrec {E#1;E#2} in S#3)])]
     )
  )

where

   Delta1 = {A#12,T#15,T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#16[(app A#17[[.]] T#18[(letrec {E#1;E#2} in S#3)])]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[(app A#17[[.]] T#18[(letrec {E#1;E#2} in S#3)])])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#7)] T#18)],
           A#12  |->  A#16[(app A#17 T#18[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(letrec {E#1;E#2} in S#3)])])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(letrec {E#1} in (letrec {E#2} in S#3))])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(letrec {E#1;E#2} in S#3)])])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(letrec {E#1;E#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(letrec {E#1} in (letrec {E#2} in S#3))]
       ;X#5= (\ X#6.S#10)
       ;E#18
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {E#1;E#2} in S#3)]
       ;X#5= (\ X#6.S#10)
       ;E#18
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#16=T#15;X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           E#9   |->  {X#16=T#15[(letrec {E#1;E#2} in S#3)];E#18},
           E#17  |->  {X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|}}

and instantiated rules:

                                  (letrec {X#16=T#15[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -llet-in1->                   (letrec {X#16=T#15[(letrec {E#1} in (letrec {E#2} in S#3))];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#16=T#15[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#16=T#15[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[(var X#8)] T#23[(letrec {E#1} in (letrec {E#2} in S#3))])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {E#1;E#2} in S#3)])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#4,A#11,A#19}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[(letrec {E#1;E#2} in S#3)])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19,
           T#15         |->  A#19[A#21[(app A#22[(var X#8)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[(letrec {E#1;E#2} in S#3)])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[(letrec {E#1} in (letrec {E#2} in S#3))])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[(letrec {E#1;E#2} in S#3)])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {E#1;E#2} in S#3)])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[A#11[(var X#8)]] T#21[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[A#11[(\ X#6.S#10)]] T#21[(letrec {E#1;E#2} in S#3)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[(letrec {E#1;E#2} in S#3)])]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  A#19[(app A#20[A#11[(var X#8)]] T#21)],
           A#18         |->  A#19[(app A#20 T#21[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[(letrec {E#1;E#2} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[(letrec {E#1} in (letrec {E#2} in S#3))])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[(letrec {E#1;E#2} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(\ X#6.S#10)]] T#21[(letrec {E#1;E#2} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[(var X#8)] T#21[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[(\ X#6.S#10)] T#21[(letrec {E#1;E#2} in S#3)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#19[(app A#20[[.]] T#21[(letrec {E#1;E#2} in S#3)])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           T#15         |->  A#19[(app A#20[(var X#8)] T#21)],
           A#11         |->  A#19[(app A#20 T#21[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[(letrec {E#1;E#2} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[(letrec {E#1} in (letrec {E#2} in S#3))])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[(letrec {E#1;E#2} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(\ X#6.S#10)] T#21[(letrec {E#1;E#2} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(app A#22[(var X#19)] T#23[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#9
       ;EE#20[X#19,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(app A#22[(var X#19)] T#23[(letrec {E#1;E#2} in S#3)])]
       ;E#9
       ;EE#20[X#19,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23)];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[(letrec {E#1;E#2} in S#3)])];EE#20[X#19,[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(letrec {E#1;E#2} in S#3)])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(letrec {E#1} in (letrec {E#2} in S#3))])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(letrec {E#1;E#2} in S#3)])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(letrec {E#1;E#2} in S#3)])];E#9;EE#20[X#19,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {E#1;E#2} in S#3)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {E#1;E#2} in S#3)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -llet-in1->                   (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {E#1} in (letrec {E#2} in S#3))])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(app A#24[(var X#8)] T#25[(letrec {E#1} in (letrec {E#2} in S#3))])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[(letrec {E#1;E#2} in S#3)])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#4,A#11,A#21}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[(app A#24[[.]] T#25[(letrec {E#1;E#2} in S#3)])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[A#23[(app A#24[(var X#8)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#8)] T#25)],
           A#11         |->  A#23[(app A#24 T#25[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[(letrec {E#1;E#2} in S#3)])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -llet-in1->                   (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[(letrec {E#1} in (letrec {E#2} in S#3))])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[(letrec {E#1;E#2} in S#3)])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[(letrec {E#1;E#2} in S#3)])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[A#11[(var X#8)]] T#23[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[(letrec {E#1;E#2} in S#3)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[(letrec {E#1;E#2} in S#3)])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  A#21[(app A#22[A#11[(var X#8)]] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -llet-in1->                   (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[(letrec {E#1} in (letrec {E#2} in S#3))])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(var X#8)] T#23[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {E#1;E#2} in S#3)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[(letrec {E#1;E#2} in S#3)])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           T#15         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -llet-in1->                   (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {E#1} in (letrec {E#2} in S#3))])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#19
       ;E#20
       ;E#21
     in
        (letrec {X#5=(\ X#6.S#10);E#16;E#17;E#18} in A#12[(var X#7)])
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#18
       ;E#21
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#11}
   Delta2 = {E#1,E#2,E#16,E#17,E#21}
   Delta3 = {[{E#19;E#20;E#21},(letrec {X#5=(\ X#6.S#10);E#16;E#17;E#18} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#16;E#19} =?= {VV#14|X#8,(var X#5)|},
             {E#17;E#20} =?= {EE#13[X#7,A#11[(var X#8)]]}}

from overlapping -llet-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           S#3   |->  A#12[(var X#7)],
           E#2   |->  {X#5=(\ X#6.S#10);E#16;E#17;E#18},
           E#9   |->  {E#18;E#21},
           E#1   |->  {E#19;E#20;E#21},
           E#15  |->  {E#16;E#17;E#18}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#16;E#17;E#18;E#19;E#20;E#21} in A#12[(var X#7)])
    -llet-in1->                   (letrec {E#19;E#20;E#21} in (letrec {X#5=(\ X#6.S#10);E#16;E#17;E#18} in A#12[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#18;E#21;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#18;E#21;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#16;E#19} =?= {VV#14|X#8,(var X#5)|},
    {E#17;E#20} =?= {EE#13[X#7,A#11[(var X#8)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#16
       ;E#17
       ;E#18
     in
        (letrec {E#19;E#20;E#21} in A#12[(var X#7)])
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#18
       ;E#21
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#11}
   Delta2 = {E#1,E#2,E#16,E#17,E#21}
   Delta3 = {[{X#5=(\ X#6.S#10);E#16;E#17;E#18},(letrec {E#19;E#20;E#21} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#16;E#19} =?= {VV#14|X#8,(var X#5)|},
             {E#17;E#20} =?= {EE#13[X#7,A#11[(var X#8)]]}}

from overlapping -llet-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           S#3   |->  A#12[(var X#7)],
           E#1   |->  {X#5=(\ X#6.S#10);E#16;E#17;E#18},
           E#9   |->  {E#18;E#21},
           E#2   |->  {E#19;E#20;E#21},
           E#15  |->  {E#16;E#17;E#18}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#16;E#17;E#18;E#19;E#20;E#21} in A#12[(var X#7)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#10);E#16;E#17;E#18} in (letrec {E#19;E#20;E#21} in A#12[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#18;E#21;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#18;E#21;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#16;E#19} =?= {VV#14|X#8,(var X#5)|},
    {E#17;E#20} =?= {EE#13[X#7,A#11[(var X#8)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#16
       ;E#17
       ;E#18
     in
        (letrec {E#19;E#20;E#21} in A#12[(var X#7)])
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#18
       ;E#21
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#11}
   Delta2 = {E#1,E#2,E#16,E#20}
   Delta3 = {[{X#5=(\ X#6.S#10);E#16;E#17;E#18},(letrec {E#19;E#20;E#21} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#16;E#19} =?= {VV#14|X#8,(var X#5)|},
             {E#17;E#20} =?= {EE#13[X#7,A#11[(var X#8)]]}}

from overlapping -llet-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           S#3   |->  A#12[(var X#7)],
           E#1   |->  {X#5=(\ X#6.S#10);E#16;E#17;E#18},
           E#9   |->  {E#18;E#21},
           E#2   |->  {E#19;E#20;E#21},
           E#15  |->  {E#16;E#17;E#18}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#16;E#17;E#18;E#19;E#20;E#21} in A#12[(var X#7)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#10);E#16;E#17;E#18} in (letrec {E#19;E#20;E#21} in A#12[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#18;E#21;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#18;E#21;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#16;E#19} =?= {VV#14|X#8,(var X#5)|},
    {E#17;E#20} =?= {EE#13[X#7,A#11[(var X#8)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#16
       ;E#17
       ;E#18
     in
        (letrec {E#19;E#20;E#21} in A#12[(var X#7)])
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#18
       ;E#21
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#11}
   Delta2 = {E#1,E#2,E#19,E#20}
   Delta3 = {[{X#5=(\ X#6.S#10);E#16;E#17;E#18},(letrec {E#19;E#20;E#21} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#16;E#19} =?= {VV#14|X#8,(var X#5)|},
             {E#17;E#20} =?= {EE#13[X#7,A#11[(var X#8)]]}}

from overlapping -llet-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           S#3   |->  A#12[(var X#7)],
           E#1   |->  {X#5=(\ X#6.S#10);E#16;E#17;E#18},
           E#9   |->  {E#18;E#21},
           E#2   |->  {E#19;E#20;E#21},
           E#15  |->  {E#16;E#17;E#18}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#16;E#17;E#18;E#19;E#20;E#21} in A#12[(var X#7)])
    -llet-in1->                   (letrec {X#5=(\ X#6.S#10);E#16;E#17;E#18} in (letrec {E#19;E#20;E#21} in A#12[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#18;E#21;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#18;E#21;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#16;E#19} =?= {VV#14|X#8,(var X#5)|},
    {E#17;E#20} =?= {EE#13[X#7,A#11[(var X#8)]]}

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (letrec {E#6} in T#9[(letrec {E#1} in (letrec {E#2} in S#3))]))
    ,
     (letrec {E#5;E#6} in T#9[(letrec {E#1;E#2} in S#3)])
  )

where

   Delta1 = {T#8,T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             [{E#5},(letrec {E#6} in [.])]}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4  |->  (letrec {E#5} in (letrec {E#6} in T#9)),
           T#8  |->  (letrec {E#6} in T#9),
           S#7  |->  T#9[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {E#5} in (letrec {E#6} in T#9[(letrec {E#1;E#2} in S#3)]))
    -llet-in1->                   (letrec {E#5} in (letrec {E#6} in T#9[(letrec {E#1} in (letrec {E#2} in S#3))]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in T#9[(letrec {E#1;E#2} in S#3)]))
    -SR,llet-in1->                (letrec {E#5;E#6} in T#9[(letrec {E#1;E#2} in S#3)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (letrec {X#10=T#9[(letrec {E#1} in (letrec {E#2} in S#3))];E#12} in S#7)
     )
    ,
     (letrec {X#10=T#9[(letrec {E#1;E#2} in S#3)];E#12;E#5} in S#7)
  )

where

   Delta1 = {T#8,T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             [{E#5},(letrec {X#10=T#9[(letrec {E#1;E#2} in S#3)];E#12} in [.])]}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (letrec {X#10=T#9;E#12} in S#7)),
           T#8   |->  (letrec {X#10=T#9;E#12} in S#7),
           E#6   |->  {X#10=T#9[(letrec {E#1;E#2} in S#3)];E#12},
           E#11  |->  {E#12}}

and instantiated rules:

                                  (letrec {E#5} in (letrec {X#10=T#9[(letrec {E#1;E#2} in S#3)];E#12} in S#7))
    -llet-in1->                   (letrec {E#5} in (letrec {X#10=T#9[(letrec {E#1} in (letrec {E#2} in S#3))];E#12} in S#7))
    ................................................................................
                                  (letrec {E#5} in (letrec {X#10=T#9[(letrec {E#1;E#2} in S#3)];E#12} in S#7))
    -SR,llet-in1->                (letrec {X#10=T#9[(letrec {E#1;E#2} in S#3)];E#12;E#5} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (letrec {E#1} in (letrec {E#2} in S#7)))
    ,
     (letrec {E#1;E#2;E#5} in S#7)
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             [{E#5},(letrec {E#1;E#2} in [.])]}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4  |->  (letrec {E#5} in [.]),
           T#8  |->  [.],
           S#3  |->  S#7,
           E#6  |->  {E#1;E#2}}

and instantiated rules:

                                  (letrec {E#5} in (letrec {E#1;E#2} in S#7))
    -llet-in1->                   (letrec {E#5} in (letrec {E#1} in (letrec {E#2} in S#7)))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#1;E#2} in S#7))
    -SR,llet-in1->                (letrec {E#1;E#2;E#5} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= T#8[(letrec {E#1} in (letrec {E#2} in S#3))]
       ;E#11
     in
        (letrec {E#6} in S#7)
     )
    ,
     (letrec {X#9=T#8[(letrec {E#1;E#2} in S#3)];E#11;E#6} in S#7)
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             [{X#9=T#8[(letrec {E#1;E#2} in S#3)];E#11},(letrec {E#6} in [.])]}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4   |->  (letrec {X#9=T#8;E#11} in (letrec {E#6} in S#7)),
           E#5   |->  {X#9=T#8[(letrec {E#1;E#2} in S#3)];E#11},
           E#10  |->  {E#11}}

and instantiated rules:

                                  (letrec {X#9=T#8[(letrec {E#1;E#2} in S#3)];E#11} in (letrec {E#6} in S#7))
    -llet-in1->                   (letrec {X#9=T#8[(letrec {E#1} in (letrec {E#2} in S#3))];E#11} in (letrec {E#6} in S#7))
    ................................................................................
                                  (letrec {X#9=T#8[(letrec {E#1;E#2} in S#3)];E#11} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {X#9=T#8[(letrec {E#1;E#2} in S#3)];E#11;E#6} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {E#1} in (letrec {E#2} in (letrec {E#6} in S#7)))
    ,
     (letrec {E#1;E#2;E#6} in S#7)
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             [{E#1;E#2},(letrec {E#6} in [.])]}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  (letrec {E#6} in S#7),
           E#5  |->  {E#1;E#2}}

and instantiated rules:

                                  (letrec {E#1;E#2} in (letrec {E#6} in S#7))
    -llet-in1->                   (letrec {E#1} in (letrec {E#2} in (letrec {E#6} in S#7)))
    ................................................................................
                                  (letrec {E#1;E#2} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#1;E#2;E#6} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in S#8)
       ;E#7
     in
        A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in (letrec {E#2} in S#3))])]
     )
    ,
     (letrec
        X#5= S#8
       ;E#6
       ;E#7
     in
        A#11[(app A#12[(var X#5)] T#13[(letrec {E#1;E#2} in S#3)])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (A#11[(app A#12[(var X#5)] T#13[(letrec {E#1;E#2} in S#3)])],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#5),A#11[(app A#12[[.]] T#13[(letrec {E#1;E#2} in S#3)])]),
             ((var X#5),A#11[(app A#12[[.]] T#13[(letrec {E#1;E#2} in S#3)])])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)]),
           T#10  |->  A#11[(app A#12[(var X#5)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1;E#2} in S#3)])])
    -llet-in1->                   (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in (letrec {E#2} in S#3))])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1;E#2} in S#3)])])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1;E#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in T#13[(letrec {E#1} in (letrec {E#2} in S#3))])
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#5=T#13[(letrec {E#1;E#2} in S#3)];E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#6} in T#13);E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  (letrec {E#6} in T#13),
           S#8   |->  T#13[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in T#13[(letrec {E#1;E#2} in S#3)]);E#7} in A#9[(var X#5)])
    -llet-in1->                   (letrec {X#5=(letrec {E#6} in T#13[(letrec {E#1} in (letrec {E#2} in S#3))]);E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in T#13[(letrec {E#1;E#2} in S#3)]);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=T#13[(letrec {E#1;E#2} in S#3)];E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#14=T#13[(letrec {E#1} in (letrec {E#2} in S#3))];E#16} in S#8)
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {E#1;E#2} in S#3)]
       ;X#5= S#8
       ;E#16
       ;E#7
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (A#9[(var X#5)],(letrec {X#14=T#13[(letrec {E#1;E#2} in S#3)];E#16} in [.])),
             [{E#7},(letrec {X#14=T#13[(letrec {E#1;E#2} in S#3)];E#16} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {X#14=T#13;E#16} in S#8);E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  (letrec {X#14=T#13;E#16} in S#8),
           E#6   |->  {X#14=T#13[(letrec {E#1;E#2} in S#3)];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#14=T#13[(letrec {E#1;E#2} in S#3)];E#16} in S#8);E#7} in A#9[(var X#5)])
    -llet-in1->                   (letrec {X#5=(letrec {X#14=T#13[(letrec {E#1} in (letrec {E#2} in S#3))];E#16} in S#8);E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {X#14=T#13[(letrec {E#1;E#2} in S#3)];E#16} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#14=T#13[(letrec {E#1;E#2} in S#3)];X#5=S#8;E#16;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(letrec {E#1} in (letrec {E#2} in S#8));E#7} in A#9[(var X#5)])
    ,
     (letrec {X#5=S#8;E#1;E#2;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (A#9[(var X#5)],(letrec {E#1;E#2} in [.])),
             [{E#7},(letrec {E#1;E#2} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=[.];E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  [.],
           S#3   |->  S#8,
           E#6   |->  {E#1;E#2}}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#1;E#2} in S#8);E#7} in A#9[(var X#5)])
    -llet-in1->                   (letrec {X#5=(letrec {E#1} in (letrec {E#2} in S#8));E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#1;E#2} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#1;E#2;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(letrec {E#1} in (letrec {E#2} in S#3))]
       ;X#5= (letrec {E#6} in S#8)
       ;E#13
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#11= T#10[(letrec {E#1;E#2} in S#3)]
       ;X#5= S#8
       ;E#13
       ;E#6
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13},(letrec {E#6} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)]),
           E#7   |->  {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13},
           E#12  |->  {X#5=(letrec {E#6} in S#8);E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    -llet-in1->                   (letrec {X#11=T#10[(letrec {E#1} in (letrec {E#2} in S#3))];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];X#5=S#8;E#13;E#6} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#1} in (letrec {X#5=(letrec {E#6} in S#8);E#10} in A#9[(var X#5)]))
    ,
     (letrec {X#5=S#8;E#1;E#10;E#6} in A#9[(var X#5)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {[{E#1},(letrec {X#5=(letrec {E#6} in S#8);E#10} in [.])],
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#1;E#10},(letrec {E#6} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#9[(var X#5)],
           E#2  |->  {X#5=(letrec {E#6} in S#8);E#10},
           E#7  |->  {E#1;E#10}}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#1;E#10} in A#9[(var X#5)])
    -llet-in1->                   (letrec {E#1} in (letrec {X#5=(letrec {E#6} in S#8);E#10} in A#9[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#1;E#10} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#1;E#10;E#6} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(letrec {E#6} in S#8);E#10} in (letrec {E#2} in A#9[(var X#5)]))
    ,
     (letrec {X#5=S#8;E#10;E#2;E#6} in A#9[(var X#5)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {[{X#5=(letrec {E#6} in S#8);E#10},(letrec {E#2} in [.])],
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#10;E#2},(letrec {E#6} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#9[(var X#5)],
           E#1  |->  {X#5=(letrec {E#6} in S#8);E#10},
           E#7  |->  {E#10;E#2}}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#10;E#2} in A#9[(var X#5)])
    -llet-in1->                   (letrec {X#5=(letrec {E#6} in S#8);E#10} in (letrec {E#2} in A#9[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#10;E#2} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#10;E#2;E#6} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(app A#14[(var X#6)] T#15[(letrec {E#1} in (letrec {E#2} in S#3))])]
     )
    ,
     (letrec
        X#5= S#9
       ;E#7
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(app A#14[(var X#6)] T#15[(letrec {E#1;E#2} in S#3)])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#13[(app A#14[(var X#6)] T#15[(letrec {E#1;E#2} in S#3)])],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#13[(app A#14[[.]] T#15[(letrec {E#1;E#2} in S#3)])]),
             ((var X#5),[.]),
             ((var X#6),A#13[(app A#14[[.]] T#15[(letrec {E#1;E#2} in S#3)])])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#6)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(letrec {E#1;E#2} in S#3)])])
    -llet-in1->                   (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(letrec {E#1} in (letrec {E#2} in S#3))])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(letrec {E#1;E#2} in S#3)])])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(letrec {E#1;E#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in T#15[(letrec {E#1} in (letrec {E#2} in S#3))])
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= T#15[(letrec {E#1;E#2} in S#3)]
       ;E#7
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#7} in T#15);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  (letrec {E#7} in T#15),
           S#9   |->  T#15[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in T#15[(letrec {E#1;E#2} in S#3)]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -llet-in1->                   (letrec {X#5=(letrec {E#7} in T#15[(letrec {E#1} in (letrec {E#2} in S#3))]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in T#15[(letrec {E#1;E#2} in S#3)]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=T#15[(letrec {E#1;E#2} in S#3)];E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#16=T#15[(letrec {E#1} in (letrec {E#2} in S#3))];E#18} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {E#1;E#2} in S#3)]
       ;X#5= S#9
       ;E#18
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {X#16=T#15[(letrec {E#1;E#2} in S#3)];E#18;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {X#16=T#15[(letrec {E#1;E#2} in S#3)];E#18} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {X#16=T#15[(letrec {E#1;E#2} in S#3)];E#18} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {X#16=T#15;E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  (letrec {X#16=T#15;E#18} in S#9),
           E#7   |->  {X#16=T#15[(letrec {E#1;E#2} in S#3)];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#16=T#15[(letrec {E#1;E#2} in S#3)];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -llet-in1->                   (letrec {X#5=(letrec {X#16=T#15[(letrec {E#1} in (letrec {E#2} in S#3))];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {X#16=T#15[(letrec {E#1;E#2} in S#3)];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=T#15[(letrec {E#1;E#2} in S#3)];X#5=S#9;E#18;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#1} in (letrec {E#2} in S#9))
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#5=S#9;E#1;E#2;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {E#1;E#2;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#1;E#2} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#1;E#2} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=[.];E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  [.],
           S#3   |->  S#9,
           E#7   |->  {E#1;E#2}}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#1;E#2} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -llet-in1->                   (letrec {X#5=(letrec {E#1} in (letrec {E#2} in S#9));E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#1;E#2} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#1;E#2;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {E#1} in (letrec {E#2} in S#3))]
       ;X#5= (letrec {E#7} in S#9)
       ;E#15
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {E#1;E#2} in S#3)]
       ;X#5= S#9
       ;E#15
       ;E#7
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15;E#7;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           E#8   |->  {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15},
           E#14  |->  {X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -llet-in1->                   (letrec {X#13=T#12[(letrec {E#1} in (letrec {E#2} in S#3))];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];X#5=S#9;E#15;E#7;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#16[(app A#17[(var X#5)] T#18[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#16[(app A#17[(var X#5)] T#18[(letrec {E#1;E#2} in S#3)])]
       ;E#7
       ;E#8
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1;E#2} in S#3)])];E#7;E#8} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1;E#2} in S#3)])];E#8},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18)];E#8} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[(letrec {E#1;E#2} in S#3)])]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8},
           T#12         |->  A#16[(app A#17[(var X#5)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1;E#2} in S#3)])];E#8} in A#10[(var X#6)])
    -llet-in1->                   (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1} in (letrec {E#2} in S#3))])];E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1;E#2} in S#3)])];E#8} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1;E#2} in S#3)])];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])]
       ;E#7
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];E#7;E#8;EE#17[X#16,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];E#8;EE#17[X#16,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20)];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#16,(var X#5)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -llet-in1->                   (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (letrec {E#2} in S#3))])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];E#7;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -llet-in1->                   (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (letrec {E#2} in S#3))])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];X#5=S#9;E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(var X#5)] T#20[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(var X#5)] T#20[(letrec {E#1;E#2} in S#3)])]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1;E#2} in S#3)])];E#7;E#8;EE#17[X#6,(var X#16)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1;E#2} in S#3)])];E#8;EE#17[X#6,(var X#16)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20)];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[(letrec {E#1;E#2} in S#3)])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]},
           T#12         |->  A#18[(app A#19[(var X#5)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1;E#2} in S#3)])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -llet-in1->                   (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1} in (letrec {E#2} in S#3))])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1;E#2} in S#3)])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1;E#2} in S#3)])];X#5=S#9;E#7;E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#15
       ;E#16
     in
        (letrec {X#5=(letrec {E#7} in S#9);E#13;E#14} in A#10[(var X#6)])
     )
    ,
     (letrec {X#5=S#9;E#14;E#16;E#7;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#7,E#13,E#16}
   Delta3 = {[{E#15;E#16},(letrec {X#5=(letrec {E#7} in S#9);E#13;E#14} in [.])],
             ((var X#5),(letrec {E#14;E#16;E#7;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#14;E#16;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {
             {E#13;E#15} =?= {EE#11[X#6,(var X#5)]}}

from overlapping -llet-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           S#3   |->  A#10[(var X#6)],
           E#2   |->  {X#5=(letrec {E#7} in S#9);E#13;E#14},
           E#8   |->  {E#14;E#16},
           E#1   |->  {E#15;E#16},
           E#12  |->  {E#13;E#14}}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#13;E#14;E#15;E#16} in A#10[(var X#6)])
    -llet-in1->                   (letrec {E#15;E#16} in (letrec {X#5=(letrec {E#7} in S#9);E#13;E#14} in A#10[(var X#6)]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#14;E#16;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#14;E#16;E#7;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
        ............................
    Delta4:
    {E#13;E#15} =?= {EE#11[X#6,(var X#5)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#13
       ;E#14
     in
        (letrec {E#15;E#16} in A#10[(var X#6)])
     )
    ,
     (letrec {X#5=S#9;E#14;E#16;E#7;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#7,E#13,E#16}
   Delta3 = {[{X#5=(letrec {E#7} in S#9);E#13;E#14},(letrec {E#15;E#16} in [.])],
             ((var X#5),(letrec {E#14;E#16;E#7;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#14;E#16;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {
             {E#13;E#15} =?= {EE#11[X#6,(var X#5)]}}

from overlapping -llet-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           S#3   |->  A#10[(var X#6)],
           E#1   |->  {X#5=(letrec {E#7} in S#9);E#13;E#14},
           E#8   |->  {E#14;E#16},
           E#2   |->  {E#15;E#16},
           E#12  |->  {E#13;E#14}}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#13;E#14;E#15;E#16} in A#10[(var X#6)])
    -llet-in1->                   (letrec {X#5=(letrec {E#7} in S#9);E#13;E#14} in (letrec {E#15;E#16} in A#10[(var X#6)]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#14;E#16;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#14;E#16;E#7;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
        ............................
    Delta4:
    {E#13;E#15} =?= {EE#11[X#6,(var X#5)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#13
       ;E#14
     in
        (letrec {E#15;E#16} in A#10[(var X#6)])
     )
    ,
     (letrec {X#5=S#9;E#14;E#16;E#7;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#7,E#15}
   Delta3 = {[{X#5=(letrec {E#7} in S#9);E#13;E#14},(letrec {E#15;E#16} in [.])],
             ((var X#5),(letrec {E#14;E#16;E#7;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#14;E#16;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {
             {E#13;E#15} =?= {EE#11[X#6,(var X#5)]}}

from overlapping -llet-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           S#3   |->  A#10[(var X#6)],
           E#1   |->  {X#5=(letrec {E#7} in S#9);E#13;E#14},
           E#8   |->  {E#14;E#16},
           E#2   |->  {E#15;E#16},
           E#12  |->  {E#13;E#14}}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#13;E#14;E#15;E#16} in A#10[(var X#6)])
    -llet-in1->                   (letrec {X#5=(letrec {E#7} in S#9);E#13;E#14} in (letrec {E#15;E#16} in A#10[(var X#6)]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#14;E#16;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#14;E#16;E#7;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
        ............................
    Delta4:
    {E#13;E#15} =?= {EE#11[X#6,(var X#5)]}

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {E#5} in T#12[(letrec {E#1} in (letrec {E#2} in S#3))]) S#6)]
    ,
     A#9[(letrec {E#5} in (app T#12[(letrec {E#1;E#2} in S#3)] S#6))]
  )

where

   Delta1 = {T#11,T#10,A#8,T#4,A#9}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (letrec {E#5} in T#12) S#6)],
           T#10  |->  (app (letrec {E#5} in T#12) S#6),
           T#11  |->  (letrec {E#5} in T#12),
           S#7   |->  T#12[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in T#12[(letrec {E#1;E#2} in S#3)]) S#6)]
    -llet-in1->                   A#9[(app (letrec {E#5} in T#12[(letrec {E#1} in (letrec {E#2} in S#3))]) S#6)]
    ................................................................................
                                  A#9[(app (letrec {E#5} in T#12[(letrec {E#1;E#2} in S#3)]) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app T#12[(letrec {E#1;E#2} in S#3)] S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {X#13=T#12[(letrec {E#1} in (letrec {E#2} in S#3))];E#15} in S#7) S#6)]
    ,
     A#9[(letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15} in (app S#7 S#6))]
  )

where

   Delta1 = {T#11,T#10,A#8,T#4,A#9}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#6,(letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (letrec {X#13=T#12;E#15} in S#7) S#6)],
           T#10  |->  (app (letrec {X#13=T#12;E#15} in S#7) S#6),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#7),
           E#5   |->  {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  A#9[(app (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15} in S#7) S#6)]
    -llet-in1->                   A#9[(app (letrec {X#13=T#12[(letrec {E#1} in (letrec {E#2} in S#3))];E#15} in S#7) S#6)]
    ................................................................................
                                  A#9[(app (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {E#1} in (letrec {E#2} in S#7)) S#6)]
    ,
     A#9[(letrec {E#1;E#2} in (app S#7 S#6))]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#6,(letrec {E#1;E#2} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app [.] S#6)],
           T#10  |->  (app [.] S#6),
           T#11  |->  [.],
           S#3   |->  S#7,
           E#5   |->  {E#1;E#2}}

and instantiated rules:

                                  A#9[(app (letrec {E#1;E#2} in S#7) S#6)]
    -llet-in1->                   A#9[(app (letrec {E#1} in (letrec {E#2} in S#7)) S#6)]
    ................................................................................
                                  A#9[(app (letrec {E#1;E#2} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#1;E#2} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {E#5} in S#7) T#11[(letrec {E#1} in (letrec {E#2} in S#3))])]
    ,
     A#9[(letrec {E#5} in (app S#7 T#11[(letrec {E#1;E#2} in S#3)]))]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#11[(letrec {E#1;E#2} in S#3)],(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (letrec {E#5} in S#7) T#11)],
           T#10  |->  (app (letrec {E#5} in S#7) T#11),
           S#6   |->  T#11[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in S#7) T#11[(letrec {E#1;E#2} in S#3)])]
    -llet-in1->                   A#9[(app (letrec {E#5} in S#7) T#11[(letrec {E#1} in (letrec {E#2} in S#3))])]
    ................................................................................
                                  A#9[(app (letrec {E#5} in S#7) T#11[(letrec {E#1;E#2} in S#3)])]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app S#7 T#11[(letrec {E#1;E#2} in S#3)]))]
    

================================================================================
Critical Pair:

  (
     A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(letrec {E#1} in (letrec {E#2} in S#3))])]
    ,
     A#9[(app A#10[(letrec {E#5} in (app S#7 S#6))] T#11[(letrec {E#1;E#2} in S#3)])]
  )

where

   Delta1 = {A#8,T#4}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#4  |->  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11)],
           A#8  |->  A#9[(app A#10 T#11[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(letrec {E#1;E#2} in S#3)])]
    -llet-in1->                   A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(letrec {E#1} in (letrec {E#2} in S#3))])]
    ................................................................................
                                  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(letrec {E#1;E#2} in S#3)])]
    -SR,lapp1->                   A#9[(app A#10[(letrec {E#5} in (app S#7 S#6))] T#11[(letrec {E#1;E#2} in S#3)])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#5} in T#10[(letrec {E#1} in (letrec {E#2} in S#3))]) S#6)
    ,
     (letrec {E#5} in (app T#10[(letrec {E#1;E#2} in S#3)] S#6))
  )

where

   Delta1 = {T#9,T#4}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8  |->  [.],
           T#4  |->  (app (letrec {E#5} in T#10) S#6),
           T#9  |->  (letrec {E#5} in T#10),
           S#7  |->  T#10[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (app (letrec {E#5} in T#10[(letrec {E#1;E#2} in S#3)]) S#6)
    -llet-in1->                   (app (letrec {E#5} in T#10[(letrec {E#1} in (letrec {E#2} in S#3))]) S#6)
    ................................................................................
                                  (app (letrec {E#5} in T#10[(letrec {E#1;E#2} in S#3)]) S#6)
    -SR,lapp1->                   (letrec {E#5} in (app T#10[(letrec {E#1;E#2} in S#3)] S#6))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#11=T#10[(letrec {E#1} in (letrec {E#2} in S#3))];E#13} in S#7) S#6)
    ,
     (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13} in (app S#7 S#6))
  )

where

   Delta1 = {T#9,T#4}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#6,(letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  [.],
           T#4   |->  (app (letrec {X#11=T#10;E#13} in S#7) S#6),
           T#9   |->  (letrec {X#11=T#10;E#13} in S#7),
           E#5   |->  {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (app (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13} in S#7) S#6)
    -llet-in1->                   (app (letrec {X#11=T#10[(letrec {E#1} in (letrec {E#2} in S#3))];E#13} in S#7) S#6)
    ................................................................................
                                  (app (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13} in S#7) S#6)
    -SR,lapp1->                   (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13} in (app S#7 S#6))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#1} in (letrec {E#2} in S#7)) S#6)
    ,
     (letrec {E#1;E#2} in (app S#7 S#6))
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#6,(letrec {E#1;E#2} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8  |->  [.],
           T#4  |->  (app [.] S#6),
           T#9  |->  [.],
           S#3  |->  S#7,
           E#5  |->  {E#1;E#2}}

and instantiated rules:

                                  (app (letrec {E#1;E#2} in S#7) S#6)
    -llet-in1->                   (app (letrec {E#1} in (letrec {E#2} in S#7)) S#6)
    ................................................................................
                                  (app (letrec {E#1;E#2} in S#7) S#6)
    -SR,lapp1->                   (letrec {E#1;E#2} in (app S#7 S#6))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#5} in S#7) T#9[(letrec {E#1} in (letrec {E#2} in S#3))])
    ,
     (letrec {E#5} in (app S#7 T#9[(letrec {E#1;E#2} in S#3)]))
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#9[(letrec {E#1;E#2} in S#3)],(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8  |->  [.],
           T#4  |->  (app (letrec {E#5} in S#7) T#9),
           S#6  |->  T#9[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (app (letrec {E#5} in S#7) T#9[(letrec {E#1;E#2} in S#3)])
    -llet-in1->                   (app (letrec {E#5} in S#7) T#9[(letrec {E#1} in (letrec {E#2} in S#3))])
    ................................................................................
                                  (app (letrec {E#5} in S#7) T#9[(letrec {E#1;E#2} in S#3)])
    -SR,lapp1->                   (letrec {E#5} in (app S#7 T#9[(letrec {E#1;E#2} in S#3)]))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {E#6} in T#14[(letrec {E#1} in (letrec {E#2} in S#3))]) S#7)]
     )
    ,
     (letrec
        E#5
     in
        A#11[(letrec {E#6} in (app T#14[(letrec {E#1;E#2} in S#3)] S#7))]
     )
  )

where

   Delta1 = {T#13,T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14) S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {E#6} in T#14) S#7)],
           T#12  |->  (app (letrec {E#6} in T#14) S#7),
           T#13  |->  (letrec {E#6} in T#14),
           S#8   |->  T#14[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(letrec {E#1;E#2} in S#3)]) S#7)])
    -llet-in1->                   (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(letrec {E#1} in (letrec {E#2} in S#3))]) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(letrec {E#1;E#2} in S#3)]) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[(letrec {E#1;E#2} in S#3)] S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {X#15=T#14[(letrec {E#1} in (letrec {E#2} in S#3))];E#17} in S#8) S#7)]
     )
    ,
     (letrec
        E#5
     in
        A#11[(letrec {X#15=T#14[(letrec {E#1;E#2} in S#3)];E#17} in (app S#8 S#7))]
     )
  )

where

   Delta1 = {T#13,T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#7,(letrec {X#15=T#14[(letrec {E#1;E#2} in S#3)];E#17} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)],
           T#12  |->  (app (letrec {X#15=T#14;E#17} in S#8) S#7),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#8),
           E#6   |->  {X#15=T#14[(letrec {E#1;E#2} in S#3)];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[(letrec {E#1;E#2} in S#3)];E#17} in S#8) S#7)])
    -llet-in1->                   (letrec {E#5} in A#11[(app (letrec {X#15=T#14[(letrec {E#1} in (letrec {E#2} in S#3))];E#17} in S#8) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[(letrec {E#1;E#2} in S#3)];E#17} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {X#15=T#14[(letrec {E#1;E#2} in S#3)];E#17} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in A#11[(app (letrec {E#1} in (letrec {E#2} in S#8)) S#7)])
    ,
     (letrec {E#5} in A#11[(letrec {E#1;E#2} in (app S#8 S#7))])
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#7,(letrec {E#1;E#2} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app [.] S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app [.] S#7)],
           T#12  |->  (app [.] S#7),
           T#13  |->  [.],
           S#3   |->  S#8,
           E#6   |->  {E#1;E#2}}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#1;E#2} in S#8) S#7)])
    -llet-in1->                   (letrec {E#5} in A#11[(app (letrec {E#1} in (letrec {E#2} in S#8)) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#1;E#2} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#1;E#2} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {E#6} in S#8) T#13[(letrec {E#1} in (letrec {E#2} in S#3))])]
     )
    ,
     (letrec
        E#5
     in
        A#11[(letrec {E#6} in (app S#8 T#13[(letrec {E#1;E#2} in S#3)]))]
     )
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#13[(letrec {E#1;E#2} in S#3)],(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {E#6} in S#8) T#13)],
           T#12  |->  (app (letrec {E#6} in S#8) T#13),
           S#7   |->  T#13[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(letrec {E#1;E#2} in S#3)])])
    -llet-in1->                   (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(letrec {E#1} in (letrec {E#2} in S#3))])])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(letrec {E#1;E#2} in S#3)])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 T#13[(letrec {E#1;E#2} in S#3)]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(letrec {E#1} in (letrec {E#2} in S#3))])]
     )
    ,
     (letrec
        E#5
     in
        A#11[(app A#12[(letrec {E#6} in (app S#8 S#7))] T#13[(letrec {E#1;E#2} in S#3)])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)]),
           T#10  |->  A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(letrec {E#1;E#2} in S#3)])])
    -llet-in1->                   (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(letrec {E#1} in (letrec {E#2} in S#3))])])
    ................................................................................
                                  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(letrec {E#1;E#2} in S#3)])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(app A#12[(letrec {E#6} in (app S#8 S#7))] T#13[(letrec {E#1;E#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (app (letrec {E#6} in T#12[(letrec {E#1} in (letrec {E#2} in S#3))]) S#7)
     )
    ,
     (letrec {E#5} in (letrec {E#6} in (app T#12[(letrec {E#1;E#2} in S#3)] S#7)))
  )

where

   Delta1 = {T#11,T#10,T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app (letrec {E#6} in T#12) S#7)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {E#6} in T#12) S#7),
           T#11  |->  (letrec {E#6} in T#12),
           S#8   |->  T#12[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in T#12[(letrec {E#1;E#2} in S#3)]) S#7))
    -llet-in1->                   (letrec {E#5} in (app (letrec {E#6} in T#12[(letrec {E#1} in (letrec {E#2} in S#3))]) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in T#12[(letrec {E#1;E#2} in S#3)]) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app T#12[(letrec {E#1;E#2} in S#3)] S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (app (letrec {X#13=T#12[(letrec {E#1} in (letrec {E#2} in S#3))];E#15} in S#8) S#7)
     )
    ,
     (letrec
        E#5
     in
        (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15} in (app S#8 S#7))
     )
  )

where

   Delta1 = {T#11,T#10,T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#7,(letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app (letrec {X#13=T#12;E#15} in S#8) S#7)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {X#13=T#12;E#15} in S#8) S#7),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#8),
           E#6   |->  {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15} in S#8) S#7))
    -llet-in1->                   (letrec {E#5} in (app (letrec {X#13=T#12[(letrec {E#1} in (letrec {E#2} in S#3))];E#15} in S#8) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15} in S#8) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15} in (app S#8 S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (app (letrec {E#1} in (letrec {E#2} in S#8)) S#7))
    ,
     (letrec {E#5} in (letrec {E#1;E#2} in (app S#8 S#7)))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#7,(letrec {E#1;E#2} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app [.] S#7)),
           A#9   |->  [.],
           T#10  |->  (app [.] S#7),
           T#11  |->  [.],
           S#3   |->  S#8,
           E#6   |->  {E#1;E#2}}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#1;E#2} in S#8) S#7))
    -llet-in1->                   (letrec {E#5} in (app (letrec {E#1} in (letrec {E#2} in S#8)) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#1;E#2} in S#8) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#1;E#2} in (app S#8 S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (app (letrec {E#6} in S#8) T#11[(letrec {E#1} in (letrec {E#2} in S#3))])
     )
    ,
     (letrec {E#5} in (letrec {E#6} in (app S#8 T#11[(letrec {E#1;E#2} in S#3)])))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#11[(letrec {E#1;E#2} in S#3)],(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {E#6} in S#8) T#11),
           S#7   |->  T#11[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(letrec {E#1;E#2} in S#3)]))
    -llet-in1->                   (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(letrec {E#1} in (letrec {E#2} in S#3))]))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(letrec {E#1;E#2} in S#3)]))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app S#8 T#11[(letrec {E#1;E#2} in S#3)])))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(letrec {E#1} in (letrec {E#2} in S#3))]
       ;E#13
     in
        A#9[(app (letrec {E#6} in S#8) S#7)]
     )
    ,
     (letrec
        X#11= T#10[(letrec {E#1;E#2} in S#3)]
       ;E#13
     in
        A#9[(letrec {E#6} in (app S#8 S#7))]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;E#13} in A#9[(app (letrec {E#6} in S#8) S#7)]),
           E#5   |->  {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -llet-in1->                   (letrec {X#11=T#10[(letrec {E#1} in (letrec {E#2} in S#3))];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13} in A#9[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec {E#1} in (letrec {E#2} in A#9[(app (letrec {E#6} in S#8) S#7)]))
    ,
     (letrec {E#1;E#2} in A#9[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#9[(app (letrec {E#6} in S#8) S#7)],
           E#5  |->  {E#1;E#2}}

and instantiated rules:

                                  (letrec {E#1;E#2} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -llet-in1->                   (letrec {E#1} in (letrec {E#2} in A#9[(app (letrec {E#6} in S#8) S#7)]))
    ................................................................................
                                  (letrec {E#1;E#2} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#1;E#2} in A#9[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in (letrec {E#2} in S#3))])]
     )
    ,
     (letrec
        E#6
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#13[(app A#14[(var X#5)] T#15[(letrec {E#1;E#2} in S#3)])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {E#1;E#2} in S#3)])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {E#1;E#2} in S#3)])])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#5)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1;E#2} in S#3)])])
    -llet-in1->                   (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in (letrec {E#2} in S#3))])])
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1;E#2} in S#3)])])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1;E#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {E#1} in (letrec {E#2} in S#3))]
       ;E#15
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {E#1;E#2} in S#3)]
       ;E#15
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           E#6   |->  {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15},
           E#14  |->  {E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#13=T#12[(letrec {E#1} in (letrec {E#2} in S#3))];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {E#7} in T#19[(letrec {E#1} in (letrec {E#2} in S#3))]) S#8)]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app T#19[(letrec {E#1;E#2} in S#3)] S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (letrec {E#7} in T#19) S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {E#7} in T#19) S#8)],
           T#17         |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[(letrec {E#1;E#2} in S#3)]) S#8)];E#6} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#5=A#16[(app (letrec {E#7} in T#19[(letrec {E#1} in (letrec {E#2} in S#3))]) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[(letrec {E#1;E#2} in S#3)]) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app T#19[(letrec {E#1;E#2} in S#3)] S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {X#20=T#19[(letrec {E#1} in (letrec {E#2} in S#3))];E#22} in S#9) S#8)]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22} in (app S#9 S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)],
           T#17         |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#5=A#16[(app (letrec {X#20=T#19[(letrec {E#1} in (letrec {E#2} in S#3))];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {E#1} in (letrec {E#2} in S#9)) S#8)]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {E#1;E#2} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#1;E#2} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app [.] S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app [.] S#8)],
           T#17         |->  (app [.] S#8),
           T#18         |->  [.],
           S#3          |->  S#9,
           E#7          |->  {E#1;E#2}}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#1;E#2} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#5=A#16[(app (letrec {E#1} in (letrec {E#2} in S#9)) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#1;E#2} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#1;E#2} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {E#7} in S#9) T#18[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app S#9 T#18[(letrec {E#1;E#2} in S#3)]))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#18[(letrec {E#1;E#2} in S#3)],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {E#7} in S#9) T#18)],
           T#17         |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[(letrec {E#1;E#2} in S#3)])];E#6} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[(letrec {E#1} in (letrec {E#2} in S#3))])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[(letrec {E#1;E#2} in S#3)])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 T#18[(letrec {E#1;E#2} in S#3)]))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(app A#17[(letrec {E#7} in (app S#9 S#8))] T#18[(letrec {E#1;E#2} in S#3)])]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[(letrec {E#1;E#2} in S#3)])]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(letrec {E#1;E#2} in S#3)])];E#6} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(letrec {E#1} in (letrec {E#2} in S#3))])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(letrec {E#1;E#2} in S#3)])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(app A#17[(letrec {E#7} in (app S#9 S#8))] T#18[(letrec {E#1;E#2} in S#3)])];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {E#7} in T#17[(letrec {E#1} in (letrec {E#2} in S#3))]) S#8)
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {E#7} in (app T#17[(letrec {E#1;E#2} in S#3)] S#8))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#16,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (letrec {E#7} in T#17) S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in T#17) S#8),
           T#16         |->  (letrec {E#7} in T#17),
           S#9          |->  T#17[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in T#17[(letrec {E#1;E#2} in S#3)]) S#8);E#6} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#5=(app (letrec {E#7} in T#17[(letrec {E#1} in (letrec {E#2} in S#3))]) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in T#17[(letrec {E#1;E#2} in S#3)]) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app T#17[(letrec {E#1;E#2} in S#3)] S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {X#18=T#17[(letrec {E#1} in (letrec {E#2} in S#3))];E#20} in S#9) S#8)
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {X#18=T#17[(letrec {E#1;E#2} in S#3)];E#20} in (app S#9 S#8))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#16,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {X#18=T#17[(letrec {E#1;E#2} in S#3)];E#20} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (letrec {X#18=T#17;E#20} in S#9) S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {X#18=T#17;E#20} in S#9) S#8),
           T#16         |->  (letrec {X#18=T#17;E#20} in S#9),
           E#7          |->  {X#18=T#17[(letrec {E#1;E#2} in S#3)];E#20},
           E#19         |->  {E#20}}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {X#18=T#17[(letrec {E#1;E#2} in S#3)];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#5=(app (letrec {X#18=T#17[(letrec {E#1} in (letrec {E#2} in S#3))];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {X#18=T#17[(letrec {E#1;E#2} in S#3)];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {X#18=T#17[(letrec {E#1;E#2} in S#3)];E#20} in (app S#9 S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {E#1} in (letrec {E#2} in S#9)) S#8)
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=(letrec {E#1;E#2} in (app S#9 S#8));E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#1;E#2} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app [.] S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#16         |->  [.],
           S#3          |->  S#9,
           E#7          |->  {E#1;E#2}}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#1;E#2} in S#9) S#8);E#6} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#5=(app (letrec {E#1} in (letrec {E#2} in S#9)) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#1;E#2} in S#9) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#1;E#2} in (app S#9 S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {E#7} in S#9) T#16[(letrec {E#1} in (letrec {E#2} in S#3))])
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {E#7} in (app S#9 T#16[(letrec {E#1;E#2} in S#3)]))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#16[(letrec {E#1;E#2} in S#3)],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (letrec {E#7} in S#9) T#16);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in S#9) T#16),
           S#8          |->  T#16[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in S#9) T#16[(letrec {E#1;E#2} in S#3)]);E#6} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#5=(app (letrec {E#7} in S#9) T#16[(letrec {E#1} in (letrec {E#2} in S#3))]);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in S#9) T#16[(letrec {E#1;E#2} in S#3)]);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app S#9 T#16[(letrec {E#1;E#2} in S#3)]));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#6
       ;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])]
       ;E#6
       ;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (letrec {E#2} in S#3))])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];E#6;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (letrec {E#2} in S#3))])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {E#7} in T#21[(letrec {E#1} in (letrec {E#2} in S#3))]) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app T#21[(letrec {E#1;E#2} in S#3)] S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (letrec {E#7} in T#21) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {E#7} in T#21) S#8)],
           T#19         |->  (app (letrec {E#7} in T#21) S#8),
           T#20         |->  (letrec {E#7} in T#21),
           S#9          |->  T#21[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[(letrec {E#1;E#2} in S#3)]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#16=A#18[(app (letrec {E#7} in T#21[(letrec {E#1} in (letrec {E#2} in S#3))]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[(letrec {E#1;E#2} in S#3)]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app T#21[(letrec {E#1;E#2} in S#3)] S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {X#22=T#21[(letrec {E#1} in (letrec {E#2} in S#3))];E#24} in S#9) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#22=T#21[(letrec {E#1;E#2} in S#3)];E#24} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {X#22=T#21[(letrec {E#1;E#2} in S#3)];E#24} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)],
           T#19         |->  (app (letrec {X#22=T#21;E#24} in S#9) S#8),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#9),
           E#7          |->  {X#22=T#21[(letrec {E#1;E#2} in S#3)];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[(letrec {E#1;E#2} in S#3)];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#16=A#18[(app (letrec {X#22=T#21[(letrec {E#1} in (letrec {E#2} in S#3))];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[(letrec {E#1;E#2} in S#3)];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {X#22=T#21[(letrec {E#1;E#2} in S#3)];E#24} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {E#1} in (letrec {E#2} in S#9)) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#1;E#2} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#1;E#2} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app [.] S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app [.] S#8)],
           T#19         |->  (app [.] S#8),
           T#20         |->  [.],
           S#3          |->  S#9,
           E#7          |->  {E#1;E#2}}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#1;E#2} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#16=A#18[(app (letrec {E#1} in (letrec {E#2} in S#9)) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#1;E#2} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#1;E#2} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {E#7} in S#9) T#20[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 T#20[(letrec {E#1;E#2} in S#3)]))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#20[(letrec {E#1;E#2} in S#3)],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {E#7} in S#9) T#20)],
           T#19         |->  (app (letrec {E#7} in S#9) T#20),
           S#8          |->  T#20[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[(letrec {E#1;E#2} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[(letrec {E#1} in (letrec {E#2} in S#3))])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[(letrec {E#1;E#2} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 T#20[(letrec {E#1;E#2} in S#3)]))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(letrec {E#1} in (letrec {E#2} in S#3))])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[(letrec {E#1;E#2} in S#3)])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[(letrec {E#1;E#2} in S#3)])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1;E#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(letrec {E#1;E#2} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(letrec {E#1} in (letrec {E#2} in S#3))])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(letrec {E#1;E#2} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[(letrec {E#1;E#2} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {E#7} in T#19[(letrec {E#1} in (letrec {E#2} in S#3))]) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app T#19[(letrec {E#1;E#2} in S#3)] S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (letrec {E#7} in T#19) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in T#19[(letrec {E#1;E#2} in S#3)]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#16=(app (letrec {E#7} in T#19[(letrec {E#1} in (letrec {E#2} in S#3))]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in T#19[(letrec {E#1;E#2} in S#3)]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app T#19[(letrec {E#1;E#2} in S#3)] S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {X#20=T#19[(letrec {E#1} in (letrec {E#2} in S#3))];E#22} in S#9) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22} in (app S#9 S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (letrec {X#20=T#19;E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#16=(app (letrec {X#20=T#19[(letrec {E#1} in (letrec {E#2} in S#3))];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22} in (app S#9 S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {E#1} in (letrec {E#2} in S#9)) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#1;E#2} in (app S#9 S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#1;E#2} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app [.] S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#18         |->  [.],
           S#3          |->  S#9,
           E#7          |->  {E#1;E#2}}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#1;E#2} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#16=(app (letrec {E#1} in (letrec {E#2} in S#9)) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#1;E#2} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#1;E#2} in (app S#9 S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {E#7} in S#9) T#18[(letrec {E#1} in (letrec {E#2} in S#3))])
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app S#9 T#18[(letrec {E#1;E#2} in S#3)]))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {[{E#1},(letrec {E#2} in [.])],
             (T#18[(letrec {E#1;E#2} in S#3)],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (letrec {E#7} in S#9) T#18);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[(letrec {E#1;E#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in S#9) T#18[(letrec {E#1;E#2} in S#3)]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -llet-in1->                   (letrec {X#16=(app (letrec {E#7} in S#9) T#18[(letrec {E#1} in (letrec {E#2} in S#3))]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in S#9) T#18[(letrec {E#1;E#2} in S#3)]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app S#9 T#18[(letrec {E#1;E#2} in S#3)]));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#14;E#15} in (letrec {E#12;E#13} in A#10[(var X#5)]))
    ,
     (letrec
        E#13
       ;E#15
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#7,E#12,E#14}
   Delta3 = {[{E#14;E#15},(letrec {E#12;E#13} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {
             {E#12;E#14} =?= {EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]}}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#10[(var X#5)],
           E#6  |->  {E#13;E#15},
           E#1  |->  {E#14;E#15},
           E#2  |->  {E#12;E#13}}

and instantiated rules:

                                  (letrec {E#12;E#13;E#14;E#15} in A#10[(var X#5)])
    -llet-in1->                   (letrec {E#14;E#15} in (letrec {E#12;E#13} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {E#13;E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#13;E#15;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
        ............................
    Delta4:
    {E#12;E#14} =?= {EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]}

================================================================================
Critical Pair:

  (
     (letrec {E#14;E#15} in (letrec {E#12;E#13} in A#10[(var X#5)]))
    ,
     (letrec
        E#13
       ;E#15
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#7,E#12,E#15}
   Delta3 = {[{E#14;E#15},(letrec {E#12;E#13} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {
             {E#12;E#14} =?= {EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]}}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#10[(var X#5)],
           E#6  |->  {E#13;E#15},
           E#1  |->  {E#14;E#15},
           E#2  |->  {E#12;E#13}}

and instantiated rules:

                                  (letrec {E#12;E#13;E#14;E#15} in A#10[(var X#5)])
    -llet-in1->                   (letrec {E#14;E#15} in (letrec {E#12;E#13} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {E#13;E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#13;E#15;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
        ............................
    Delta4:
    {E#12;E#14} =?= {EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]}

================================================================================
Critical Pair:

  (
     (letrec {E#14;E#15} in (letrec {E#12;E#13} in A#10[(var X#5)]))
    ,
     (letrec
        E#13
       ;E#15
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#7,E#13,E#14}
   Delta3 = {[{E#14;E#15},(letrec {E#12;E#13} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {
             {E#12;E#14} =?= {EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]}}

from overlapping -llet-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1;E#2} in S#3)]
    -llet-in1->                   T#4[(letrec {E#1} in (letrec {E#2} in S#3))]
    and constraints: E#1/= {}, E#2/= {}, ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1;E#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#10[(var X#5)],
           E#6  |->  {E#13;E#15},
           E#1  |->  {E#14;E#15},
           E#2  |->  {E#12;E#13}}

and instantiated rules:

                                  (letrec {E#12;E#13;E#14;E#15} in A#10[(var X#5)])
    -llet-in1->                   (letrec {E#14;E#15} in (letrec {E#12;E#13} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {E#13;E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#13;E#15;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
        ............................
    Delta4:
    {E#12;E#14} =?= {EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]}

================================================================================
Critical Pair:

  (
     A#11[(app (\ X#7.S#9) T#13[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
    ,
     A#11[(letrec {X#7=T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#9)]
  )

where

   Delta1 = {T#12,A#10,T#6,A#11}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)],(\ X#7.[.])),
             (T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {X#7=[.]} in S#9))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  A#10[(app (\ X#7.S#9) S#8)]
    -SR,lbeta1->                  A#10[(letrec {X#7=S#8} in S#9)]
    and constraints: (S#8,(\ X#7.[.])), (S#8,(letrec {X#7=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)] =?= A#10[(app (\ X#7.S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#8,(\ X#7.[.])),(S#8,(letrec {X#7=[.]} in S#9))}


and found solution:

    Sol = {A#10  |->  A#11,
           T#6   |->  A#11[(app (\ X#7.S#9) T#13)],
           T#12  |->  (app (\ X#7.S#9) T#13),
           S#8   |->  T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  A#11[(app (\ X#7.S#9) T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
    -llet-e1->                    A#11[(app (\ X#7.S#9) T#13[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
    ................................................................................
                                  A#11[(app (\ X#7.S#9) T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
    -SR,lbeta1->                  A#11[(letrec {X#7=T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#9)]
    

================================================================================
Critical Pair:

  (
     A#11[(app A#12[(app (\ X#7.S#9) S#8)] T#13[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
    ,
     A#11[(app A#12[(letrec {X#7=S#8} in S#9)] T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
  )

where

   Delta1 = {A#10,T#6}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#8,(\ X#7.[.])),
             (S#8,(letrec {X#7=[.]} in S#9))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  A#10[(app (\ X#7.S#9) S#8)]
    -SR,lbeta1->                  A#10[(letrec {X#7=S#8} in S#9)]
    and constraints: (S#8,(\ X#7.[.])), (S#8,(letrec {X#7=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)] =?= A#10[(app (\ X#7.S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#8,(\ X#7.[.])),(S#8,(letrec {X#7=[.]} in S#9))}


and found solution:

    Sol = {T#6   |->  A#11[(app A#12[(app (\ X#7.S#9) S#8)] T#13)],
           A#10  |->  A#11[(app A#12 T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  A#11[(app A#12[(app (\ X#7.S#9) S#8)] T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
    -llet-e1->                    A#11[(app A#12[(app (\ X#7.S#9) S#8)] T#13[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
    ................................................................................
                                  A#11[(app A#12[(app (\ X#7.S#9) S#8)] T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
    -SR,lbeta1->                  A#11[(app A#12[(letrec {X#7=S#8} in S#9)] T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
    

================================================================================
Critical Pair:

  (
     (app (\ X#7.S#9) T#11[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])
    ,
     (letrec {X#7=T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#9)
  )

where

   Delta1 = {T#6}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)],(\ X#7.[.])),
             (T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {X#7=[.]} in S#9))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  A#10[(app (\ X#7.S#9) S#8)]
    -SR,lbeta1->                  A#10[(letrec {X#7=S#8} in S#9)]
    and constraints: (S#8,(\ X#7.[.])), (S#8,(letrec {X#7=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)] =?= A#10[(app (\ X#7.S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#8,(\ X#7.[.])),(S#8,(letrec {X#7=[.]} in S#9))}


and found solution:

    Sol = {A#10  |->  [.],
           T#6   |->  (app (\ X#7.S#9) T#11),
           S#8   |->  T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (app (\ X#7.S#9) T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)])
    -llet-e1->                    (app (\ X#7.S#9) T#11[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])
    ................................................................................
                                  (app (\ X#7.S#9) T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)])
    -SR,lbeta1->                  (letrec {X#7=T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#9)
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#13[(app (\ X#7.S#10) T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
     )
    ,
     (letrec
        E#8
     in
        A#13[(letrec {X#7=T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#10)]
     )
  )

where

   Delta1 = {T#14,A#11,T#12,T#6,A#13}
   Delta2 = {E#2,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)],(\ X#7.[.])),
             (T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {X#7=[.]} in S#10))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10))}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in A#13[(app (\ X#7.S#10) T#15)]),
           A#11  |->  A#13,
           T#12  |->  A#13[(app (\ X#7.S#10) T#15)],
           T#14  |->  (app (\ X#7.S#10) T#15),
           S#9   |->  T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#8} in A#13[(app (\ X#7.S#10) T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -llet-e1->                    (letrec {E#8} in A#13[(app (\ X#7.S#10) T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#8} in A#13[(app (\ X#7.S#10) T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -SR,lbeta2->                  (letrec {E#8} in A#13[(letrec {X#7=T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
     )
    ,
     (letrec
        E#8
     in
        A#13[(app A#14[(letrec {X#7=S#9} in S#10)] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#11,T#12,T#6}
   Delta2 = {E#2,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10))}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15)]),
           T#12  |->  A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {E#8} in A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -llet-e1->                    (letrec {E#8} in A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#8} in A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -SR,lbeta2->                  (letrec {E#8} in A#13[(app A#14[(letrec {X#7=S#9} in S#10)] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        (app (\ X#7.S#10) T#13[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])
     )
    ,
     (letrec {E#8} in (letrec {X#7=T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#10))
  )

where

   Delta1 = {T#12,T#6}
   Delta2 = {E#2,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)],(\ X#7.[.])),
             (T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {X#7=[.]} in S#10))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10))}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in (app (\ X#7.S#10) T#13)),
           A#11  |->  [.],
           T#12  |->  (app (\ X#7.S#10) T#13),
           S#9   |->  T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#8} in (app (\ X#7.S#10) T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)]))
    -llet-e1->                    (letrec {E#8} in (app (\ X#7.S#10) T#13[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]))
    ................................................................................
                                  (letrec {E#8} in (app (\ X#7.S#10) T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)]))
    -SR,lbeta2->                  (letrec {E#8} in (letrec {X#7=T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#10))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
       ;E#15
     in
        A#11[(app (\ X#7.S#10) S#9)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)]
       ;E#15
     in
        A#11[(letrec {X#7=S#9} in S#10)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#2,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10))}


and found solution:

    Sol = {T#6   |->  (letrec {X#13=T#12;E#15} in A#11[(app (\ X#7.S#10) S#9)]),
           E#8   |->  {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15} in A#11[(app (\ X#7.S#10) S#9)])
    -llet-e1->                    (letrec {X#13=T#12[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#15} in A#11[(app (\ X#7.S#10) S#9)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15} in A#11[(letrec {X#7=S#9} in S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {E#2} in S#4);E#3} in A#11[(app (\ X#7.S#10) S#9)])
    ,
     (letrec {X#1=S#4;E#2;E#3} in A#11[(letrec {X#7=S#9} in S#10)])
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#8}
   Delta3 = {(A#11[(app (\ X#7.S#10) S#9)],(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10))}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#11[(app (\ X#7.S#10) S#9)],
           E#8   |->  {X#1=S#4;E#2;E#3},
           E#12  |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {X#1=S#4;E#2;E#3} in A#11[(app (\ X#7.S#10) S#9)])
    -llet-e1->                    (letrec {X#1=(letrec {E#2} in S#4);E#3} in A#11[(app (\ X#7.S#10) S#9)])
    ................................................................................
                                  (letrec {X#1=S#4;E#2;E#3} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {X#1=S#4;E#2;E#3} in A#11[(letrec {X#7=S#9} in S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
       ;EE#13[X#7,(app (\ X#8.S#11) S#10)]
     in
        A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
     )
    ,
     (letrec
        E#9
       ;EE#13[X#7,(letrec {X#8=S#10} in S#11)]
     in
        A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#14,T#6}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#15[(app A#16[[.]] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])]),
             ((var X#7),A#15[(app A#16[[.]] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#7)] T#17)],
           A#12  |->  A#15[(app A#16 T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -llet-e1->                    (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
       ;E#17
       ;EE#13[X#7,(app (\ X#8.S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)]
       ;E#17
       ;EE#13[X#7,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#15=T#14;E#17;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)]),
           E#9   |->  {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17},
           E#16  |->  {E#17;EE#13[X#7,(app (\ X#8.S#11) S#10)]}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#15=T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#17;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app (\ X#8.S#11) T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#9
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(letrec {X#8=T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#11)]
       ;E#9
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#19,A#17,T#14,T#6,A#18}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)],(\ X#8.[.])),
             (T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#18[(app (\ X#8.S#11) T#20)];E#9} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#9},
           A#17         |->  A#18,
           T#14         |->  A#18[(app (\ X#8.S#11) T#20)],
           T#19         |->  (app (\ X#8.S#11) T#20),
           S#10         |->  T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=A#18[(app (\ X#8.S#11) T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=A#18[(app (\ X#8.S#11) T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#9} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app (\ X#8.S#11) T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#7=A#18[(letrec {X#8=T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#11)];E#9} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#9
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(app A#19[(letrec {X#8=S#10} in S#11)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#9
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20)];E#9} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])]},
           X#15         |->  X#7,
           E#16         |->  {E#9},
           T#14         |->  A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20)],
           A#17         |->  A#18[(app A#19 T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#9} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#7=A#18[(app A#19[(letrec {X#8=S#10} in S#11)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (app (\ X#8.S#11) T#18[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])
       ;E#9
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= (letrec {X#8=T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#11)
       ;E#9
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)],(\ X#8.[.])),
             (T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(app (\ X#8.S#11) T#18);E#9} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {E#9},
           A#17         |->  [.],
           T#14         |->  (app (\ X#8.S#11) T#18),
           S#10         |->  T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=(app (\ X#8.S#11) T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)]);E#9} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=(app (\ X#8.S#11) T#18[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]);E#9} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(app (\ X#8.S#11) T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)]);E#9} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#7=(letrec {X#8=T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#11);E#9} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#9
       ;EE#19[X#18,(app (\ X#8.S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#9
       ;EE#19[X#18,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22)];E#9;EE#19[X#18,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];EE#19[X#18,[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#9;EE#19[X#18,(app (\ X#8.S#11) S#10)]},
           T#14         |->  A#20[(app A#21[(var X#18)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9;EE#19[X#18,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#9;EE#19[X#18,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9;EE#19[X#18,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9;EE#19[X#18,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#9
       ;EE#20[X#7,(var X#18)]
       ;EE#21[X#19,(app (\ X#8.S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#9
       ;EE#20[X#7,(var X#18)]
       ;EE#21[X#19,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24)];E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#15         |->  X#18,
           E#16         |->  {E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(app (\ X#8.S#11) S#10)]},
           T#14         |->  A#22[(app A#23[(var X#19)] T#24)],
           A#17         |->  A#22[(app A#23 T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (\ X#8.S#11) T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {X#8=T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#11)]
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#21,A#17,T#14,T#6,A#20}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)],(\ X#8.[.])),
             (T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app (\ X#8.S#11) T#22)];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#9;EE#19[X#7,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[(app (\ X#8.S#11) T#22)],
           T#21         |->  (app (\ X#8.S#11) T#22),
           S#10         |->  T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (\ X#8.S#11) T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#18=A#20[(app (\ X#8.S#11) T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (\ X#8.S#11) T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#18=A#20[(letrec {X#8=T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#11)];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(letrec {X#8=S#10} in S#11)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22)];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#9;EE#19[X#7,(var X#18)]},
           T#14         |->  A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#18=A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#18=A#20[(app A#21[(letrec {X#8=S#10} in S#11)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (\ X#8.S#11) T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= (letrec {X#8=T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#11)
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)],(\ X#8.[.])),
             (T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=(app (\ X#8.S#11) T#20);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#9;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  (app (\ X#8.S#11) T#20),
           S#10         |->  T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#18=(app (\ X#8.S#11) T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#18=(app (\ X#8.S#11) T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=(app (\ X#8.S#11) T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#18=(letrec {X#8=T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]} in S#11);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {E#17;E#18} in S#4);E#15;E#16} in A#12[(var X#7)])
    ,
     (letrec
        X#1= S#4
       ;E#16
       ;E#18
       ;EE#13[X#7,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#15,E#18}
   Delta3 = {(A#12[(var X#7)],(letrec {E#17;E#18} in [.])),
             [{E#15;E#16},(letrec {E#17;E#18} in [.])],
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#15;E#17} =?= {EE#13[X#7,(app (\ X#8.S#11) S#10)]}}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#7)],
           E#9   |->  {X#1=S#4;E#16;E#18},
           E#14  |->  {E#16;E#18},
           E#2   |->  {E#17;E#18},
           E#3   |->  {E#15;E#16}}

and instantiated rules:

                                  (letrec {X#1=S#4;E#15;E#16;E#17;E#18} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#1=(letrec {E#17;E#18} in S#4);E#15;E#16} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#1=S#4;E#16;E#18;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#1=S#4;E#16;E#18;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#15;E#17} =?= {EE#13[X#7,(app (\ X#8.S#11) S#10)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#2} in A#14[(app (\ X#8.S#11) S#10)])
       ;E#3
     in
        A#12[(var X#7)]
     )
    ,
     (letrec {X#7=A#14[(letrec {X#8=S#10} in S#11)];E#2;E#3} in A#12[(var X#7)])
  )

where

   Delta1 = {}
   Delta2 = {E#2}
   Delta3 = {(A#12[(var X#7)],(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {[.1]=A#14[[.2]]},
           X#1          |->  X#7,
           S#4          |->  A#14[(app (\ X#8.S#11) S#10)],
           E#9          |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {X#7=A#14[(app (\ X#8.S#11) S#10)];E#2;E#3} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=(letrec {E#2} in A#14[(app (\ X#8.S#11) S#10)]);E#3} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#14[(app (\ X#8.S#11) S#10)];E#2;E#3} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#7=A#14[(letrec {X#8=S#10} in S#11)];E#2;E#3} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#19;E#20} in A#14[(var X#15)])
       ;E#17
       ;E#18
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#14[(var X#15)]
       ;E#18
       ;E#20
       ;EE#16[X#15,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#17,E#20}
   Delta3 = {(A#12[(var X#7)],(letrec {E#19;E#20} in [.])),
             [{E#17;E#18},(letrec {E#19;E#20} in [.])],
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#17;E#19} =?= {EE#16[X#15,(app (\ X#8.S#11) S#10)]}}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {[.1]=A#14[(var X#15)];EE#16[X#15,[.2]]},
           X#1          |->  X#7,
           S#4          |->  A#14[(var X#15)],
           E#9          |->  {E#18;E#20},
           E#2          |->  {E#19;E#20},
           E#3          |->  {E#17;E#18}}

and instantiated rules:

                                  (letrec {X#7=A#14[(var X#15)];E#17;E#18;E#19;E#20} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=(letrec {E#19;E#20} in A#14[(var X#15)]);E#17;E#18} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#14[(var X#15)];E#18;E#20;EE#16[X#15,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#7=A#14[(var X#15)];E#18;E#20;EE#16[X#15,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#17;E#19} =?= {EE#16[X#15,(app (\ X#8.S#11) S#10)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#19;E#20} in A#14[(var X#15)])
       ;E#17
       ;E#18
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#14[(var X#15)]
       ;E#18
       ;E#20
       ;EE#16[X#15,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#19}
   Delta3 = {(A#12[(var X#7)],(letrec {E#19;E#20} in [.])),
             [{E#17;E#18},(letrec {E#19;E#20} in [.])],
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#17;E#19} =?= {EE#16[X#15,(app (\ X#8.S#11) S#10)]}}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {[.1]=A#14[(var X#15)];EE#16[X#15,[.2]]},
           X#1          |->  X#7,
           S#4          |->  A#14[(var X#15)],
           E#9          |->  {E#18;E#20},
           E#2          |->  {E#19;E#20},
           E#3          |->  {E#17;E#18}}

and instantiated rules:

                                  (letrec {X#7=A#14[(var X#15)];E#17;E#18;E#19;E#20} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=(letrec {E#19;E#20} in A#14[(var X#15)]);E#17;E#18} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#14[(var X#15)];E#18;E#20;EE#16[X#15,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#7=A#14[(var X#15)];E#18;E#20;EE#16[X#15,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#17;E#19} =?= {EE#16[X#15,(app (\ X#8.S#11) S#10)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#22;E#23;E#24} in A#14[(var X#16)])
       ;E#19
       ;E#20
       ;E#21
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;E#21
       ;E#24
       ;EE#17[X#7,(var X#15)]
       ;EE#18[X#16,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#19,E#20,E#24}
   Delta3 = {(A#12[(var X#7)],(letrec {E#22;E#23;E#24} in [.])),
             [{E#19;E#20;E#21},(letrec {E#22;E#23;E#24} in [.])],
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#19;E#22} =?= {EE#17[X#7,(var X#15)]},
             {E#20;E#23} =?= {EE#18[X#16,(app (\ X#8.S#11) S#10)]}}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#1          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           E#9          |->  {E#21;E#24},
           E#2          |->  {E#22;E#23;E#24},
           E#3          |->  {E#19;E#20;E#21}}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];E#19;E#20;E#21;E#22;E#23;E#24} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#15=(letrec {E#22;E#23;E#24} in A#14[(var X#16)]);E#19;E#20;E#21} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];E#21;E#24;EE#17[X#7,(var X#15)];EE#18[X#16,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#15=A#14[(var X#16)];E#21;E#24;EE#17[X#7,(var X#15)];EE#18[X#16,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#19;E#22} =?= {EE#17[X#7,(var X#15)]},
    {E#20;E#23} =?= {EE#18[X#16,(app (\ X#8.S#11) S#10)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#22;E#23;E#24} in A#14[(var X#16)])
       ;E#19
       ;E#20
       ;E#21
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;E#21
       ;E#24
       ;EE#17[X#7,(var X#15)]
       ;EE#18[X#16,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#19,E#23}
   Delta3 = {(A#12[(var X#7)],(letrec {E#22;E#23;E#24} in [.])),
             [{E#19;E#20;E#21},(letrec {E#22;E#23;E#24} in [.])],
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#19;E#22} =?= {EE#17[X#7,(var X#15)]},
             {E#20;E#23} =?= {EE#18[X#16,(app (\ X#8.S#11) S#10)]}}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#1          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           E#9          |->  {E#21;E#24},
           E#2          |->  {E#22;E#23;E#24},
           E#3          |->  {E#19;E#20;E#21}}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];E#19;E#20;E#21;E#22;E#23;E#24} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#15=(letrec {E#22;E#23;E#24} in A#14[(var X#16)]);E#19;E#20;E#21} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];E#21;E#24;EE#17[X#7,(var X#15)];EE#18[X#16,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#15=A#14[(var X#16)];E#21;E#24;EE#17[X#7,(var X#15)];EE#18[X#16,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#19;E#22} =?= {EE#17[X#7,(var X#15)]},
    {E#20;E#23} =?= {EE#18[X#16,(app (\ X#8.S#11) S#10)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#19;E#20} in A#14[(app (\ X#8.S#11) S#10)])
       ;E#17
       ;E#18
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= A#14[(letrec {X#8=S#10} in S#11)]
       ;E#18
       ;E#20
       ;EE#16[X#7,(var X#15)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#17,E#20}
   Delta3 = {(A#12[(var X#7)],(letrec {E#19;E#20} in [.])),
             [{E#17;E#18},(letrec {E#19;E#20} in [.])],
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#17;E#19} =?= {EE#16[X#7,(var X#15)]}}

from overlapping -llet-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[[.2]];EE#16[[.1],(var X#15)]},
           X#1          |->  X#15,
           S#4          |->  A#14[(app (\ X#8.S#11) S#10)],
           E#9          |->  {E#18;E#20},
           E#2          |->  {E#19;E#20},
           E#3          |->  {E#17;E#18}}

and instantiated rules:

                                  (letrec {X#15=A#14[(app (\ X#8.S#11) S#10)];E#17;E#18;E#19;E#20} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#15=(letrec {E#19;E#20} in A#14[(app (\ X#8.S#11) S#10)]);E#17;E#18} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=A#14[(app (\ X#8.S#11) S#10)];E#18;E#20;EE#16[X#7,(var X#15)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#15=A#14[(letrec {X#8=S#10} in S#11)];E#18;E#20;EE#16[X#7,(var X#15)]} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#17;E#19} =?= {EE#16[X#7,(var X#15)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#10)
       ;E#9
     in
        A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
     )
    ,
     (letrec
        X#7= (\ X#8.S#10)
       ;E#9
     in
        A#13[(app A#14[(\ X#8.S#10)] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#11,T#12,T#6}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),A#13[(app A#14[[.]] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(\ X#8.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(\ X#8.S#10);E#9} in A#13[(app A#14[(var X#7)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#7)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#13[(app A#14[(\ X#8.S#10)] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
       ;X#7= (\ X#8.S#10)
       ;E#15
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)]
       ;X#7= (\ X#8.S#10)
       ;E#15
     in
        A#11[(\ X#8.S#10)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(\ X#8.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#13=T#12;X#7=(\ X#8.S#10);E#15} in A#11[(var X#7)]),
           E#9   |->  {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15},
           E#14  |->  {X#7=(\ X#8.S#10);E#15}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(\ X#8.S#10);E#15} in A#11[(var X#7)])
    -llet-e1->                    (letrec {X#13=T#12[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];X#7=(\ X#8.S#10);E#15} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(\ X#8.S#10);E#15} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(\ X#8.S#10);E#15} in A#11[(\ X#8.S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#7=(letrec {E#2} in (\ X#8.S#10));E#3} in A#11[(var X#7)])
    ,
     (letrec {X#7=(\ X#8.S#10);E#2;E#3} in A#11[(\ X#8.S#10)])
  )

where

   Delta1 = {}
   Delta2 = {E#2}
   Delta3 = {(A#11[(var X#7)],(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(\ X#8.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6  |->  [.],
           S#5  |->  A#11[(var X#7)],
           X#1  |->  X#7,
           S#4  |->  (\ X#8.S#10),
           E#9  |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#10);E#2;E#3} in A#11[(var X#7)])
    -llet-e1->                    (letrec {X#7=(letrec {E#2} in (\ X#8.S#10));E#3} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#2;E#3} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#2;E#3} in A#11[(\ X#8.S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {E#2} in S#4);X#7=(\ X#8.S#10);E#13} in A#11[(var X#7)])
    ,
     (letrec {X#1=S#4;X#7=(\ X#8.S#10);E#13;E#2} in A#11[(\ X#8.S#10)])
  )

where

   Delta1 = {}
   Delta2 = {E#2}
   Delta3 = {(A#11[(var X#7)],(letrec {E#2} in [.])),
             [{X#7=(\ X#8.S#10);E#13},(letrec {E#2} in [.])],
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(\ X#8.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#11[(var X#7)],
           E#9   |->  {X#1=S#4;E#13;E#2},
           E#3   |->  {X#7=(\ X#8.S#10);E#13},
           E#12  |->  {E#13;E#2}}

and instantiated rules:

                                  (letrec {X#1=S#4;X#7=(\ X#8.S#10);E#13;E#2} in A#11[(var X#7)])
    -llet-e1->                    (letrec {X#1=(letrec {E#2} in S#4);X#7=(\ X#8.S#10);E#13} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#1=S#4;X#7=(\ X#8.S#10);E#13;E#2} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#1=S#4;X#7=(\ X#8.S#10);E#13;E#2} in A#11[(\ X#8.S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;VV#13|X#9,(var X#7)|
     in
        A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;VV#13|X#9,(var X#7)|
     in
        A#15[(app A#16[(\ X#8.S#11)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#14,T#6}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#15[(app A#16[[.]] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(var X#9)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#9)] T#17)],
           A#12  |->  A#15[(app A#16 T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(\ X#8.S#11)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
       ;X#7= (\ X#8.S#11)
       ;E#17
       ;VV#13|X#9,(var X#7)|
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)]
       ;X#7= (\ X#8.S#11)
       ;E#17
       ;VV#13|X#9,(var X#7)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {X#15=T#14;X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|} in A#12[(var X#9)]),
           E#10  |->  {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17},
           E#16  |->  {X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -llet-e1->                    (letrec {X#15=T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#7=(letrec {E#16;E#17} in (\ X#8.S#11));E#14;E#15} in A#12[(var X#9)])
    ,
     (letrec {X#7=(\ X#8.S#11);E#15;E#17;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#14,E#17}
   Delta3 = {(A#12[(var X#9)],(letrec {E#16;E#17} in [.])),
             [{E#14;E#15},(letrec {E#16;E#17} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {
             {E#14;E#16} =?= {VV#13|X#9,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#9)],
           X#1   |->  X#7,
           S#4   |->  (\ X#8.S#11),
           E#10  |->  {E#15;E#17},
           E#2   |->  {E#16;E#17},
           E#3   |->  {E#14;E#15}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);E#14;E#15;E#16;E#17} in A#12[(var X#9)])
    -llet-e1->                    (letrec {X#7=(letrec {E#16;E#17} in (\ X#8.S#11));E#14;E#15} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#15;E#17;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#15;E#17;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
        ............................
    Delta4:
    {E#14;E#16} =?= {VV#13|X#9,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#18;E#19} in S#4)
       ;X#7= (\ X#8.S#11)
       ;E#16
       ;E#17
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#1= S#4
       ;X#7= (\ X#8.S#11)
       ;E#17
       ;E#19
       ;VV#13|X#9,(var X#7)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#16,E#19}
   Delta3 = {(A#12[(var X#9)],(letrec {E#18;E#19} in [.])),
             [{X#7=(\ X#8.S#11);E#16;E#17},(letrec {E#18;E#19} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {
             {E#16;E#18} =?= {VV#13|X#9,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#9)],
           E#10  |->  {X#1=S#4;E#17;E#19},
           E#3   |->  {X#7=(\ X#8.S#11);E#16;E#17},
           E#14  |->  {E#17;E#19},
           E#2   |->  {E#18;E#19},
           E#15  |->  {E#16;E#17}}

and instantiated rules:

                                  (letrec {X#1=S#4;X#7=(\ X#8.S#11);E#16;E#17;E#18;E#19} in A#12[(var X#9)])
    -llet-e1->                    (letrec {X#1=(letrec {E#18;E#19} in S#4);X#7=(\ X#8.S#11);E#16;E#17} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#1=S#4;X#7=(\ X#8.S#11);E#17;E#19;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#1=S#4;X#7=(\ X#8.S#11);E#17;E#19;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
        ............................
    Delta4:
    {E#16;E#18} =?= {VV#13|X#9,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= (letrec {E#2} in (var X#7))
       ;E#15
     in
        A#12[(var X#9)]
     )
    ,
     (letrec {X#7=(\ X#8.S#11);X#9=(var X#7);E#15;E#2} in A#12[(\ X#8.S#11)])
  )

where

   Delta1 = {}
   Delta2 = {E#2}
   Delta3 = {(A#12[(var X#9)],(letrec {E#2} in [.])),
             [{X#7=(\ X#8.S#11);E#15},(letrec {E#2} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#9,
           S#4          |->  (var X#7),
           E#3          |->  {X#7=(\ X#8.S#11);E#15},
           E#10         |->  {E#15;E#2}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#7);E#15;E#2} in A#12[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#11);X#9=(letrec {E#2} in (var X#7));E#15} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#7);E#15;E#2} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#7);E#15;E#2} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (letrec {X#7=(\ X#8.S#11);E#15} in (var X#7))
       ;E#3
     in
        A#12[(var X#9)]
     )
    ,
     (letrec {X#7=(\ X#8.S#11);X#9=(var X#7);E#15;E#3} in A#12[(\ X#8.S#11)])
  )

where

   Delta1 = {}
   Delta2 = {E#2}
   Delta3 = {(A#12[(var X#9)],(letrec {X#7=(\ X#8.S#11);E#15} in [.])),
             [{E#3},(letrec {X#7=(\ X#8.S#11);E#15} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#9,
           S#4          |->  (var X#7),
           E#2          |->  {X#7=(\ X#8.S#11);E#15},
           E#10         |->  {E#15;E#3}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#7);E#15;E#3} in A#12[(var X#9)])
    -llet-e1->                    (letrec {X#9=(letrec {X#7=(\ X#8.S#11);E#15} in (var X#7));E#3} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#7);E#15;E#3} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#7);E#15;E#3} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= (letrec {E#20;E#21} in (var X#15))
       ;E#18
       ;E#19
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= (var X#15)
       ;E#19
       ;E#21
       ;VV#16|X#15,(var X#7)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#18,E#21}
   Delta3 = {(A#12[(var X#9)],(letrec {E#20;E#21} in [.])),
             [{X#7=(\ X#8.S#11);E#18;E#19},(letrec {E#20;E#21} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {
             {E#18;E#20} =?= {VV#16|X#15,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {[.1]=(var X#15);VV#16|X#15,[.2]|},
           X#1          |->  X#9,
           S#4          |->  (var X#15),
           E#3          |->  {X#7=(\ X#8.S#11);E#18;E#19},
           E#10         |->  {E#19;E#21},
           E#2          |->  {E#20;E#21},
           E#17         |->  {E#18;E#19}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#15);E#18;E#19;E#20;E#21} in A#12[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#11);X#9=(letrec {E#20;E#21} in (var X#15));E#18;E#19} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#15);E#19;E#21;VV#16|X#15,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#15);E#19;E#21;VV#16|X#15,(var X#7)|} in A#12[(\ X#8.S#11)])
        ............................
    Delta4:
    {E#18;E#20} =?= {VV#16|X#15,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= (letrec {E#20;E#21} in (var X#15))
       ;E#18
       ;E#19
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= (var X#15)
       ;E#19
       ;E#21
       ;VV#16|X#15,(var X#7)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#20}
   Delta3 = {(A#12[(var X#9)],(letrec {E#20;E#21} in [.])),
             [{X#7=(\ X#8.S#11);E#18;E#19},(letrec {E#20;E#21} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {
             {E#18;E#20} =?= {VV#16|X#15,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {[.1]=(var X#15);VV#16|X#15,[.2]|},
           X#1          |->  X#9,
           S#4          |->  (var X#15),
           E#3          |->  {X#7=(\ X#8.S#11);E#18;E#19},
           E#10         |->  {E#19;E#21},
           E#2          |->  {E#20;E#21},
           E#17         |->  {E#18;E#19}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#15);E#18;E#19;E#20;E#21} in A#12[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#11);X#9=(letrec {E#20;E#21} in (var X#15));E#18;E#19} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#15);E#19;E#21;VV#16|X#15,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#15);E#19;E#21;VV#16|X#15,(var X#7)|} in A#12[(\ X#8.S#11)])
        ............................
    Delta4:
    {E#18;E#20} =?= {VV#16|X#15,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (letrec {X#7=(\ X#8.S#11);E#18;E#19} in (var X#15))
       ;E#20
       ;E#21
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= (var X#15)
       ;E#19
       ;E#21
       ;VV#16|X#15,(var X#7)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#18}
   Delta3 = {(A#12[(var X#9)],(letrec {X#7=(\ X#8.S#11);E#18;E#19} in [.])),
             [{E#20;E#21},(letrec {X#7=(\ X#8.S#11);E#18;E#19} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {
             {E#18;E#20} =?= {VV#16|X#15,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {[.1]=(var X#15);VV#16|X#15,[.2]|},
           X#1          |->  X#9,
           S#4          |->  (var X#15),
           E#2          |->  {X#7=(\ X#8.S#11);E#18;E#19},
           E#10         |->  {E#19;E#21},
           E#3          |->  {E#20;E#21},
           E#17         |->  {E#18;E#19}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#15);E#18;E#19;E#20;E#21} in A#12[(var X#9)])
    -llet-e1->                    (letrec {X#9=(letrec {X#7=(\ X#8.S#11);E#18;E#19} in (var X#15));E#20;E#21} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#15);E#19;E#21;VV#16|X#15,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#15);E#19;E#21;VV#16|X#15,(var X#7)|} in A#12[(\ X#8.S#11)])
        ............................
    Delta4:
    {E#18;E#20} =?= {VV#16|X#15,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#23;E#24;E#25} in (var X#16))
       ;X#7= (\ X#8.S#11)
       ;E#20
       ;E#21
       ;E#22
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#15= (var X#16)
       ;X#7= (\ X#8.S#11)
       ;E#22
       ;E#25
       ;VV#17|X#9,(var X#15)|
       ;VV#18|X#16,(var X#7)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#20,E#21,E#25}
   Delta3 = {(A#12[(var X#9)],(letrec {E#23;E#24;E#25} in [.])),
             [{X#7=(\ X#8.S#11);E#20;E#21;E#22},(letrec {E#23;E#24;E#25} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {
             {E#20;E#23} =?= {VV#17|X#9,(var X#15)|},
             {E#21;E#24} =?= {VV#18|X#16,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {X#15=(var X#16);VV#17|[.1],(var X#15)|;VV#18|X#16,[.2]|},
           X#1          |->  X#15,
           S#4          |->  (var X#16),
           E#3          |->  {X#7=(\ X#8.S#11);E#20;E#21;E#22},
           E#10         |->  {E#22;E#25},
           E#2          |->  {E#23;E#24;E#25},
           E#19         |->  {E#20;E#21;E#22}}

and instantiated rules:

                                  (letrec {X#15=(var X#16);X#7=(\ X#8.S#11);E#20;E#21;E#22;E#23;E#24;E#25} in A#12[(var X#9)])
    -llet-e1->                    (letrec {X#15=(letrec {E#23;E#24;E#25} in (var X#16));X#7=(\ X#8.S#11);E#20;E#21;E#22} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#15=(var X#16);X#7=(\ X#8.S#11);E#22;E#25;VV#17|X#9,(var X#15)|;VV#18|X#16,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#15=(var X#16);X#7=(\ X#8.S#11);E#22;E#25;VV#17|X#9,(var X#15)|;VV#18|X#16,(var X#7)|} in A#12[(\ X#8.S#11)])
        ............................
    Delta4:
    {E#20;E#23} =?= {VV#17|X#9,(var X#15)|},
    {E#21;E#24} =?= {VV#18|X#16,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#23;E#24;E#25} in (var X#16))
       ;X#7= (\ X#8.S#11)
       ;E#20
       ;E#21
       ;E#22
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#15= (var X#16)
       ;X#7= (\ X#8.S#11)
       ;E#22
       ;E#25
       ;VV#17|X#9,(var X#15)|
       ;VV#18|X#16,(var X#7)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#20,E#24}
   Delta3 = {(A#12[(var X#9)],(letrec {E#23;E#24;E#25} in [.])),
             [{X#7=(\ X#8.S#11);E#20;E#21;E#22},(letrec {E#23;E#24;E#25} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {
             {E#20;E#23} =?= {VV#17|X#9,(var X#15)|},
             {E#21;E#24} =?= {VV#18|X#16,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {X#15=(var X#16);VV#17|[.1],(var X#15)|;VV#18|X#16,[.2]|},
           X#1          |->  X#15,
           S#4          |->  (var X#16),
           E#3          |->  {X#7=(\ X#8.S#11);E#20;E#21;E#22},
           E#10         |->  {E#22;E#25},
           E#2          |->  {E#23;E#24;E#25},
           E#19         |->  {E#20;E#21;E#22}}

and instantiated rules:

                                  (letrec {X#15=(var X#16);X#7=(\ X#8.S#11);E#20;E#21;E#22;E#23;E#24;E#25} in A#12[(var X#9)])
    -llet-e1->                    (letrec {X#15=(letrec {E#23;E#24;E#25} in (var X#16));X#7=(\ X#8.S#11);E#20;E#21;E#22} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#15=(var X#16);X#7=(\ X#8.S#11);E#22;E#25;VV#17|X#9,(var X#15)|;VV#18|X#16,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#15=(var X#16);X#7=(\ X#8.S#11);E#22;E#25;VV#17|X#9,(var X#15)|;VV#18|X#16,(var X#7)|} in A#12[(\ X#8.S#11)])
        ............................
    Delta4:
    {E#20;E#23} =?= {VV#17|X#9,(var X#15)|},
    {E#21;E#24} =?= {VV#18|X#16,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {X#7=(\ X#8.S#11);E#20;E#21;E#22} in (var X#16))
       ;E#23
       ;E#24
       ;E#25
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#15= (var X#16)
       ;X#7= (\ X#8.S#11)
       ;E#22
       ;E#25
       ;VV#17|X#9,(var X#15)|
       ;VV#18|X#16,(var X#7)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#21,E#23}
   Delta3 = {(A#12[(var X#9)],(letrec {X#7=(\ X#8.S#11);E#20;E#21;E#22} in [.])),
             [{E#23;E#24;E#25},(letrec {X#7=(\ X#8.S#11);E#20;E#21;E#22} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {
             {E#20;E#23} =?= {VV#17|X#9,(var X#15)|},
             {E#21;E#24} =?= {VV#18|X#16,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {X#15=(var X#16);VV#17|[.1],(var X#15)|;VV#18|X#16,[.2]|},
           X#1          |->  X#15,
           S#4          |->  (var X#16),
           E#2          |->  {X#7=(\ X#8.S#11);E#20;E#21;E#22},
           E#10         |->  {E#22;E#25},
           E#3          |->  {E#23;E#24;E#25},
           E#19         |->  {E#20;E#21;E#22}}

and instantiated rules:

                                  (letrec {X#15=(var X#16);X#7=(\ X#8.S#11);E#20;E#21;E#22;E#23;E#24;E#25} in A#12[(var X#9)])
    -llet-e1->                    (letrec {X#15=(letrec {X#7=(\ X#8.S#11);E#20;E#21;E#22} in (var X#16));E#23;E#24;E#25} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#15=(var X#16);X#7=(\ X#8.S#11);E#22;E#25;VV#17|X#9,(var X#15)|;VV#18|X#16,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#15=(var X#16);X#7=(\ X#8.S#11);E#22;E#25;VV#17|X#9,(var X#15)|;VV#18|X#16,(var X#7)|} in A#12[(\ X#8.S#11)])
        ............................
    Delta4:
    {E#20;E#23} =?= {VV#17|X#9,(var X#15)|},
    {E#21;E#24} =?= {VV#18|X#16,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#20;E#21} in (var X#7))
       ;X#7= (\ X#8.S#11)
       ;E#18
       ;E#19
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#15= (var X#7)
       ;X#7= (\ X#8.S#11)
       ;E#19
       ;E#21
       ;VV#16|X#9,(var X#15)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#18,E#21}
   Delta3 = {(A#12[(var X#9)],(letrec {E#20;E#21} in [.])),
             [{X#7=(\ X#8.S#11);E#18;E#19},(letrec {E#20;E#21} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {
             {E#18;E#20} =?= {VV#16|X#9,(var X#15)|}}

from overlapping -llet-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {X#15=[.2];VV#16|[.1],(var X#15)|},
           X#1          |->  X#15,
           S#4          |->  (var X#7),
           E#3          |->  {X#7=(\ X#8.S#11);E#18;E#19},
           E#10         |->  {E#19;E#21},
           E#2          |->  {E#20;E#21},
           E#17         |->  {E#18;E#19}}

and instantiated rules:

                                  (letrec {X#15=(var X#7);X#7=(\ X#8.S#11);E#18;E#19;E#20;E#21} in A#12[(var X#9)])
    -llet-e1->                    (letrec {X#15=(letrec {E#20;E#21} in (var X#7));X#7=(\ X#8.S#11);E#18;E#19} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#15=(var X#7);X#7=(\ X#8.S#11);E#19;E#21;VV#16|X#9,(var X#15)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#15=(var X#7);X#7=(\ X#8.S#11);E#19;E#21;VV#16|X#9,(var X#15)|} in A#12[(\ X#8.S#11)])
        ............................
    Delta4:
    {E#18;E#20} =?= {VV#16|X#9,(var X#15)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {X#7=(\ X#8.S#11);E#18;E#19} in (var X#7))
       ;E#20
       ;E#21
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#15= (var X#7)
       ;X#7= (\ X#8.S#11)
       ;E#19
       ;E#21
       ;VV#16|X#9,(var X#15)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#20}
   Delta3 = {(A#12[(var X#9)],(letrec {X#7=(\ X#8.S#11);E#18;E#19} in [.])),
             [{E#20;E#21},(letrec {X#7=(\ X#8.S#11);E#18;E#19} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {
             {E#18;E#20} =?= {VV#16|X#9,(var X#15)|}}

from overlapping -llet-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {X#15=[.2];VV#16|[.1],(var X#15)|},
           X#1          |->  X#15,
           S#4          |->  (var X#7),
           E#2          |->  {X#7=(\ X#8.S#11);E#18;E#19},
           E#10         |->  {E#19;E#21},
           E#3          |->  {E#20;E#21},
           E#17         |->  {E#18;E#19}}

and instantiated rules:

                                  (letrec {X#15=(var X#7);X#7=(\ X#8.S#11);E#18;E#19;E#20;E#21} in A#12[(var X#9)])
    -llet-e1->                    (letrec {X#15=(letrec {X#7=(\ X#8.S#11);E#18;E#19} in (var X#7));E#20;E#21} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#15=(var X#7);X#7=(\ X#8.S#11);E#19;E#21;VV#16|X#9,(var X#15)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#15=(var X#7);X#7=(\ X#8.S#11);E#19;E#21;VV#16|X#9,(var X#15)|} in A#12[(\ X#8.S#11)])
        ............................
    Delta4:
    {E#18;E#20} =?= {VV#16|X#9,(var X#15)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;EE#14[X#9,A#12[(var X#7)]]
     in
        A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;EE#14[X#9,A#12[(\ X#8.S#11)]]
     in
        A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#13,T#15,T#6,A#12}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#16[(app A#17[[.]] T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)])]),
             ((var X#9),A#16[(app A#17[[.]] T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)])])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#16[(app A#17[(var X#9)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#9)] T#18)],
           A#13  |->  A#16[(app A#17 T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
       ;X#7= (\ X#8.S#11)
       ;E#18
       ;EE#14[X#9,A#12[(var X#7)]]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)]
       ;X#7= (\ X#8.S#11)
       ;E#18
       ;EE#14[X#9,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#6,A#12}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#16=T#15;X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)]),
           E#10  |->  {X#16=T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#18},
           E#17  |->  {X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(var X#7)]]}}

and instantiated rules:

                                  (letrec {X#16=T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#16=T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#16=T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]]
       ;E#10
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[A#21[(app A#22[(\ X#8.S#11)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]]
       ;E#10
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#6,A#12,A#19}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),A#21[(app A#22[[.]] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#11);X#9=A#19[A#21[(app A#22[(var X#7)] T#23)]];E#10} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#9,
           E#17         |->  {X#7=(\ X#8.S#11);E#10},
           A#18         |->  A#19,
           T#15         |->  A#19[A#21[(app A#22[(var X#7)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#7)] T#23)],
           A#12         |->  A#21[(app A#22 T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]];E#10} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#11);X#9=A#19[A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]];E#10} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]];E#10} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#19[A#21[(app A#22[(\ X#8.S#11)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]];E#10} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[(app A#20[A#12[(var X#7)]] T#21[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#10
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[(app A#20[A#12[(\ X#8.S#11)]] T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#10
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6,A#12}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[A#12[(var X#7)]] T#21)];E#10} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)])]},
           X#16         |->  X#9,
           E#17         |->  {X#7=(\ X#8.S#11);E#10},
           T#15         |->  A#19[(app A#20[A#12[(var X#7)]] T#21)],
           A#18         |->  A#19[(app A#20 T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[A#12[(var X#7)]] T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[A#12[(var X#7)]] T#21[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#10} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[A#12[(var X#7)]] T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[A#12[(\ X#8.S#11)]] T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[(app A#20[(var X#7)] T#21[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#10
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[(app A#20[(\ X#8.S#11)] T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#10
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#15,T#6,A#12}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),A#19[(app A#20[[.]] T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)])]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[(var X#7)] T#21)];E#10} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#9,
           E#17         |->  {X#7=(\ X#8.S#11);E#10},
           A#18         |->  [.],
           T#15         |->  A#19[(app A#20[(var X#7)] T#21)],
           A#12         |->  A#19[(app A#20 T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[(var X#7)] T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[(var X#7)] T#21[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#10} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[(var X#7)] T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[(\ X#8.S#11)] T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#10
       ;EE#20[X#19,A#12[(var X#7)]]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#10
       ;EE#20[X#19,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6,A#12}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#11);X#9=A#21[(app A#22[(var X#19)] T#23)];E#10;EE#20[X#19,A#12[(var X#7)]]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];EE#20[X#19,[.2]]},
           X#16         |->  X#9,
           E#17         |->  {X#7=(\ X#8.S#11);E#10;EE#20[X#19,A#12[(var X#7)]]},
           T#15         |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10;EE#20[X#19,A#12[(var X#7)]]} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#11);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#10;EE#20[X#19,A#12[(var X#7)]]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10;EE#20[X#19,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10;EE#20[X#19,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#21[X#9,(var X#19)]
       ;EE#22[X#20,A#12[(var X#7)]]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#21[X#9,(var X#19)]
       ;EE#22[X#20,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6,A#12}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(var X#7)]]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(var X#7)]]},
           T#15         |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(var X#7)]]} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(var X#7)]]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(app A#24[(var X#7)] T#25[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[(\ X#8.S#11)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#6,A#12,A#21}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),A#23[(app A#24[[.]] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[A#23[(app A#24[(var X#7)] T#25)]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]},
           A#18         |->  A#21,
           T#15         |->  A#21[A#23[(app A#24[(var X#7)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#7)] T#25)],
           A#12         |->  A#23[(app A#24 T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#7)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#19=A#21[A#23[(app A#24[(var X#7)] T#25[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#7)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#19=A#21[A#23[(app A#24[(\ X#8.S#11)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[A#12[(var X#7)]] T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[A#12[(\ X#8.S#11)]] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6,A#12}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app A#22[A#12[(var X#7)]] T#23)];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]},
           T#15         |->  A#21[(app A#22[A#12[(var X#7)]] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[A#12[(var X#7)]] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#19=A#21[(app A#22[A#12[(var X#7)]] T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[A#12[(var X#7)]] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#19=A#21[(app A#22[A#12[(\ X#8.S#11)]] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(\ X#8.S#11)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#15,T#6,A#12}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),A#21[(app A#22[[.]] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app A#22[(var X#7)] T#23)];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]},
           A#18         |->  [.],
           T#15         |->  A#21[(app A#22[(var X#7)] T#23)],
           A#12         |->  A#21[(app A#22 T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#19=A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#19=A#21[(app A#22[(\ X#8.S#11)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#7=(letrec {E#17;E#18} in (\ X#8.S#11));E#15;E#16} in A#13[(var X#9)])
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;E#16
       ;E#18
       ;EE#14[X#9,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {E#2,E#15,E#18}
   Delta3 = {(A#13[(var X#9)],(letrec {E#17;E#18} in [.])),
             [{E#15;E#16},(letrec {E#17;E#18} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {
             {E#15;E#17} =?= {EE#14[X#9,A#12[(var X#7)]]}}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#9)],
           X#1   |->  X#7,
           S#4   |->  (\ X#8.S#11),
           E#10  |->  {E#16;E#18},
           E#2   |->  {E#17;E#18},
           E#3   |->  {E#15;E#16}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);E#15;E#16;E#17;E#18} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#7=(letrec {E#17;E#18} in (\ X#8.S#11));E#15;E#16} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#16;E#18;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#16;E#18;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
        ............................
    Delta4:
    {E#15;E#17} =?= {EE#14[X#9,A#12[(var X#7)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#19;E#20} in S#4)
       ;X#7= (\ X#8.S#11)
       ;E#17
       ;E#18
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= S#4
       ;X#7= (\ X#8.S#11)
       ;E#18
       ;E#20
       ;EE#14[X#9,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {E#2,E#17,E#20}
   Delta3 = {(A#13[(var X#9)],(letrec {E#19;E#20} in [.])),
             [{X#7=(\ X#8.S#11);E#17;E#18},(letrec {E#19;E#20} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {
             {E#17;E#19} =?= {EE#14[X#9,A#12[(var X#7)]]}}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#9)],
           E#10  |->  {X#1=S#4;E#18;E#20},
           E#3   |->  {X#7=(\ X#8.S#11);E#17;E#18},
           E#15  |->  {E#18;E#20},
           E#2   |->  {E#19;E#20},
           E#16  |->  {E#17;E#18}}

and instantiated rules:

                                  (letrec {X#1=S#4;X#7=(\ X#8.S#11);E#17;E#18;E#19;E#20} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#1=(letrec {E#19;E#20} in S#4);X#7=(\ X#8.S#11);E#17;E#18} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=S#4;X#7=(\ X#8.S#11);E#18;E#20;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#1=S#4;X#7=(\ X#8.S#11);E#18;E#20;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
        ............................
    Delta4:
    {E#17;E#19} =?= {EE#14[X#9,A#12[(var X#7)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= (letrec {E#2} in A#15[A#12[(var X#7)]])
       ;E#16
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#15[A#12[(\ X#8.S#11)]]
       ;E#16
       ;E#2
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {E#2}
   Delta3 = {(A#13[(var X#9)],(letrec {E#2} in [.])),
             [{X#7=(\ X#8.S#11);E#16},(letrec {E#2} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#1          |->  X#9,
           S#4          |->  A#15[A#12[(var X#7)]],
           E#3          |->  {X#7=(\ X#8.S#11);E#16},
           E#10         |->  {E#16;E#2}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#15[A#12[(var X#7)]];E#16;E#2} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#11);X#9=(letrec {E#2} in A#15[A#12[(var X#7)]]);E#16} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#15[A#12[(var X#7)]];E#16;E#2} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#15[A#12[(\ X#8.S#11)]];E#16;E#2} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (letrec {X#7=(\ X#8.S#11);E#16} in A#15[A#12[(var X#7)]])
       ;E#3
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#15[A#12[(\ X#8.S#11)]]
       ;E#16
       ;E#3
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {E#2}
   Delta3 = {(A#13[(var X#9)],(letrec {X#7=(\ X#8.S#11);E#16} in [.])),
             [{E#3},(letrec {X#7=(\ X#8.S#11);E#16} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#1          |->  X#9,
           S#4          |->  A#15[A#12[(var X#7)]],
           E#2          |->  {X#7=(\ X#8.S#11);E#16},
           E#10         |->  {E#16;E#3}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#15[A#12[(var X#7)]];E#16;E#3} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#9=(letrec {X#7=(\ X#8.S#11);E#16} in A#15[A#12[(var X#7)]]);E#3} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#15[A#12[(var X#7)]];E#16;E#3} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#15[A#12[(\ X#8.S#11)]];E#16;E#3} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= (letrec {E#21;E#22} in A#15[(var X#16)])
       ;E#19
       ;E#20
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#15[(var X#16)]
       ;E#20
       ;E#22
       ;EE#17[X#16,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {E#2,E#19,E#22}
   Delta3 = {(A#13[(var X#9)],(letrec {E#21;E#22} in [.])),
             [{X#7=(\ X#8.S#11);E#19;E#20},(letrec {E#21;E#22} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {
             {E#19;E#21} =?= {EE#17[X#16,A#12[(var X#7)]]}}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=A#15[(var X#16)];EE#17[X#16,[.2]]},
           X#1          |->  X#9,
           S#4          |->  A#15[(var X#16)],
           E#3          |->  {X#7=(\ X#8.S#11);E#19;E#20},
           E#10         |->  {E#20;E#22},
           E#2          |->  {E#21;E#22},
           E#18         |->  {E#19;E#20}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#15[(var X#16)];E#19;E#20;E#21;E#22} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#11);X#9=(letrec {E#21;E#22} in A#15[(var X#16)]);E#19;E#20} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#15[(var X#16)];E#20;E#22;EE#17[X#16,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#15[(var X#16)];E#20;E#22;EE#17[X#16,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
        ............................
    Delta4:
    {E#19;E#21} =?= {EE#17[X#16,A#12[(var X#7)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= (letrec {E#21;E#22} in A#15[(var X#16)])
       ;E#19
       ;E#20
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#15[(var X#16)]
       ;E#20
       ;E#22
       ;EE#17[X#16,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {E#2,E#21}
   Delta3 = {(A#13[(var X#9)],(letrec {E#21;E#22} in [.])),
             [{X#7=(\ X#8.S#11);E#19;E#20},(letrec {E#21;E#22} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {
             {E#19;E#21} =?= {EE#17[X#16,A#12[(var X#7)]]}}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=A#15[(var X#16)];EE#17[X#16,[.2]]},
           X#1          |->  X#9,
           S#4          |->  A#15[(var X#16)],
           E#3          |->  {X#7=(\ X#8.S#11);E#19;E#20},
           E#10         |->  {E#20;E#22},
           E#2          |->  {E#21;E#22},
           E#18         |->  {E#19;E#20}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#15[(var X#16)];E#19;E#20;E#21;E#22} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#11);X#9=(letrec {E#21;E#22} in A#15[(var X#16)]);E#19;E#20} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#15[(var X#16)];E#20;E#22;EE#17[X#16,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#15[(var X#16)];E#20;E#22;EE#17[X#16,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
        ............................
    Delta4:
    {E#19;E#21} =?= {EE#17[X#16,A#12[(var X#7)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (letrec {X#7=(\ X#8.S#11);E#19;E#20} in A#15[(var X#16)])
       ;E#21
       ;E#22
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#15[(var X#16)]
       ;E#20
       ;E#22
       ;EE#17[X#16,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {E#2,E#19}
   Delta3 = {(A#13[(var X#9)],(letrec {X#7=(\ X#8.S#11);E#19;E#20} in [.])),
             [{E#21;E#22},(letrec {X#7=(\ X#8.S#11);E#19;E#20} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {
             {E#19;E#21} =?= {EE#17[X#16,A#12[(var X#7)]]}}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=A#15[(var X#16)];EE#17[X#16,[.2]]},
           X#1          |->  X#9,
           S#4          |->  A#15[(var X#16)],
           E#2          |->  {X#7=(\ X#8.S#11);E#19;E#20},
           E#10         |->  {E#20;E#22},
           E#3          |->  {E#21;E#22},
           E#18         |->  {E#19;E#20}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#15[(var X#16)];E#19;E#20;E#21;E#22} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#9=(letrec {X#7=(\ X#8.S#11);E#19;E#20} in A#15[(var X#16)]);E#21;E#22} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#15[(var X#16)];E#20;E#22;EE#17[X#16,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#15[(var X#16)];E#20;E#22;EE#17[X#16,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
        ............................
    Delta4:
    {E#19;E#21} =?= {EE#17[X#16,A#12[(var X#7)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {E#24;E#25;E#26} in A#15[(var X#17)])
       ;X#7= (\ X#8.S#11)
       ;E#21
       ;E#22
       ;E#23
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#15[(var X#17)]
       ;X#7= (\ X#8.S#11)
       ;E#23
       ;E#26
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#17,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {E#2,E#21,E#22,E#26}
   Delta3 = {(A#13[(var X#9)],(letrec {E#24;E#25;E#26} in [.])),
             [{X#7=(\ X#8.S#11);E#21;E#22;E#23},(letrec {E#24;E#25;E#26} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {
             {E#21;E#24} =?= {EE#18[X#9,(var X#16)]},
             {E#22;E#25} =?= {EE#19[X#17,A#12[(var X#7)]]}}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#15[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#1          |->  X#16,
           S#4          |->  A#15[(var X#17)],
           E#3          |->  {X#7=(\ X#8.S#11);E#21;E#22;E#23},
           E#10         |->  {E#23;E#26},
           E#2          |->  {E#24;E#25;E#26},
           E#20         |->  {E#21;E#22;E#23}}

and instantiated rules:

                                  (letrec {X#16=A#15[(var X#17)];X#7=(\ X#8.S#11);E#21;E#22;E#23;E#24;E#25;E#26} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#16=(letrec {E#24;E#25;E#26} in A#15[(var X#17)]);X#7=(\ X#8.S#11);E#21;E#22;E#23} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#15[(var X#17)];X#7=(\ X#8.S#11);E#23;E#26;EE#18[X#9,(var X#16)];EE#19[X#17,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#16=A#15[(var X#17)];X#7=(\ X#8.S#11);E#23;E#26;EE#18[X#9,(var X#16)];EE#19[X#17,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
        ............................
    Delta4:
    {E#21;E#24} =?= {EE#18[X#9,(var X#16)]},
    {E#22;E#25} =?= {EE#19[X#17,A#12[(var X#7)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {E#24;E#25;E#26} in A#15[(var X#17)])
       ;X#7= (\ X#8.S#11)
       ;E#21
       ;E#22
       ;E#23
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#15[(var X#17)]
       ;X#7= (\ X#8.S#11)
       ;E#23
       ;E#26
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#17,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {E#2,E#21,E#25}
   Delta3 = {(A#13[(var X#9)],(letrec {E#24;E#25;E#26} in [.])),
             [{X#7=(\ X#8.S#11);E#21;E#22;E#23},(letrec {E#24;E#25;E#26} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {
             {E#21;E#24} =?= {EE#18[X#9,(var X#16)]},
             {E#22;E#25} =?= {EE#19[X#17,A#12[(var X#7)]]}}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#15[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#1          |->  X#16,
           S#4          |->  A#15[(var X#17)],
           E#3          |->  {X#7=(\ X#8.S#11);E#21;E#22;E#23},
           E#10         |->  {E#23;E#26},
           E#2          |->  {E#24;E#25;E#26},
           E#20         |->  {E#21;E#22;E#23}}

and instantiated rules:

                                  (letrec {X#16=A#15[(var X#17)];X#7=(\ X#8.S#11);E#21;E#22;E#23;E#24;E#25;E#26} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#16=(letrec {E#24;E#25;E#26} in A#15[(var X#17)]);X#7=(\ X#8.S#11);E#21;E#22;E#23} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#15[(var X#17)];X#7=(\ X#8.S#11);E#23;E#26;EE#18[X#9,(var X#16)];EE#19[X#17,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#16=A#15[(var X#17)];X#7=(\ X#8.S#11);E#23;E#26;EE#18[X#9,(var X#16)];EE#19[X#17,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
        ............................
    Delta4:
    {E#21;E#24} =?= {EE#18[X#9,(var X#16)]},
    {E#22;E#25} =?= {EE#19[X#17,A#12[(var X#7)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#7=(\ X#8.S#11);E#21;E#22;E#23} in A#15[(var X#17)])
       ;E#24
       ;E#25
       ;E#26
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#15[(var X#17)]
       ;X#7= (\ X#8.S#11)
       ;E#23
       ;E#26
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#17,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {E#2,E#22,E#24}
   Delta3 = {(A#13[(var X#9)],(letrec {X#7=(\ X#8.S#11);E#21;E#22;E#23} in [.])),
             [{E#24;E#25;E#26},(letrec {X#7=(\ X#8.S#11);E#21;E#22;E#23} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {
             {E#21;E#24} =?= {EE#18[X#9,(var X#16)]},
             {E#22;E#25} =?= {EE#19[X#17,A#12[(var X#7)]]}}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#15[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#1          |->  X#16,
           S#4          |->  A#15[(var X#17)],
           E#2          |->  {X#7=(\ X#8.S#11);E#21;E#22;E#23},
           E#10         |->  {E#23;E#26},
           E#3          |->  {E#24;E#25;E#26},
           E#20         |->  {E#21;E#22;E#23}}

and instantiated rules:

                                  (letrec {X#16=A#15[(var X#17)];X#7=(\ X#8.S#11);E#21;E#22;E#23;E#24;E#25;E#26} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#16=(letrec {X#7=(\ X#8.S#11);E#21;E#22;E#23} in A#15[(var X#17)]);E#24;E#25;E#26} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#15[(var X#17)];X#7=(\ X#8.S#11);E#23;E#26;EE#18[X#9,(var X#16)];EE#19[X#17,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#16=A#15[(var X#17)];X#7=(\ X#8.S#11);E#23;E#26;EE#18[X#9,(var X#16)];EE#19[X#17,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
        ............................
    Delta4:
    {E#21;E#24} =?= {EE#18[X#9,(var X#16)]},
    {E#22;E#25} =?= {EE#19[X#17,A#12[(var X#7)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {E#21;E#22} in A#15[A#12[(var X#7)]])
       ;X#7= (\ X#8.S#11)
       ;E#19
       ;E#20
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#15[A#12[(\ X#8.S#11)]]
       ;X#7= (\ X#8.S#11)
       ;E#20
       ;E#22
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {E#2,E#19,E#22}
   Delta3 = {(A#13[(var X#9)],(letrec {E#21;E#22} in [.])),
             [{X#7=(\ X#8.S#11);E#19;E#20},(letrec {E#21;E#22} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {
             {E#19;E#21} =?= {EE#17[X#9,(var X#16)]}}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#15[[.2]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           S#4          |->  A#15[A#12[(var X#7)]],
           E#3          |->  {X#7=(\ X#8.S#11);E#19;E#20},
           E#10         |->  {E#20;E#22},
           E#2          |->  {E#21;E#22},
           E#18         |->  {E#19;E#20}}

and instantiated rules:

                                  (letrec {X#16=A#15[A#12[(var X#7)]];X#7=(\ X#8.S#11);E#19;E#20;E#21;E#22} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#16=(letrec {E#21;E#22} in A#15[A#12[(var X#7)]]);X#7=(\ X#8.S#11);E#19;E#20} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#15[A#12[(var X#7)]];X#7=(\ X#8.S#11);E#20;E#22;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#16=A#15[A#12[(\ X#8.S#11)]];X#7=(\ X#8.S#11);E#20;E#22;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
        ............................
    Delta4:
    {E#19;E#21} =?= {EE#17[X#9,(var X#16)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#7=(\ X#8.S#11);E#19;E#20} in A#15[A#12[(var X#7)]])
       ;E#21
       ;E#22
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#15[A#12[(\ X#8.S#11)]]
       ;X#7= (\ X#8.S#11)
       ;E#20
       ;E#22
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {E#2,E#21}
   Delta3 = {(A#13[(var X#9)],(letrec {X#7=(\ X#8.S#11);E#19;E#20} in [.])),
             [{E#21;E#22},(letrec {X#7=(\ X#8.S#11);E#19;E#20} in [.])],
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {
             {E#19;E#21} =?= {EE#17[X#9,(var X#16)]}}

from overlapping -llet-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#15[[.2]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           S#4          |->  A#15[A#12[(var X#7)]],
           E#2          |->  {X#7=(\ X#8.S#11);E#19;E#20},
           E#10         |->  {E#20;E#22},
           E#3          |->  {E#21;E#22},
           E#18         |->  {E#19;E#20}}

and instantiated rules:

                                  (letrec {X#16=A#15[A#12[(var X#7)]];X#7=(\ X#8.S#11);E#19;E#20;E#21;E#22} in A#13[(var X#9)])
    -llet-e1->                    (letrec {X#16=(letrec {X#7=(\ X#8.S#11);E#19;E#20} in A#15[A#12[(var X#7)]]);E#21;E#22} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#15[A#12[(var X#7)]];X#7=(\ X#8.S#11);E#20;E#22;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#16=A#15[A#12[(\ X#8.S#11)]];X#7=(\ X#8.S#11);E#20;E#22;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
        ............................
    Delta4:
    {E#19;E#21} =?= {EE#17[X#9,(var X#16)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#14,T#17,T#6,A#13}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#18[(app A#19[[.]] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#18[(app A#19[[.]] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] T#20)]),
           T#17  |->  A#18[(app A#19[(var X#9)] T#20)],
           A#14  |->  A#18[(app A#19 T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= T#17[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
       ;X#7= (\ X#8.S#12)
       ;E#20
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)]
       ;X#7= (\ X#8.S#12)
       ;E#20
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#6,A#13}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#18=T#17;X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           E#11  |->  {X#18=T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#20},
           E#19  |->  {X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#18=T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#18=T#17[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[A#23[(app A#24[(\ X#8.S#12)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#22,A#20,T#17,T#6,A#13,A#21}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#23[(app A#24[[.]] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#12);X#9=A#21[A#23[(app A#24[(var X#10)] T#25)]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#21[[.2]]},
           X#18         |->  X#9,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;VV#16|X#10,(var X#7)|},
           A#20         |->  A#21,
           T#17         |->  A#21[A#23[(app A#24[(var X#10)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#10)] T#25)],
           A#13         |->  A#23[(app A#24 T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#12);X#9=A#21[A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#21[A#23[(app A#24[(\ X#8.S#12)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[(app A#22[A#13[(var X#10)]] T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[(app A#22[A#13[(\ X#8.S#12)]] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#20,T#17,T#6,A#13}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[A#13[(var X#10)]] T#23)];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#21[(app A#22[[.2]] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]},
           X#18         |->  X#9,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;VV#16|X#10,(var X#7)|},
           T#17         |->  A#21[(app A#22[A#13[(var X#10)]] T#23)],
           A#20         |->  A#21[(app A#22 T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[A#13[(var X#10)]] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[A#13[(var X#10)]] T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[A#13[(var X#10)]] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[A#13[(\ X#8.S#12)]] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[(app A#22[(var X#10)] T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[(app A#22[(\ X#8.S#12)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#17,T#6,A#13}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#21[(app A#22[[.]] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[(var X#10)] T#23)];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#18         |->  X#9,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;VV#16|X#10,(var X#7)|},
           A#20         |->  [.],
           T#17         |->  A#21[(app A#22[(var X#10)] T#23)],
           A#13         |->  A#21[(app A#22 T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[(var X#10)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[(var X#10)] T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[(var X#10)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[(\ X#8.S#12)] T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#11
       ;EE#22[X#21,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#11
       ;EE#22[X#21,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#20,T#17,T#6,A#13}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#12);X#9=A#23[(app A#24[(var X#21)] T#25)];E#11;EE#22[X#21,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])];EE#22[X#21,[.2]]},
           X#18         |->  X#9,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;EE#22[X#21,A#13[(var X#10)]];VV#16|X#10,(var X#7)|},
           T#17         |->  A#23[(app A#24[(var X#21)] T#25)],
           A#20         |->  A#23[(app A#24 T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#11;EE#22[X#21,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#12);X#9=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#11;EE#22[X#21,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#11;EE#22[X#21,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#11;EE#22[X#21,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#23[X#9,(var X#21)]
       ;EE#24[X#22,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#21= A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#23[X#9,(var X#21)]
       ;EE#24[X#22,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#20,T#17,T#6,A#13}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#21=A#25[(app A#26[(var X#22)] T#27)];X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=S#4;E#2;E#3} in S#5)])];EE#23[[.1],(var X#21)];EE#24[X#22,[.2]]},
           X#18         |->  X#21,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(var X#10)]];VV#16|X#10,(var X#7)|},
           T#17         |->  A#25[(app A#26[(var X#22)] T#27)],
           A#20         |->  A#25[(app A#26 T#27[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#23[A#25[(app A#26[(var X#10)] T#27[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#21= A#23[A#25[(app A#26[(\ X#8.S#12)] T#27[(letrec {X#1=S#4;E#2;E#3} in S#5)])]]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#24,A#20,T#17,T#6,A#13,A#23}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#25[(app A#26[[.]] T#27[(letrec {X#1=S#4;E#2;E#3} in S#5)])]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#21=A#23[A#25[(app A#26[(var X#10)] T#27)]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#21=A#23[[.2]];EE#22[[.1],(var X#21)]},
           X#18         |->  X#21,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|},
           A#20         |->  A#23,
           T#17         |->  A#23[A#25[(app A#26[(var X#10)] T#27)]],
           T#24         |->  A#25[(app A#26[(var X#10)] T#27)],
           A#13         |->  A#25[(app A#26 T#27[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#21=A#23[A#25[(app A#26[(var X#10)] T#27[(letrec {X#1=S#4;E#2;E#3} in S#5)])]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#21=A#23[A#25[(app A#26[(var X#10)] T#27[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#21=A#23[A#25[(app A#26[(var X#10)] T#27[(letrec {X#1=S#4;E#2;E#3} in S#5)])]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#21=A#23[A#25[(app A#26[(\ X#8.S#12)] T#27[(letrec {X#1=S#4;E#2;E#3} in S#5)])]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#23[(app A#24[A#13[(var X#10)]] T#25[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#21= A#23[(app A#24[A#13[(\ X#8.S#12)]] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#20,T#17,T#6,A#13}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#21=A#23[(app A#24[A#13[(var X#10)]] T#25)];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#21=A#23[(app A#24[[.2]] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])];EE#22[[.1],(var X#21)]},
           X#18         |->  X#21,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|},
           T#17         |->  A#23[(app A#24[A#13[(var X#10)]] T#25)],
           A#20         |->  A#23[(app A#24 T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#21=A#23[(app A#24[A#13[(var X#10)]] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#21=A#23[(app A#24[A#13[(var X#10)]] T#25[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#21=A#23[(app A#24[A#13[(var X#10)]] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#21=A#23[(app A#24[A#13[(\ X#8.S#12)]] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#21= A#23[(app A#24[(\ X#8.S#12)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#17,T#6,A#13}
   Delta2 = {E#2}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#23[(app A#24[[.]] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#21=A#23[(app A#24[(var X#10)] T#25)];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#21=[.2];EE#22[[.1],(var X#21)]},
           X#18         |->  X#21,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|},
           A#20         |->  [.],
           T#17         |->  A#23[(app A#24[(var X#10)] T#25)],
           A#13         |->  A#23[(app A#24 T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#21=A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#21=A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#21=A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#21=A#23[(app A#24[(\ X#8.S#12)] T#25[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#20;E#21;E#22} in (\ X#8.S#12))
       ;E#17
       ;E#18
       ;E#19
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;E#19
       ;E#22
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#17,E#18,E#22}
   Delta3 = {(A#14[(var X#9)],(letrec {E#20;E#21;E#22} in [.])),
             [{E#17;E#18;E#19},(letrec {E#20;E#21;E#22} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#17;E#20} =?= {VV#16|X#10,(var X#7)|},
             {E#18;E#21} =?= {EE#15[X#9,A#13[(var X#10)]]}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#14[(var X#9)],
           X#1   |->  X#7,
           S#4   |->  (\ X#8.S#12),
           E#11  |->  {E#19;E#22},
           E#2   |->  {E#20;E#21;E#22},
           E#3   |->  {E#17;E#18;E#19}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);E#17;E#18;E#19;E#20;E#21;E#22} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#7=(letrec {E#20;E#21;E#22} in (\ X#8.S#12));E#17;E#18;E#19} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#19;E#22;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#19;E#22;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#17;E#20} =?= {VV#16|X#10,(var X#7)|},
    {E#18;E#21} =?= {EE#15[X#9,A#13[(var X#10)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#22;E#23;E#24} in S#4)
       ;X#7= (\ X#8.S#12)
       ;E#19
       ;E#20
       ;E#21
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#1= S#4
       ;X#7= (\ X#8.S#12)
       ;E#21
       ;E#24
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#19,E#20,E#24}
   Delta3 = {(A#14[(var X#9)],(letrec {E#22;E#23;E#24} in [.])),
             [{X#7=(\ X#8.S#12);E#19;E#20;E#21},(letrec {E#22;E#23;E#24} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#19;E#22} =?= {VV#16|X#10,(var X#7)|},
             {E#20;E#23} =?= {EE#15[X#9,A#13[(var X#10)]]}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#14[(var X#9)],
           E#11  |->  {X#1=S#4;E#21;E#24},
           E#3   |->  {X#7=(\ X#8.S#12);E#19;E#20;E#21},
           E#17  |->  {E#21;E#24},
           E#2   |->  {E#22;E#23;E#24},
           E#18  |->  {E#19;E#20;E#21}}

and instantiated rules:

                                  (letrec {X#1=S#4;X#7=(\ X#8.S#12);E#19;E#20;E#21;E#22;E#23;E#24} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#1=(letrec {E#22;E#23;E#24} in S#4);X#7=(\ X#8.S#12);E#19;E#20;E#21} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#1=S#4;X#7=(\ X#8.S#12);E#21;E#24;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#1=S#4;X#7=(\ X#8.S#12);E#21;E#24;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#19;E#22} =?= {VV#16|X#10,(var X#7)|},
    {E#20;E#23} =?= {EE#15[X#9,A#13[(var X#10)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (letrec {E#21;E#22} in (var X#7))
       ;X#7= (\ X#8.S#12)
       ;E#19
       ;E#20
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#10= (var X#7)
       ;X#7= (\ X#8.S#12)
       ;E#20
       ;E#22
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#19,E#22}
   Delta3 = {(A#14[(var X#9)],(letrec {E#21;E#22} in [.])),
             [{X#7=(\ X#8.S#12);E#19;E#20},(letrec {E#21;E#22} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#19;E#21} =?= {EE#15[X#9,A#13[(var X#10)]]}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#10,
           S#4          |->  (var X#7),
           E#3          |->  {X#7=(\ X#8.S#12);E#19;E#20},
           E#11         |->  {E#20;E#22},
           E#2          |->  {E#21;E#22},
           E#18         |->  {E#19;E#20}}

and instantiated rules:

                                  (letrec {X#10=(var X#7);X#7=(\ X#8.S#12);E#19;E#20;E#21;E#22} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#10=(letrec {E#21;E#22} in (var X#7));X#7=(\ X#8.S#12);E#19;E#20} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#10=(var X#7);X#7=(\ X#8.S#12);E#20;E#22;EE#15[X#9,A#13[(var X#10)]]} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#10=(var X#7);X#7=(\ X#8.S#12);E#20;E#22;EE#15[X#9,A#13[(\ X#8.S#12)]]} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#19;E#21} =?= {EE#15[X#9,A#13[(var X#10)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (letrec {X#7=(\ X#8.S#12);E#19;E#20} in (var X#7))
       ;E#21
       ;E#22
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#10= (var X#7)
       ;X#7= (\ X#8.S#12)
       ;E#20
       ;E#22
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#21}
   Delta3 = {(A#14[(var X#9)],(letrec {X#7=(\ X#8.S#12);E#19;E#20} in [.])),
             [{E#21;E#22},(letrec {X#7=(\ X#8.S#12);E#19;E#20} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#19;E#21} =?= {EE#15[X#9,A#13[(var X#10)]]}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#10,
           S#4          |->  (var X#7),
           E#2          |->  {X#7=(\ X#8.S#12);E#19;E#20},
           E#11         |->  {E#20;E#22},
           E#3          |->  {E#21;E#22},
           E#18         |->  {E#19;E#20}}

and instantiated rules:

                                  (letrec {X#10=(var X#7);X#7=(\ X#8.S#12);E#19;E#20;E#21;E#22} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#10=(letrec {X#7=(\ X#8.S#12);E#19;E#20} in (var X#7));E#21;E#22} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#10=(var X#7);X#7=(\ X#8.S#12);E#20;E#22;EE#15[X#9,A#13[(var X#10)]]} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#10=(var X#7);X#7=(\ X#8.S#12);E#20;E#22;EE#15[X#9,A#13[(\ X#8.S#12)]]} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#19;E#21} =?= {EE#15[X#9,A#13[(var X#10)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (letrec {E#24;E#25;E#26} in (var X#18))
       ;X#7= (\ X#8.S#12)
       ;E#21
       ;E#22
       ;E#23
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#10= (var X#18)
       ;X#7= (\ X#8.S#12)
       ;E#23
       ;E#26
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#19|X#18,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#21,E#22,E#26}
   Delta3 = {(A#14[(var X#9)],(letrec {E#24;E#25;E#26} in [.])),
             [{X#7=(\ X#8.S#12);E#21;E#22;E#23},(letrec {E#24;E#25;E#26} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#21;E#24} =?= {VV#19|X#18,(var X#7)|},
             {E#22;E#25} =?= {EE#15[X#9,A#13[(var X#10)]]}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {[.1]=(var X#18);VV#19|X#18,[.2]|},
           X#1          |->  X#10,
           S#4          |->  (var X#18),
           E#3          |->  {X#7=(\ X#8.S#12);E#21;E#22;E#23},
           E#11         |->  {E#23;E#26},
           E#2          |->  {E#24;E#25;E#26},
           E#20         |->  {E#21;E#22;E#23}}

and instantiated rules:

                                  (letrec {X#10=(var X#18);X#7=(\ X#8.S#12);E#21;E#22;E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#10=(letrec {E#24;E#25;E#26} in (var X#18));X#7=(\ X#8.S#12);E#21;E#22;E#23} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#10=(var X#18);X#7=(\ X#8.S#12);E#23;E#26;EE#15[X#9,A#13[(var X#10)]];VV#19|X#18,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#10=(var X#18);X#7=(\ X#8.S#12);E#23;E#26;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#19|X#18,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#21;E#24} =?= {VV#19|X#18,(var X#7)|},
    {E#22;E#25} =?= {EE#15[X#9,A#13[(var X#10)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (letrec {E#24;E#25;E#26} in (var X#18))
       ;X#7= (\ X#8.S#12)
       ;E#21
       ;E#22
       ;E#23
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#10= (var X#18)
       ;X#7= (\ X#8.S#12)
       ;E#23
       ;E#26
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#19|X#18,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#22,E#24}
   Delta3 = {(A#14[(var X#9)],(letrec {E#24;E#25;E#26} in [.])),
             [{X#7=(\ X#8.S#12);E#21;E#22;E#23},(letrec {E#24;E#25;E#26} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#21;E#24} =?= {VV#19|X#18,(var X#7)|},
             {E#22;E#25} =?= {EE#15[X#9,A#13[(var X#10)]]}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {[.1]=(var X#18);VV#19|X#18,[.2]|},
           X#1          |->  X#10,
           S#4          |->  (var X#18),
           E#3          |->  {X#7=(\ X#8.S#12);E#21;E#22;E#23},
           E#11         |->  {E#23;E#26},
           E#2          |->  {E#24;E#25;E#26},
           E#20         |->  {E#21;E#22;E#23}}

and instantiated rules:

                                  (letrec {X#10=(var X#18);X#7=(\ X#8.S#12);E#21;E#22;E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#10=(letrec {E#24;E#25;E#26} in (var X#18));X#7=(\ X#8.S#12);E#21;E#22;E#23} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#10=(var X#18);X#7=(\ X#8.S#12);E#23;E#26;EE#15[X#9,A#13[(var X#10)]];VV#19|X#18,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#10=(var X#18);X#7=(\ X#8.S#12);E#23;E#26;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#19|X#18,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#21;E#24} =?= {VV#19|X#18,(var X#7)|},
    {E#22;E#25} =?= {EE#15[X#9,A#13[(var X#10)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in (var X#18))
       ;E#24
       ;E#25
       ;E#26
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#10= (var X#18)
       ;X#7= (\ X#8.S#12)
       ;E#23
       ;E#26
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#19|X#18,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#21,E#25}
   Delta3 = {(A#14[(var X#9)],(letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in [.])),
             [{E#24;E#25;E#26},(letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#21;E#24} =?= {VV#19|X#18,(var X#7)|},
             {E#22;E#25} =?= {EE#15[X#9,A#13[(var X#10)]]}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {[.1]=(var X#18);VV#19|X#18,[.2]|},
           X#1          |->  X#10,
           S#4          |->  (var X#18),
           E#2          |->  {X#7=(\ X#8.S#12);E#21;E#22;E#23},
           E#11         |->  {E#23;E#26},
           E#3          |->  {E#24;E#25;E#26},
           E#20         |->  {E#21;E#22;E#23}}

and instantiated rules:

                                  (letrec {X#10=(var X#18);X#7=(\ X#8.S#12);E#21;E#22;E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#10=(letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in (var X#18));E#24;E#25;E#26} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#10=(var X#18);X#7=(\ X#8.S#12);E#23;E#26;EE#15[X#9,A#13[(var X#10)]];VV#19|X#18,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#10=(var X#18);X#7=(\ X#8.S#12);E#23;E#26;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#19|X#18,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#21;E#24} =?= {VV#19|X#18,(var X#7)|},
    {E#22;E#25} =?= {EE#15[X#9,A#13[(var X#10)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {E#27;E#28;E#29;E#30} in (var X#19))
       ;X#7= (\ X#8.S#12)
       ;E#23
       ;E#24
       ;E#25
       ;E#26
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= (var X#19)
       ;X#7= (\ X#8.S#12)
       ;E#26
       ;E#30
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#20|X#10,(var X#18)|
       ;VV#21|X#19,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#23,E#24,E#25,E#30}
   Delta3 = {(A#14[(var X#9)],(letrec {E#27;E#28;E#29;E#30} in [.])),
             [{X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26},(letrec {E#27;E#28;E#29;E#30} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#23;E#27} =?= {VV#20|X#10,(var X#18)|},
             {E#24;E#28} =?= {VV#21|X#19,(var X#7)|},
             {E#25;E#29} =?= {EE#15[X#9,A#13[(var X#10)]]}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {X#18=(var X#19);VV#20|[.1],(var X#18)|;VV#21|X#19,[.2]|},
           X#1          |->  X#18,
           S#4          |->  (var X#19),
           E#3          |->  {X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26},
           E#11         |->  {E#26;E#30},
           E#2          |->  {E#27;E#28;E#29;E#30},
           E#22         |->  {E#23;E#24;E#25;E#26}}

and instantiated rules:

                                  (letrec {X#18=(var X#19);X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26;E#27;E#28;E#29;E#30} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#18=(letrec {E#27;E#28;E#29;E#30} in (var X#19));X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=(var X#19);X#7=(\ X#8.S#12);E#26;E#30;EE#15[X#9,A#13[(var X#10)]];VV#20|X#10,(var X#18)|;VV#21|X#19,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=(var X#19);X#7=(\ X#8.S#12);E#26;E#30;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#20|X#10,(var X#18)|;VV#21|X#19,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#23;E#27} =?= {VV#20|X#10,(var X#18)|},
    {E#24;E#28} =?= {VV#21|X#19,(var X#7)|},
    {E#25;E#29} =?= {EE#15[X#9,A#13[(var X#10)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {E#27;E#28;E#29;E#30} in (var X#19))
       ;X#7= (\ X#8.S#12)
       ;E#23
       ;E#24
       ;E#25
       ;E#26
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= (var X#19)
       ;X#7= (\ X#8.S#12)
       ;E#26
       ;E#30
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#20|X#10,(var X#18)|
       ;VV#21|X#19,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#23,E#25,E#28}
   Delta3 = {(A#14[(var X#9)],(letrec {E#27;E#28;E#29;E#30} in [.])),
             [{X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26},(letrec {E#27;E#28;E#29;E#30} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#23;E#27} =?= {VV#20|X#10,(var X#18)|},
             {E#24;E#28} =?= {VV#21|X#19,(var X#7)|},
             {E#25;E#29} =?= {EE#15[X#9,A#13[(var X#10)]]}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {X#18=(var X#19);VV#20|[.1],(var X#18)|;VV#21|X#19,[.2]|},
           X#1          |->  X#18,
           S#4          |->  (var X#19),
           E#3          |->  {X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26},
           E#11         |->  {E#26;E#30},
           E#2          |->  {E#27;E#28;E#29;E#30},
           E#22         |->  {E#23;E#24;E#25;E#26}}

and instantiated rules:

                                  (letrec {X#18=(var X#19);X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26;E#27;E#28;E#29;E#30} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#18=(letrec {E#27;E#28;E#29;E#30} in (var X#19));X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=(var X#19);X#7=(\ X#8.S#12);E#26;E#30;EE#15[X#9,A#13[(var X#10)]];VV#20|X#10,(var X#18)|;VV#21|X#19,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=(var X#19);X#7=(\ X#8.S#12);E#26;E#30;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#20|X#10,(var X#18)|;VV#21|X#19,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#23;E#27} =?= {VV#20|X#10,(var X#18)|},
    {E#24;E#28} =?= {VV#21|X#19,(var X#7)|},
    {E#25;E#29} =?= {EE#15[X#9,A#13[(var X#10)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26} in (var X#19))
       ;E#27
       ;E#28
       ;E#29
       ;E#30
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= (var X#19)
       ;X#7= (\ X#8.S#12)
       ;E#26
       ;E#30
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#20|X#10,(var X#18)|
       ;VV#21|X#19,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#24,E#27,E#29}
   Delta3 = {(A#14[(var X#9)],(letrec {X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26} in [.])),
             [{E#27;E#28;E#29;E#30},(letrec {X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#23;E#27} =?= {VV#20|X#10,(var X#18)|},
             {E#24;E#28} =?= {VV#21|X#19,(var X#7)|},
             {E#25;E#29} =?= {EE#15[X#9,A#13[(var X#10)]]}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {X#18=(var X#19);VV#20|[.1],(var X#18)|;VV#21|X#19,[.2]|},
           X#1          |->  X#18,
           S#4          |->  (var X#19),
           E#2          |->  {X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26},
           E#11         |->  {E#26;E#30},
           E#3          |->  {E#27;E#28;E#29;E#30},
           E#22         |->  {E#23;E#24;E#25;E#26}}

and instantiated rules:

                                  (letrec {X#18=(var X#19);X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26;E#27;E#28;E#29;E#30} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#18=(letrec {X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26} in (var X#19));E#27;E#28;E#29;E#30} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=(var X#19);X#7=(\ X#8.S#12);E#26;E#30;EE#15[X#9,A#13[(var X#10)]];VV#20|X#10,(var X#18)|;VV#21|X#19,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=(var X#19);X#7=(\ X#8.S#12);E#26;E#30;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#20|X#10,(var X#18)|;VV#21|X#19,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#23;E#27} =?= {VV#20|X#10,(var X#18)|},
    {E#24;E#28} =?= {VV#21|X#19,(var X#7)|},
    {E#25;E#29} =?= {EE#15[X#9,A#13[(var X#10)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {E#24;E#25;E#26} in (var X#7))
       ;X#7= (\ X#8.S#12)
       ;E#21
       ;E#22
       ;E#23
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= (var X#7)
       ;X#7= (\ X#8.S#12)
       ;E#23
       ;E#26
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#19|X#10,(var X#18)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#21,E#22,E#26}
   Delta3 = {(A#14[(var X#9)],(letrec {E#24;E#25;E#26} in [.])),
             [{X#7=(\ X#8.S#12);E#21;E#22;E#23},(letrec {E#24;E#25;E#26} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#21;E#24} =?= {VV#19|X#10,(var X#18)|},
             {E#22;E#25} =?= {EE#15[X#9,A#13[(var X#10)]]}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {X#18=[.2];VV#19|[.1],(var X#18)|},
           X#1          |->  X#18,
           S#4          |->  (var X#7),
           E#3          |->  {X#7=(\ X#8.S#12);E#21;E#22;E#23},
           E#11         |->  {E#23;E#26},
           E#2          |->  {E#24;E#25;E#26},
           E#20         |->  {E#21;E#22;E#23}}

and instantiated rules:

                                  (letrec {X#18=(var X#7);X#7=(\ X#8.S#12);E#21;E#22;E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#18=(letrec {E#24;E#25;E#26} in (var X#7));X#7=(\ X#8.S#12);E#21;E#22;E#23} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=(var X#7);X#7=(\ X#8.S#12);E#23;E#26;EE#15[X#9,A#13[(var X#10)]];VV#19|X#10,(var X#18)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=(var X#7);X#7=(\ X#8.S#12);E#23;E#26;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#19|X#10,(var X#18)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#21;E#24} =?= {VV#19|X#10,(var X#18)|},
    {E#22;E#25} =?= {EE#15[X#9,A#13[(var X#10)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in (var X#7))
       ;E#24
       ;E#25
       ;E#26
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= (var X#7)
       ;X#7= (\ X#8.S#12)
       ;E#23
       ;E#26
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#19|X#10,(var X#18)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#24,E#25}
   Delta3 = {(A#14[(var X#9)],(letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in [.])),
             [{E#24;E#25;E#26},(letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#21;E#24} =?= {VV#19|X#10,(var X#18)|},
             {E#22;E#25} =?= {EE#15[X#9,A#13[(var X#10)]]}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {X#18=[.2];VV#19|[.1],(var X#18)|},
           X#1          |->  X#18,
           S#4          |->  (var X#7),
           E#2          |->  {X#7=(\ X#8.S#12);E#21;E#22;E#23},
           E#11         |->  {E#23;E#26},
           E#3          |->  {E#24;E#25;E#26},
           E#20         |->  {E#21;E#22;E#23}}

and instantiated rules:

                                  (letrec {X#18=(var X#7);X#7=(\ X#8.S#12);E#21;E#22;E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#18=(letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in (var X#7));E#24;E#25;E#26} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=(var X#7);X#7=(\ X#8.S#12);E#23;E#26;EE#15[X#9,A#13[(var X#10)]];VV#19|X#10,(var X#18)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=(var X#7);X#7=(\ X#8.S#12);E#23;E#26;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#19|X#10,(var X#18)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#21;E#24} =?= {VV#19|X#10,(var X#18)|},
    {E#22;E#25} =?= {EE#15[X#9,A#13[(var X#10)]]}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= (letrec {E#21;E#22} in A#17[A#13[(var X#10)]])
       ;E#19
       ;E#20
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#17[A#13[(\ X#8.S#12)]]
       ;E#20
       ;E#22
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#19,E#22}
   Delta3 = {(A#14[(var X#9)],(letrec {E#21;E#22} in [.])),
             [{X#7=(\ X#8.S#12);E#19;E#20},(letrec {E#21;E#22} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#19;E#21} =?= {VV#16|X#10,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#1          |->  X#9,
           S#4          |->  A#17[A#13[(var X#10)]],
           E#3          |->  {X#7=(\ X#8.S#12);E#19;E#20},
           E#11         |->  {E#20;E#22},
           E#2          |->  {E#21;E#22},
           E#18         |->  {E#19;E#20}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#17[A#13[(var X#10)]];E#19;E#20;E#21;E#22} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#12);X#9=(letrec {E#21;E#22} in A#17[A#13[(var X#10)]]);E#19;E#20} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#17[A#13[(var X#10)]];E#20;E#22;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#17[A#13[(\ X#8.S#12)]];E#20;E#22;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#19;E#21} =?= {VV#16|X#10,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= (letrec {E#21;E#22} in A#17[A#13[(var X#10)]])
       ;E#19
       ;E#20
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#17[A#13[(\ X#8.S#12)]]
       ;E#20
       ;E#22
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#21}
   Delta3 = {(A#14[(var X#9)],(letrec {E#21;E#22} in [.])),
             [{X#7=(\ X#8.S#12);E#19;E#20},(letrec {E#21;E#22} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#19;E#21} =?= {VV#16|X#10,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#1          |->  X#9,
           S#4          |->  A#17[A#13[(var X#10)]],
           E#3          |->  {X#7=(\ X#8.S#12);E#19;E#20},
           E#11         |->  {E#20;E#22},
           E#2          |->  {E#21;E#22},
           E#18         |->  {E#19;E#20}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#17[A#13[(var X#10)]];E#19;E#20;E#21;E#22} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#12);X#9=(letrec {E#21;E#22} in A#17[A#13[(var X#10)]]);E#19;E#20} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#17[A#13[(var X#10)]];E#20;E#22;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#17[A#13[(\ X#8.S#12)]];E#20;E#22;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#19;E#21} =?= {VV#16|X#10,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (letrec {X#7=(\ X#8.S#12);E#19;E#20} in A#17[A#13[(var X#10)]])
       ;E#21
       ;E#22
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#17[A#13[(\ X#8.S#12)]]
       ;E#20
       ;E#22
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#19}
   Delta3 = {(A#14[(var X#9)],(letrec {X#7=(\ X#8.S#12);E#19;E#20} in [.])),
             [{E#21;E#22},(letrec {X#7=(\ X#8.S#12);E#19;E#20} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#19;E#21} =?= {VV#16|X#10,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#1          |->  X#9,
           S#4          |->  A#17[A#13[(var X#10)]],
           E#2          |->  {X#7=(\ X#8.S#12);E#19;E#20},
           E#11         |->  {E#20;E#22},
           E#3          |->  {E#21;E#22},
           E#18         |->  {E#19;E#20}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#17[A#13[(var X#10)]];E#19;E#20;E#21;E#22} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#9=(letrec {X#7=(\ X#8.S#12);E#19;E#20} in A#17[A#13[(var X#10)]]);E#21;E#22} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#17[A#13[(var X#10)]];E#20;E#22;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#17[A#13[(\ X#8.S#12)]];E#20;E#22;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#19;E#21} =?= {VV#16|X#10,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= (letrec {E#24;E#25;E#26} in A#17[(var X#18)])
       ;E#21
       ;E#22
       ;E#23
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#17[(var X#18)]
       ;E#23
       ;E#26
       ;EE#19[X#18,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#21,E#22,E#26}
   Delta3 = {(A#14[(var X#9)],(letrec {E#24;E#25;E#26} in [.])),
             [{X#7=(\ X#8.S#12);E#21;E#22;E#23},(letrec {E#24;E#25;E#26} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#21;E#24} =?= {EE#19[X#18,A#13[(var X#10)]]},
             {E#22;E#25} =?= {VV#16|X#10,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {[.1]=A#17[(var X#18)];EE#19[X#18,[.2]]},
           X#1          |->  X#9,
           S#4          |->  A#17[(var X#18)],
           E#3          |->  {X#7=(\ X#8.S#12);E#21;E#22;E#23},
           E#11         |->  {E#23;E#26},
           E#2          |->  {E#24;E#25;E#26},
           E#20         |->  {E#21;E#22;E#23}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#17[(var X#18)];E#21;E#22;E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#12);X#9=(letrec {E#24;E#25;E#26} in A#17[(var X#18)]);E#21;E#22;E#23} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#17[(var X#18)];E#23;E#26;EE#19[X#18,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#17[(var X#18)];E#23;E#26;EE#19[X#18,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#21;E#24} =?= {EE#19[X#18,A#13[(var X#10)]]},
    {E#22;E#25} =?= {VV#16|X#10,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= (letrec {E#24;E#25;E#26} in A#17[(var X#18)])
       ;E#21
       ;E#22
       ;E#23
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#17[(var X#18)]
       ;E#23
       ;E#26
       ;EE#19[X#18,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#22,E#24}
   Delta3 = {(A#14[(var X#9)],(letrec {E#24;E#25;E#26} in [.])),
             [{X#7=(\ X#8.S#12);E#21;E#22;E#23},(letrec {E#24;E#25;E#26} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#21;E#24} =?= {EE#19[X#18,A#13[(var X#10)]]},
             {E#22;E#25} =?= {VV#16|X#10,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {[.1]=A#17[(var X#18)];EE#19[X#18,[.2]]},
           X#1          |->  X#9,
           S#4          |->  A#17[(var X#18)],
           E#3          |->  {X#7=(\ X#8.S#12);E#21;E#22;E#23},
           E#11         |->  {E#23;E#26},
           E#2          |->  {E#24;E#25;E#26},
           E#20         |->  {E#21;E#22;E#23}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#17[(var X#18)];E#21;E#22;E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#12);X#9=(letrec {E#24;E#25;E#26} in A#17[(var X#18)]);E#21;E#22;E#23} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#17[(var X#18)];E#23;E#26;EE#19[X#18,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#17[(var X#18)];E#23;E#26;EE#19[X#18,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#21;E#24} =?= {EE#19[X#18,A#13[(var X#10)]]},
    {E#22;E#25} =?= {VV#16|X#10,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= (letrec {E#24;E#25;E#26} in A#17[(var X#18)])
       ;E#21
       ;E#22
       ;E#23
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#17[(var X#18)]
       ;E#23
       ;E#26
       ;EE#19[X#18,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#24,E#25}
   Delta3 = {(A#14[(var X#9)],(letrec {E#24;E#25;E#26} in [.])),
             [{X#7=(\ X#8.S#12);E#21;E#22;E#23},(letrec {E#24;E#25;E#26} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#21;E#24} =?= {EE#19[X#18,A#13[(var X#10)]]},
             {E#22;E#25} =?= {VV#16|X#10,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {[.1]=A#17[(var X#18)];EE#19[X#18,[.2]]},
           X#1          |->  X#9,
           S#4          |->  A#17[(var X#18)],
           E#3          |->  {X#7=(\ X#8.S#12);E#21;E#22;E#23},
           E#11         |->  {E#23;E#26},
           E#2          |->  {E#24;E#25;E#26},
           E#20         |->  {E#21;E#22;E#23}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#17[(var X#18)];E#21;E#22;E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#7=(\ X#8.S#12);X#9=(letrec {E#24;E#25;E#26} in A#17[(var X#18)]);E#21;E#22;E#23} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#17[(var X#18)];E#23;E#26;EE#19[X#18,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#17[(var X#18)];E#23;E#26;EE#19[X#18,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#21;E#24} =?= {EE#19[X#18,A#13[(var X#10)]]},
    {E#22;E#25} =?= {VV#16|X#10,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in A#17[(var X#18)])
       ;E#24
       ;E#25
       ;E#26
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#17[(var X#18)]
       ;E#23
       ;E#26
       ;EE#19[X#18,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#21,E#22}
   Delta3 = {(A#14[(var X#9)],(letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in [.])),
             [{E#24;E#25;E#26},(letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#21;E#24} =?= {EE#19[X#18,A#13[(var X#10)]]},
             {E#22;E#25} =?= {VV#16|X#10,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {[.1]=A#17[(var X#18)];EE#19[X#18,[.2]]},
           X#1          |->  X#9,
           S#4          |->  A#17[(var X#18)],
           E#2          |->  {X#7=(\ X#8.S#12);E#21;E#22;E#23},
           E#11         |->  {E#23;E#26},
           E#3          |->  {E#24;E#25;E#26},
           E#20         |->  {E#21;E#22;E#23}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#17[(var X#18)];E#21;E#22;E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#9=(letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in A#17[(var X#18)]);E#24;E#25;E#26} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#17[(var X#18)];E#23;E#26;EE#19[X#18,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#17[(var X#18)];E#23;E#26;EE#19[X#18,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#21;E#24} =?= {EE#19[X#18,A#13[(var X#10)]]},
    {E#22;E#25} =?= {VV#16|X#10,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {E#27;E#28;E#29;E#30} in A#17[(var X#19)])
       ;X#7= (\ X#8.S#12)
       ;E#23
       ;E#24
       ;E#25
       ;E#26
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#17[(var X#19)]
       ;X#7= (\ X#8.S#12)
       ;E#26
       ;E#30
       ;EE#20[X#9,(var X#18)]
       ;EE#21[X#19,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#23,E#24,E#25,E#30}
   Delta3 = {(A#14[(var X#9)],(letrec {E#27;E#28;E#29;E#30} in [.])),
             [{X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26},(letrec {E#27;E#28;E#29;E#30} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#23;E#27} =?= {EE#20[X#9,(var X#18)]},
             {E#24;E#28} =?= {EE#21[X#19,A#13[(var X#10)]]},
             {E#25;E#29} =?= {VV#16|X#10,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {X#18=A#17[(var X#19)];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#1          |->  X#18,
           S#4          |->  A#17[(var X#19)],
           E#3          |->  {X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26},
           E#11         |->  {E#26;E#30},
           E#2          |->  {E#27;E#28;E#29;E#30},
           E#22         |->  {E#23;E#24;E#25;E#26}}

and instantiated rules:

                                  (letrec {X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26;E#27;E#28;E#29;E#30} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#18=(letrec {E#27;E#28;E#29;E#30} in A#17[(var X#19)]);X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);E#26;E#30;EE#20[X#9,(var X#18)];EE#21[X#19,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);E#26;E#30;EE#20[X#9,(var X#18)];EE#21[X#19,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#23;E#27} =?= {EE#20[X#9,(var X#18)]},
    {E#24;E#28} =?= {EE#21[X#19,A#13[(var X#10)]]},
    {E#25;E#29} =?= {VV#16|X#10,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {E#27;E#28;E#29;E#30} in A#17[(var X#19)])
       ;X#7= (\ X#8.S#12)
       ;E#23
       ;E#24
       ;E#25
       ;E#26
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#17[(var X#19)]
       ;X#7= (\ X#8.S#12)
       ;E#26
       ;E#30
       ;EE#20[X#9,(var X#18)]
       ;EE#21[X#19,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#23,E#25,E#28}
   Delta3 = {(A#14[(var X#9)],(letrec {E#27;E#28;E#29;E#30} in [.])),
             [{X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26},(letrec {E#27;E#28;E#29;E#30} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#23;E#27} =?= {EE#20[X#9,(var X#18)]},
             {E#24;E#28} =?= {EE#21[X#19,A#13[(var X#10)]]},
             {E#25;E#29} =?= {VV#16|X#10,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {X#18=A#17[(var X#19)];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#1          |->  X#18,
           S#4          |->  A#17[(var X#19)],
           E#3          |->  {X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26},
           E#11         |->  {E#26;E#30},
           E#2          |->  {E#27;E#28;E#29;E#30},
           E#22         |->  {E#23;E#24;E#25;E#26}}

and instantiated rules:

                                  (letrec {X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26;E#27;E#28;E#29;E#30} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#18=(letrec {E#27;E#28;E#29;E#30} in A#17[(var X#19)]);X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);E#26;E#30;EE#20[X#9,(var X#18)];EE#21[X#19,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);E#26;E#30;EE#20[X#9,(var X#18)];EE#21[X#19,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#23;E#27} =?= {EE#20[X#9,(var X#18)]},
    {E#24;E#28} =?= {EE#21[X#19,A#13[(var X#10)]]},
    {E#25;E#29} =?= {VV#16|X#10,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {E#27;E#28;E#29;E#30} in A#17[(var X#19)])
       ;X#7= (\ X#8.S#12)
       ;E#23
       ;E#24
       ;E#25
       ;E#26
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#17[(var X#19)]
       ;X#7= (\ X#8.S#12)
       ;E#26
       ;E#30
       ;EE#20[X#9,(var X#18)]
       ;EE#21[X#19,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#23,E#28,E#29}
   Delta3 = {(A#14[(var X#9)],(letrec {E#27;E#28;E#29;E#30} in [.])),
             [{X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26},(letrec {E#27;E#28;E#29;E#30} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#23;E#27} =?= {EE#20[X#9,(var X#18)]},
             {E#24;E#28} =?= {EE#21[X#19,A#13[(var X#10)]]},
             {E#25;E#29} =?= {VV#16|X#10,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {X#18=A#17[(var X#19)];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#1          |->  X#18,
           S#4          |->  A#17[(var X#19)],
           E#3          |->  {X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26},
           E#11         |->  {E#26;E#30},
           E#2          |->  {E#27;E#28;E#29;E#30},
           E#22         |->  {E#23;E#24;E#25;E#26}}

and instantiated rules:

                                  (letrec {X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26;E#27;E#28;E#29;E#30} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#18=(letrec {E#27;E#28;E#29;E#30} in A#17[(var X#19)]);X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);E#26;E#30;EE#20[X#9,(var X#18)];EE#21[X#19,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);E#26;E#30;EE#20[X#9,(var X#18)];EE#21[X#19,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#23;E#27} =?= {EE#20[X#9,(var X#18)]},
    {E#24;E#28} =?= {EE#21[X#19,A#13[(var X#10)]]},
    {E#25;E#29} =?= {VV#16|X#10,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26} in A#17[(var X#19)])
       ;E#27
       ;E#28
       ;E#29
       ;E#30
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#17[(var X#19)]
       ;X#7= (\ X#8.S#12)
       ;E#26
       ;E#30
       ;EE#20[X#9,(var X#18)]
       ;EE#21[X#19,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#24,E#25,E#27}
   Delta3 = {(A#14[(var X#9)],(letrec {X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26} in [.])),
             [{E#27;E#28;E#29;E#30},(letrec {X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#23;E#27} =?= {EE#20[X#9,(var X#18)]},
             {E#24;E#28} =?= {EE#21[X#19,A#13[(var X#10)]]},
             {E#25;E#29} =?= {VV#16|X#10,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {X#18=A#17[(var X#19)];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#1          |->  X#18,
           S#4          |->  A#17[(var X#19)],
           E#2          |->  {X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26},
           E#11         |->  {E#26;E#30},
           E#3          |->  {E#27;E#28;E#29;E#30},
           E#22         |->  {E#23;E#24;E#25;E#26}}

and instantiated rules:

                                  (letrec {X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26;E#27;E#28;E#29;E#30} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#18=(letrec {X#7=(\ X#8.S#12);E#23;E#24;E#25;E#26} in A#17[(var X#19)]);E#27;E#28;E#29;E#30} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);E#26;E#30;EE#20[X#9,(var X#18)];EE#21[X#19,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);E#26;E#30;EE#20[X#9,(var X#18)];EE#21[X#19,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#23;E#27} =?= {EE#20[X#9,(var X#18)]},
    {E#24;E#28} =?= {EE#21[X#19,A#13[(var X#10)]]},
    {E#25;E#29} =?= {VV#16|X#10,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {E#24;E#25;E#26} in A#17[A#13[(var X#10)]])
       ;X#7= (\ X#8.S#12)
       ;E#21
       ;E#22
       ;E#23
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#17[A#13[(\ X#8.S#12)]]
       ;X#7= (\ X#8.S#12)
       ;E#23
       ;E#26
       ;EE#19[X#9,(var X#18)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#21,E#22,E#26}
   Delta3 = {(A#14[(var X#9)],(letrec {E#24;E#25;E#26} in [.])),
             [{X#7=(\ X#8.S#12);E#21;E#22;E#23},(letrec {E#24;E#25;E#26} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#21;E#24} =?= {EE#19[X#9,(var X#18)]},
             {E#22;E#25} =?= {VV#16|X#10,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {X#18=A#17[[.2]];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           S#4          |->  A#17[A#13[(var X#10)]],
           E#3          |->  {X#7=(\ X#8.S#12);E#21;E#22;E#23},
           E#11         |->  {E#23;E#26},
           E#2          |->  {E#24;E#25;E#26},
           E#20         |->  {E#21;E#22;E#23}}

and instantiated rules:

                                  (letrec {X#18=A#17[A#13[(var X#10)]];X#7=(\ X#8.S#12);E#21;E#22;E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#18=(letrec {E#24;E#25;E#26} in A#17[A#13[(var X#10)]]);X#7=(\ X#8.S#12);E#21;E#22;E#23} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#17[A#13[(var X#10)]];X#7=(\ X#8.S#12);E#23;E#26;EE#19[X#9,(var X#18)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=A#17[A#13[(\ X#8.S#12)]];X#7=(\ X#8.S#12);E#23;E#26;EE#19[X#9,(var X#18)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#21;E#24} =?= {EE#19[X#9,(var X#18)]},
    {E#22;E#25} =?= {VV#16|X#10,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {E#24;E#25;E#26} in A#17[A#13[(var X#10)]])
       ;X#7= (\ X#8.S#12)
       ;E#21
       ;E#22
       ;E#23
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#17[A#13[(\ X#8.S#12)]]
       ;X#7= (\ X#8.S#12)
       ;E#23
       ;E#26
       ;EE#19[X#9,(var X#18)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#21,E#25}
   Delta3 = {(A#14[(var X#9)],(letrec {E#24;E#25;E#26} in [.])),
             [{X#7=(\ X#8.S#12);E#21;E#22;E#23},(letrec {E#24;E#25;E#26} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#21;E#24} =?= {EE#19[X#9,(var X#18)]},
             {E#22;E#25} =?= {VV#16|X#10,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {X#18=A#17[[.2]];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           S#4          |->  A#17[A#13[(var X#10)]],
           E#3          |->  {X#7=(\ X#8.S#12);E#21;E#22;E#23},
           E#11         |->  {E#23;E#26},
           E#2          |->  {E#24;E#25;E#26},
           E#20         |->  {E#21;E#22;E#23}}

and instantiated rules:

                                  (letrec {X#18=A#17[A#13[(var X#10)]];X#7=(\ X#8.S#12);E#21;E#22;E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#18=(letrec {E#24;E#25;E#26} in A#17[A#13[(var X#10)]]);X#7=(\ X#8.S#12);E#21;E#22;E#23} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#17[A#13[(var X#10)]];X#7=(\ X#8.S#12);E#23;E#26;EE#19[X#9,(var X#18)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=A#17[A#13[(\ X#8.S#12)]];X#7=(\ X#8.S#12);E#23;E#26;EE#19[X#9,(var X#18)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#21;E#24} =?= {EE#19[X#9,(var X#18)]},
    {E#22;E#25} =?= {VV#16|X#10,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in A#17[A#13[(var X#10)]])
       ;E#24
       ;E#25
       ;E#26
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#17[A#13[(\ X#8.S#12)]]
       ;X#7= (\ X#8.S#12)
       ;E#23
       ;E#26
       ;EE#19[X#9,(var X#18)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {E#2,E#22,E#24}
   Delta3 = {(A#14[(var X#9)],(letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in [.])),
             [{E#24;E#25;E#26},(letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in [.])],
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {
             {E#21;E#24} =?= {EE#19[X#9,(var X#18)]},
             {E#22;E#25} =?= {VV#16|X#10,(var X#7)|}}

from overlapping -llet-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {E#2}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {X#18=A#17[[.2]];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           S#4          |->  A#17[A#13[(var X#10)]],
           E#2          |->  {X#7=(\ X#8.S#12);E#21;E#22;E#23},
           E#11         |->  {E#23;E#26},
           E#3          |->  {E#24;E#25;E#26},
           E#20         |->  {E#21;E#22;E#23}}

and instantiated rules:

                                  (letrec {X#18=A#17[A#13[(var X#10)]];X#7=(\ X#8.S#12);E#21;E#22;E#23;E#24;E#25;E#26} in A#14[(var X#9)])
    -llet-e1->                    (letrec {X#18=(letrec {X#7=(\ X#8.S#12);E#21;E#22;E#23} in A#17[A#13[(var X#10)]]);E#24;E#25;E#26} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#17[A#13[(var X#10)]];X#7=(\ X#8.S#12);E#23;E#26;EE#19[X#9,(var X#18)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=A#17[A#13[(\ X#8.S#12)]];X#7=(\ X#8.S#12);E#23;E#26;EE#19[X#9,(var X#18)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
        ............................
    Delta4:
    {E#21;E#24} =?= {EE#19[X#9,(var X#18)]},
    {E#22;E#25} =?= {VV#16|X#10,(var X#7)|}

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (letrec {E#8} in T#11[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])
     )
    ,
     (letrec {E#7;E#8} in T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)])
  )

where

   Delta1 = {T#10,T#6}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             [{E#7},(letrec {E#8} in [.])]}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],[{E#7},(letrec {E#8} in [.])]}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in (letrec {E#8} in T#11)),
           T#10  |->  (letrec {E#8} in T#11),
           S#9   |->  T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#7} in (letrec {E#8} in T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)]))
    -llet-e1->                    (letrec {E#7} in (letrec {E#8} in T#11[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]))
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)]))
    -SR,llet-in1->                (letrec {E#7;E#8} in T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (letrec
           X#12= T#11[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
          ;E#14
        in
           S#9
        )
     )
    ,
     (letrec {X#12=T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#14;E#7} in S#9)
  )

where

   Delta1 = {T#10,T#6}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             [{E#7},(letrec {X#12=T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#14} in [.])]}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],[{E#7},(letrec {E#8} in [.])]}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in (letrec {X#12=T#11;E#14} in S#9)),
           T#10  |->  (letrec {X#12=T#11;E#14} in S#9),
           E#8   |->  {X#12=T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#14},
           E#13  |->  {E#14}}

and instantiated rules:

                                  (letrec {E#7} in (letrec {X#12=T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#14} in S#9))
    -llet-e1->                    (letrec {E#7} in (letrec {X#12=T#11[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#14} in S#9))
    ................................................................................
                                  (letrec {E#7} in (letrec {X#12=T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#14} in S#9))
    -SR,llet-in1->                (letrec {X#12=T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#14;E#7} in S#9)
    

================================================================================
Critical Pair:

  (
     (letrec {E#7} in (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#9))
    ,
     (letrec {X#1=S#4;E#2;E#3;E#7} in S#9)
  )

where

   Delta1 = {T#6}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {(S#9,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             [{E#7},(letrec {X#1=S#4;E#2;E#3} in [.])]}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],[{E#7},(letrec {E#8} in [.])]}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in [.]),
           T#10  |->  [.],
           S#5   |->  S#9,
           E#8   |->  {X#1=S#4;E#2;E#3},
           E#11  |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {E#7} in (letrec {X#1=S#4;E#2;E#3} in S#9))
    -llet-e1->                    (letrec {E#7} in (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#9))
    ................................................................................
                                  (letrec {E#7} in (letrec {X#1=S#4;E#2;E#3} in S#9))
    -SR,llet-in1->                (letrec {X#1=S#4;E#2;E#3;E#7} in S#9)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
       ;E#13
     in
        (letrec {E#8} in S#9)
     )
    ,
     (letrec {X#11=T#10[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#13;E#8} in S#9)
  )

where

   Delta1 = {T#6}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             [{X#11=T#10[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#13},(letrec {E#8} in [.])]}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],[{E#7},(letrec {E#8} in [.])]}


and found solution:

    Sol = {T#6   |->  (letrec {X#11=T#10;E#13} in (letrec {E#8} in S#9)),
           E#7   |->  {X#11=T#10[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#13} in (letrec {E#8} in S#9))
    -llet-e1->                    (letrec {X#11=T#10[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#13} in (letrec {E#8} in S#9))
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#13} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {X#11=T#10[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#13;E#8} in S#9)
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {E#2} in S#4);E#3} in (letrec {E#8} in S#9))
    ,
     (letrec {X#1=S#4;E#2;E#3;E#8} in S#9)
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {((letrec {E#8} in S#9),(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             [{X#1=S#4;E#2;E#3},(letrec {E#8} in [.])]}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],[{E#7},(letrec {E#8} in [.])]}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  (letrec {E#8} in S#9),
           E#7   |->  {X#1=S#4;E#2;E#3},
           E#10  |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {X#1=S#4;E#2;E#3} in (letrec {E#8} in S#9))
    -llet-e1->                    (letrec {X#1=(letrec {E#2} in S#4);E#3} in (letrec {E#8} in S#9))
    ................................................................................
                                  (letrec {X#1=S#4;E#2;E#3} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {X#1=S#4;E#2;E#3;E#8} in S#9)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#8} in S#10)
       ;E#9
     in
        A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
     )
    ,
     (letrec
        X#7= S#10
       ;E#8
       ;E#9
     in
        A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#11,T#12,T#6}
   Delta2 = {E#2,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])],(letrec {E#8} in [.])),
             [{E#9},(letrec {E#8} in [.])],
             ((var X#7),A#13[(app A#14[[.]] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])]),
             ((var X#7),A#13[(app A#14[[.]] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#13[(app A#14[(var X#7)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#7)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -llet-e1->                    (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#8} in T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])
       ;E#9
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#7= T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)]
       ;E#8
       ;E#9
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#12,T#6}
   Delta2 = {E#2,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{E#9},(letrec {E#8} in [.])],
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(letrec {E#8} in T#15);E#9} in A#11[(var X#7)]),
           X#13  |->  X#7,
           E#14  |->  {E#9},
           T#12  |->  (letrec {E#8} in T#15),
           S#10  |->  T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#8} in T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)]);E#9} in A#11[(var X#7)])
    -llet-e1->                    (letrec {X#7=(letrec {E#8} in T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]);E#9} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)]);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#8;E#9} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec
                X#16= T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
               ;E#18
             in
                S#10
             )
       ;E#9
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)]
       ;X#7= S#10
       ;E#18
       ;E#9
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#12,T#6}
   Delta2 = {E#2,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (A#11[(var X#7)],(letrec {X#16=T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#18} in [.])),
             [{E#9},(letrec {X#16=T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#18} in [.])],
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(letrec {X#16=T#15;E#18} in S#10);E#9} in A#11[(var X#7)]),
           X#13  |->  X#7,
           E#14  |->  {E#9},
           T#12  |->  (letrec {X#16=T#15;E#18} in S#10),
           E#8   |->  {X#16=T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {X#7=(letrec {X#16=T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#18} in S#10);E#9} in A#11[(var X#7)])
    -llet-e1->                    (letrec {X#7=(letrec {X#16=T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#18} in S#10);E#9} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(letrec {X#16=T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#18} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#16=T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=S#10;E#18;E#9} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#10)
       ;E#9
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#1=S#4;X#7=S#10;E#2;E#3;E#9} in A#11[(var X#7)])
  )

where

   Delta1 = {T#6}
   Delta2 = {E#2,E#8}
   Delta3 = {(S#10,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (A#11[(var X#7)],(letrec {X#1=S#4;E#2;E#3} in [.])),
             [{E#9},(letrec {X#1=S#4;E#2;E#3} in [.])],
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=[.];E#9} in A#11[(var X#7)]),
           X#13  |->  X#7,
           E#14  |->  {E#9},
           T#12  |->  [.],
           S#5   |->  S#10,
           E#8   |->  {X#1=S#4;E#2;E#3},
           E#15  |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {X#7=(letrec {X#1=S#4;E#2;E#3} in S#10);E#9} in A#11[(var X#7)])
    -llet-e1->                    (letrec {X#7=(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#10);E#9} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(letrec {X#1=S#4;E#2;E#3} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#1=S#4;X#7=S#10;E#2;E#3;E#9} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
       ;X#7= (letrec {E#8} in S#10)
       ;E#15
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)]
       ;X#7= S#10
       ;E#15
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#2,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15},(letrec {E#8} in [.])],
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#13=T#12;X#7=(letrec {E#8} in S#10);E#15} in A#11[(var X#7)]),
           E#9   |->  {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15},
           E#14  |->  {X#7=(letrec {E#8} in S#10);E#15}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(letrec {E#8} in S#10);E#15} in A#11[(var X#7)])
    -llet-e1->                    (letrec {X#13=T#12[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];X#7=(letrec {E#8} in S#10);E#15} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(letrec {E#8} in S#10);E#15} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=S#10;E#15;E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#7=(letrec {E#2} in (letrec {E#8} in S#10));E#3} in A#11[(var X#7)])
    ,
     (letrec {X#7=S#10;E#2;E#3;E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#8}
   Delta3 = {(A#11[(var X#7)],(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{E#2;E#3},(letrec {E#8} in [.])],
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6  |->  [.],
           S#5  |->  A#11[(var X#7)],
           X#1  |->  X#7,
           S#4  |->  (letrec {E#8} in S#10),
           E#9  |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#8} in S#10);E#2;E#3} in A#11[(var X#7)])
    -llet-e1->                    (letrec {X#7=(letrec {E#2} in (letrec {E#8} in S#10));E#3} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#2;E#3} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#2;E#3;E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#2} in S#4)
       ;X#7= (letrec {E#8} in S#10)
       ;E#13
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#1=S#4;X#7=S#10;E#13;E#2;E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#8}
   Delta3 = {(A#11[(var X#7)],(letrec {E#2} in [.])),
             [{X#7=(letrec {E#8} in S#10);E#13},(letrec {E#2} in [.])],
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#1=S#4;E#13;E#2},(letrec {E#8} in [.])],
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#11[(var X#7)],
           E#9   |->  {X#1=S#4;E#13;E#2},
           E#3   |->  {X#7=(letrec {E#8} in S#10);E#13},
           E#12  |->  {E#13;E#2}}

and instantiated rules:

                                  (letrec {X#1=S#4;X#7=(letrec {E#8} in S#10);E#13;E#2} in A#11[(var X#7)])
    -llet-e1->                    (letrec {X#1=(letrec {E#2} in S#4);X#7=(letrec {E#8} in S#10);E#13} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#1=S#4;X#7=(letrec {E#8} in S#10);E#13;E#2} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#1=S#4;X#7=S#10;E#13;E#2;E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#9} in S#11)
       ;E#10
       ;EE#13[X#8,(var X#7)]
     in
        A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
     )
    ,
     (letrec
        X#7= S#11
       ;E#10
       ;E#9
       ;EE#13[X#8,(var X#7)]
     in
        A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),
             (A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])],(letrec {E#9} in [.])),
             [{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#15[(app A#16[[.]] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])]),
             ((var X#7),[.]),
             ((var X#8),A#15[(app A#16[[.]] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#8)] T#17)],
           A#12  |->  A#15[(app A#16 T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -llet-e1->                    (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#9} in T#17[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])
       ;E#10
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#7= T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)]
       ;E#10
       ;E#9
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(letrec {E#9} in T#17);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)]),
           X#15  |->  X#7,
           E#16  |->  {E#10;EE#13[X#8,(var X#7)]},
           T#14  |->  (letrec {E#9} in T#17),
           S#11  |->  T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)]);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#7=(letrec {E#9} in T#17[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)]);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec
                X#18= T#17[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
               ;E#20
             in
                S#11
             )
       ;E#10
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)]
       ;X#7= S#11
       ;E#10
       ;E#20
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),(letrec {X#18=T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#10;E#20;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {X#18=T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#20} in [.])),
             [{E#10;EE#13[X#8,(var X#7)]},(letrec {X#18=T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#20} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(letrec {X#18=T#17;E#20} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)]),
           X#15  |->  X#7,
           E#16  |->  {E#10;EE#13[X#8,(var X#7)]},
           T#14  |->  (letrec {X#18=T#17;E#20} in S#11),
           E#9   |->  {X#18=T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#20},
           E#19  |->  {E#20}}

and instantiated rules:

                                  (letrec {X#7=(letrec {X#18=T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#20} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#7=(letrec {X#18=T#17[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#20} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {X#18=T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#20} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#18=T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=S#11;E#10;E#20;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#11)
       ;E#10
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec {X#1=S#4;X#7=S#11;E#10;E#2;E#3;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
  )

where

   Delta1 = {T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#11,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),(letrec {X#1=S#4;E#10;E#2;E#3;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {X#1=S#4;E#2;E#3} in [.])),
             [{E#10;EE#13[X#8,(var X#7)]},(letrec {X#1=S#4;E#2;E#3} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=[.];E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)]),
           X#15  |->  X#7,
           E#16  |->  {E#10;EE#13[X#8,(var X#7)]},
           T#14  |->  [.],
           S#5   |->  S#11,
           E#9   |->  {X#1=S#4;E#2;E#3},
           E#17  |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {X#7=(letrec {X#1=S#4;E#2;E#3} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#7=(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {X#1=S#4;E#2;E#3} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#1=S#4;X#7=S#11;E#10;E#2;E#3;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
       ;X#7= (letrec {E#9} in S#11)
       ;E#17
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)]
       ;X#7= S#11
       ;E#17
       ;E#9
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),(letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17;E#9;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#15=T#14;X#7=(letrec {E#9} in S#11);E#17;EE#13[X#8,(var X#7)]} in A#12[(var X#8)]),
           E#10  |->  {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17},
           E#16  |->  {X#7=(letrec {E#9} in S#11);E#17;EE#13[X#8,(var X#7)]}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(letrec {E#9} in S#11);E#17;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#15=T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];X#7=(letrec {E#9} in S#11);E#17;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=(letrec {E#9} in S#11);E#17;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];X#7=S#11;E#17;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#9} in S#11)
       ;X#8= A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#10
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#7= S#11
       ;X#8= A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#10
       ;E#9
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),(letrec {X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10;E#9} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#18[(app A#19[(var X#7)] T#20)];E#10} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])]},
           X#15         |->  X#8,
           E#16         |->  {X#7=(letrec {E#9} in S#11);E#10},
           T#14         |->  A#18[(app A#19[(var X#7)] T#20)],
           A#17         |->  A#18[(app A#19 T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#7=(letrec {E#9} in S#11);X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#10} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#9} in S#11)
       ;X#8= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#10
       ;EE#19[X#18,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#7= S#11
       ;X#8= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#10
       ;E#9
       ;EE#19[X#18,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),(letrec {X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10;E#9;EE#19[X#18,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10;EE#19[X#18,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#20[(app A#21[(var X#18)] T#22)];E#10;EE#19[X#18,(var X#7)]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];EE#19[X#18,[.2]]},
           X#15         |->  X#8,
           E#16         |->  {X#7=(letrec {E#9} in S#11);E#10;EE#19[X#18,(var X#7)]},
           T#14         |->  A#20[(app A#21[(var X#18)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10;EE#19[X#18,(var X#7)]} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#7=(letrec {E#9} in S#11);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#10;EE#19[X#18,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10;EE#19[X#18,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10;E#9;EE#19[X#18,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;X#7= (letrec {E#9} in S#11)
       ;E#10
       ;EE#20[X#8,(var X#18)]
       ;EE#21[X#19,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;X#7= S#11
       ;E#10
       ;E#9
       ;EE#20[X#8,(var X#18)]
       ;EE#21[X#19,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),(letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10;E#9;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24)];X#7=(letrec {E#9} in S#11);E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#15         |->  X#18,
           E#16         |->  {X#7=(letrec {E#9} in S#11);E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]},
           T#14         |->  A#22[(app A#23[(var X#19)] T#24)],
           A#17         |->  A#22[(app A#23 T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(letrec {E#9} in S#11);E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];X#7=(letrec {E#9} in S#11);E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(letrec {E#9} in S#11);E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=S#11;E#10;E#9;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;X#7= (letrec {E#9} in S#11)
       ;E#10
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;X#7= S#11
       ;E#10
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             ((var X#7),(letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10;E#9;EE#19[X#8,(var X#18)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#10;EE#19[X#8,(var X#18)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app A#21[(var X#7)] T#22)];X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]},
           T#14         |->  A#20[(app A#21[(var X#7)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];X#7=S#11;E#10;E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#16;E#17} in (letrec {E#9} in S#11))
       ;E#14
       ;E#15
     in
        A#12[(var X#8)]
     )
    ,
     (letrec {X#7=S#11;E#15;E#17;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#14,E#17}
   Delta3 = {(A#12[(var X#8)],(letrec {E#16;E#17} in [.])),
             [{E#14;E#15},(letrec {E#16;E#17} in [.])],
             ((var X#7),(letrec {E#15;E#17;E#9;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{E#15;E#17;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {
             {E#14;E#16} =?= {EE#13[X#8,(var X#7)]}}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#8)],
           X#1   |->  X#7,
           S#4   |->  (letrec {E#9} in S#11),
           E#10  |->  {E#15;E#17},
           E#2   |->  {E#16;E#17},
           E#3   |->  {E#14;E#15}}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);E#14;E#15;E#16;E#17} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#7=(letrec {E#16;E#17} in (letrec {E#9} in S#11));E#14;E#15} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#15;E#17;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#15;E#17;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
        ............................
    Delta4:
    {E#14;E#16} =?= {EE#13[X#8,(var X#7)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#18;E#19} in S#4)
       ;X#7= (letrec {E#9} in S#11)
       ;E#16
       ;E#17
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#1= S#4
       ;X#7= S#11
       ;E#17
       ;E#19
       ;E#9
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#16,E#19}
   Delta3 = {(A#12[(var X#8)],(letrec {E#18;E#19} in [.])),
             [{X#7=(letrec {E#9} in S#11);E#16;E#17},(letrec {E#18;E#19} in [.])],
             ((var X#7),(letrec {X#1=S#4;E#17;E#19;E#9;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#1=S#4;E#17;E#19;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {
             {E#16;E#18} =?= {EE#13[X#8,(var X#7)]}}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#8)],
           E#10  |->  {X#1=S#4;E#17;E#19},
           E#3   |->  {X#7=(letrec {E#9} in S#11);E#16;E#17},
           E#14  |->  {E#17;E#19},
           E#2   |->  {E#18;E#19},
           E#15  |->  {E#16;E#17}}

and instantiated rules:

                                  (letrec {X#1=S#4;X#7=(letrec {E#9} in S#11);E#16;E#17;E#18;E#19} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#1=(letrec {E#18;E#19} in S#4);X#7=(letrec {E#9} in S#11);E#16;E#17} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#1=S#4;X#7=(letrec {E#9} in S#11);E#17;E#19;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#1=S#4;X#7=S#11;E#17;E#19;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
        ............................
    Delta4:
    {E#16;E#18} =?= {EE#13[X#8,(var X#7)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#9} in S#11)
       ;X#8= (letrec {E#2} in A#14[(var X#7)])
       ;E#15
     in
        A#12[(var X#8)]
     )
    ,
     (letrec {X#7=S#11;X#8=A#14[(var X#7)];E#15;E#2;E#9} in A#12[(var X#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9}
   Delta3 = {(A#12[(var X#8)],(letrec {E#2} in [.])),
             [{X#7=(letrec {E#9} in S#11);E#15},(letrec {E#2} in [.])],
             ((var X#7),(letrec {X#8=A#14[(var X#7)];E#15;E#2;E#9} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#8=A#14[(var X#7)];E#15;E#2},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {[.1]=A#14[[.2]]},
           X#1          |->  X#8,
           S#4          |->  A#14[(var X#7)],
           E#3          |->  {X#7=(letrec {E#9} in S#11);E#15},
           E#10         |->  {E#15;E#2}}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#7)];E#15;E#2} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#7=(letrec {E#9} in S#11);X#8=(letrec {E#2} in A#14[(var X#7)]);E#15} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#7)];E#15;E#2} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;X#8=A#14[(var X#7)];E#15;E#2;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {X#7=(letrec {E#9} in S#11);E#15} in A#14[(var X#7)])
       ;E#3
     in
        A#12[(var X#8)]
     )
    ,
     (letrec {X#7=S#11;X#8=A#14[(var X#7)];E#15;E#3;E#9} in A#12[(var X#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9}
   Delta3 = {(A#12[(var X#8)],(letrec {X#7=(letrec {E#9} in S#11);E#15} in [.])),
             [{E#3},(letrec {X#7=(letrec {E#9} in S#11);E#15} in [.])],
             ((var X#7),(letrec {X#8=A#14[(var X#7)];E#15;E#3;E#9} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#8=A#14[(var X#7)];E#15;E#3},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {[.1]=A#14[[.2]]},
           X#1          |->  X#8,
           S#4          |->  A#14[(var X#7)],
           E#2          |->  {X#7=(letrec {E#9} in S#11);E#15},
           E#10         |->  {E#15;E#3}}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#7)];E#15;E#3} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#8=(letrec {X#7=(letrec {E#9} in S#11);E#15} in A#14[(var X#7)]);E#3} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#7)];E#15;E#3} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;X#8=A#14[(var X#7)];E#15;E#3;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#9} in S#11)
       ;X#8= (letrec {E#20;E#21} in A#14[(var X#15)])
       ;E#18
       ;E#19
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#7= S#11
       ;X#8= A#14[(var X#15)]
       ;E#19
       ;E#21
       ;E#9
       ;EE#16[X#15,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#18,E#21}
   Delta3 = {(A#12[(var X#8)],(letrec {E#20;E#21} in [.])),
             [{X#7=(letrec {E#9} in S#11);E#18;E#19},(letrec {E#20;E#21} in [.])],
             ((var X#7),(letrec {X#8=A#14[(var X#15)];E#19;E#21;E#9;EE#16[X#15,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#8=A#14[(var X#15)];E#19;E#21;EE#16[X#15,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {
             {E#18;E#20} =?= {EE#16[X#15,(var X#7)]}}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {[.1]=A#14[(var X#15)];EE#16[X#15,[.2]]},
           X#1          |->  X#8,
           S#4          |->  A#14[(var X#15)],
           E#3          |->  {X#7=(letrec {E#9} in S#11);E#18;E#19},
           E#10         |->  {E#19;E#21},
           E#2          |->  {E#20;E#21},
           E#17         |->  {E#18;E#19}}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#15)];E#18;E#19;E#20;E#21} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#7=(letrec {E#9} in S#11);X#8=(letrec {E#20;E#21} in A#14[(var X#15)]);E#18;E#19} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#15)];E#19;E#21;EE#16[X#15,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;X#8=A#14[(var X#15)];E#19;E#21;E#9;EE#16[X#15,(var X#7)]} in A#12[(var X#8)])
        ............................
    Delta4:
    {E#18;E#20} =?= {EE#16[X#15,(var X#7)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#9} in S#11)
       ;X#8= (letrec {E#20;E#21} in A#14[(var X#15)])
       ;E#18
       ;E#19
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#7= S#11
       ;X#8= A#14[(var X#15)]
       ;E#19
       ;E#21
       ;E#9
       ;EE#16[X#15,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#20}
   Delta3 = {(A#12[(var X#8)],(letrec {E#20;E#21} in [.])),
             [{X#7=(letrec {E#9} in S#11);E#18;E#19},(letrec {E#20;E#21} in [.])],
             ((var X#7),(letrec {X#8=A#14[(var X#15)];E#19;E#21;E#9;EE#16[X#15,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#8=A#14[(var X#15)];E#19;E#21;EE#16[X#15,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {
             {E#18;E#20} =?= {EE#16[X#15,(var X#7)]}}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {[.1]=A#14[(var X#15)];EE#16[X#15,[.2]]},
           X#1          |->  X#8,
           S#4          |->  A#14[(var X#15)],
           E#3          |->  {X#7=(letrec {E#9} in S#11);E#18;E#19},
           E#10         |->  {E#19;E#21},
           E#2          |->  {E#20;E#21},
           E#17         |->  {E#18;E#19}}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#15)];E#18;E#19;E#20;E#21} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#7=(letrec {E#9} in S#11);X#8=(letrec {E#20;E#21} in A#14[(var X#15)]);E#18;E#19} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#15)];E#19;E#21;EE#16[X#15,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;X#8=A#14[(var X#15)];E#19;E#21;E#9;EE#16[X#15,(var X#7)]} in A#12[(var X#8)])
        ............................
    Delta4:
    {E#18;E#20} =?= {EE#16[X#15,(var X#7)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {X#7=(letrec {E#9} in S#11);E#18;E#19} in A#14[(var X#15)])
       ;E#20
       ;E#21
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#7= S#11
       ;X#8= A#14[(var X#15)]
       ;E#19
       ;E#21
       ;E#9
       ;EE#16[X#15,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#18}
   Delta3 = {(A#12[(var X#8)],(letrec {X#7=(letrec {E#9} in S#11);E#18;E#19} in [.])),
             [{E#20;E#21},(letrec {X#7=(letrec {E#9} in S#11);E#18;E#19} in [.])],
             ((var X#7),(letrec {X#8=A#14[(var X#15)];E#19;E#21;E#9;EE#16[X#15,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#8=A#14[(var X#15)];E#19;E#21;EE#16[X#15,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {
             {E#18;E#20} =?= {EE#16[X#15,(var X#7)]}}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {[.1]=A#14[(var X#15)];EE#16[X#15,[.2]]},
           X#1          |->  X#8,
           S#4          |->  A#14[(var X#15)],
           E#2          |->  {X#7=(letrec {E#9} in S#11);E#18;E#19},
           E#10         |->  {E#19;E#21},
           E#3          |->  {E#20;E#21},
           E#17         |->  {E#18;E#19}}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#15)];E#18;E#19;E#20;E#21} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#8=(letrec {X#7=(letrec {E#9} in S#11);E#18;E#19} in A#14[(var X#15)]);E#20;E#21} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#15)];E#19;E#21;EE#16[X#15,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;X#8=A#14[(var X#15)];E#19;E#21;E#9;EE#16[X#15,(var X#7)]} in A#12[(var X#8)])
        ............................
    Delta4:
    {E#18;E#20} =?= {EE#16[X#15,(var X#7)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#23;E#24;E#25} in A#14[(var X#16)])
       ;X#7= (letrec {E#9} in S#11)
       ;E#20
       ;E#21
       ;E#22
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;X#7= S#11
       ;E#22
       ;E#25
       ;E#9
       ;EE#17[X#8,(var X#15)]
       ;EE#18[X#16,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#20,E#21,E#25}
   Delta3 = {(A#12[(var X#8)],(letrec {E#23;E#24;E#25} in [.])),
             [{X#7=(letrec {E#9} in S#11);E#20;E#21;E#22},(letrec {E#23;E#24;E#25} in [.])],
             ((var X#7),(letrec {X#15=A#14[(var X#16)];E#22;E#25;E#9;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#15=A#14[(var X#16)];E#22;E#25;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {
             {E#20;E#23} =?= {EE#17[X#8,(var X#15)]},
             {E#21;E#24} =?= {EE#18[X#16,(var X#7)]}}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#1          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           E#3          |->  {X#7=(letrec {E#9} in S#11);E#20;E#21;E#22},
           E#10         |->  {E#22;E#25},
           E#2          |->  {E#23;E#24;E#25},
           E#19         |->  {E#20;E#21;E#22}}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];X#7=(letrec {E#9} in S#11);E#20;E#21;E#22;E#23;E#24;E#25} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#15=(letrec {E#23;E#24;E#25} in A#14[(var X#16)]);X#7=(letrec {E#9} in S#11);E#20;E#21;E#22} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];X#7=(letrec {E#9} in S#11);E#22;E#25;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#15=A#14[(var X#16)];X#7=S#11;E#22;E#25;E#9;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]} in A#12[(var X#8)])
        ............................
    Delta4:
    {E#20;E#23} =?= {EE#17[X#8,(var X#15)]},
    {E#21;E#24} =?= {EE#18[X#16,(var X#7)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#23;E#24;E#25} in A#14[(var X#16)])
       ;X#7= (letrec {E#9} in S#11)
       ;E#20
       ;E#21
       ;E#22
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;X#7= S#11
       ;E#22
       ;E#25
       ;E#9
       ;EE#17[X#8,(var X#15)]
       ;EE#18[X#16,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#20,E#24}
   Delta3 = {(A#12[(var X#8)],(letrec {E#23;E#24;E#25} in [.])),
             [{X#7=(letrec {E#9} in S#11);E#20;E#21;E#22},(letrec {E#23;E#24;E#25} in [.])],
             ((var X#7),(letrec {X#15=A#14[(var X#16)];E#22;E#25;E#9;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#15=A#14[(var X#16)];E#22;E#25;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {
             {E#20;E#23} =?= {EE#17[X#8,(var X#15)]},
             {E#21;E#24} =?= {EE#18[X#16,(var X#7)]}}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#1          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           E#3          |->  {X#7=(letrec {E#9} in S#11);E#20;E#21;E#22},
           E#10         |->  {E#22;E#25},
           E#2          |->  {E#23;E#24;E#25},
           E#19         |->  {E#20;E#21;E#22}}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];X#7=(letrec {E#9} in S#11);E#20;E#21;E#22;E#23;E#24;E#25} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#15=(letrec {E#23;E#24;E#25} in A#14[(var X#16)]);X#7=(letrec {E#9} in S#11);E#20;E#21;E#22} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];X#7=(letrec {E#9} in S#11);E#22;E#25;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#15=A#14[(var X#16)];X#7=S#11;E#22;E#25;E#9;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]} in A#12[(var X#8)])
        ............................
    Delta4:
    {E#20;E#23} =?= {EE#17[X#8,(var X#15)]},
    {E#21;E#24} =?= {EE#18[X#16,(var X#7)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {X#7=(letrec {E#9} in S#11);E#20;E#21;E#22} in A#14[(var X#16)])
       ;E#23
       ;E#24
       ;E#25
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;X#7= S#11
       ;E#22
       ;E#25
       ;E#9
       ;EE#17[X#8,(var X#15)]
       ;EE#18[X#16,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#21,E#23}
   Delta3 = {(A#12[(var X#8)],(letrec {X#7=(letrec {E#9} in S#11);E#20;E#21;E#22} in [.])),
             [{E#23;E#24;E#25},(letrec {X#7=(letrec {E#9} in S#11);E#20;E#21;E#22} in [.])],
             ((var X#7),(letrec {X#15=A#14[(var X#16)];E#22;E#25;E#9;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#15=A#14[(var X#16)];E#22;E#25;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {
             {E#20;E#23} =?= {EE#17[X#8,(var X#15)]},
             {E#21;E#24} =?= {EE#18[X#16,(var X#7)]}}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#1          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           E#2          |->  {X#7=(letrec {E#9} in S#11);E#20;E#21;E#22},
           E#10         |->  {E#22;E#25},
           E#3          |->  {E#23;E#24;E#25},
           E#19         |->  {E#20;E#21;E#22}}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];X#7=(letrec {E#9} in S#11);E#20;E#21;E#22;E#23;E#24;E#25} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#15=(letrec {X#7=(letrec {E#9} in S#11);E#20;E#21;E#22} in A#14[(var X#16)]);E#23;E#24;E#25} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];X#7=(letrec {E#9} in S#11);E#22;E#25;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#15=A#14[(var X#16)];X#7=S#11;E#22;E#25;E#9;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]} in A#12[(var X#8)])
        ............................
    Delta4:
    {E#20;E#23} =?= {EE#17[X#8,(var X#15)]},
    {E#21;E#24} =?= {EE#18[X#16,(var X#7)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#20;E#21} in A#14[(var X#7)])
       ;X#7= (letrec {E#9} in S#11)
       ;E#18
       ;E#19
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= A#14[(var X#7)]
       ;X#7= S#11
       ;E#19
       ;E#21
       ;E#9
       ;EE#16[X#8,(var X#15)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#18,E#21}
   Delta3 = {(A#12[(var X#8)],(letrec {E#20;E#21} in [.])),
             [{X#7=(letrec {E#9} in S#11);E#18;E#19},(letrec {E#20;E#21} in [.])],
             ((var X#7),(letrec {X#15=A#14[(var X#7)];E#19;E#21;E#9;EE#16[X#8,(var X#15)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#15=A#14[(var X#7)];E#19;E#21;EE#16[X#8,(var X#15)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {
             {E#18;E#20} =?= {EE#16[X#8,(var X#15)]}}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {X#15=A#14[[.2]];EE#16[[.1],(var X#15)]},
           X#1          |->  X#15,
           S#4          |->  A#14[(var X#7)],
           E#3          |->  {X#7=(letrec {E#9} in S#11);E#18;E#19},
           E#10         |->  {E#19;E#21},
           E#2          |->  {E#20;E#21},
           E#17         |->  {E#18;E#19}}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#7)];X#7=(letrec {E#9} in S#11);E#18;E#19;E#20;E#21} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#15=(letrec {E#20;E#21} in A#14[(var X#7)]);X#7=(letrec {E#9} in S#11);E#18;E#19} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#7)];X#7=(letrec {E#9} in S#11);E#19;E#21;EE#16[X#8,(var X#15)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#15=A#14[(var X#7)];X#7=S#11;E#19;E#21;E#9;EE#16[X#8,(var X#15)]} in A#12[(var X#8)])
        ............................
    Delta4:
    {E#18;E#20} =?= {EE#16[X#8,(var X#15)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {X#7=(letrec {E#9} in S#11);E#18;E#19} in A#14[(var X#7)])
       ;E#20
       ;E#21
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= A#14[(var X#7)]
       ;X#7= S#11
       ;E#19
       ;E#21
       ;E#9
       ;EE#16[X#8,(var X#15)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#20}
   Delta3 = {(A#12[(var X#8)],(letrec {X#7=(letrec {E#9} in S#11);E#18;E#19} in [.])),
             [{E#20;E#21},(letrec {X#7=(letrec {E#9} in S#11);E#18;E#19} in [.])],
             ((var X#7),(letrec {X#15=A#14[(var X#7)];E#19;E#21;E#9;EE#16[X#8,(var X#15)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#15=A#14[(var X#7)];E#19;E#21;EE#16[X#8,(var X#15)]},(letrec {E#9} in [.])],
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {
             {E#18;E#20} =?= {EE#16[X#8,(var X#15)]}}

from overlapping -llet-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {X#15=A#14[[.2]];EE#16[[.1],(var X#15)]},
           X#1          |->  X#15,
           S#4          |->  A#14[(var X#7)],
           E#2          |->  {X#7=(letrec {E#9} in S#11);E#18;E#19},
           E#10         |->  {E#19;E#21},
           E#3          |->  {E#20;E#21},
           E#17         |->  {E#18;E#19}}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#7)];X#7=(letrec {E#9} in S#11);E#18;E#19;E#20;E#21} in A#12[(var X#8)])
    -llet-e1->                    (letrec {X#15=(letrec {X#7=(letrec {E#9} in S#11);E#18;E#19} in A#14[(var X#7)]);E#20;E#21} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#7)];X#7=(letrec {E#9} in S#11);E#19;E#21;EE#16[X#8,(var X#15)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#15=A#14[(var X#7)];X#7=S#11;E#19;E#21;E#9;EE#16[X#8,(var X#15)]} in A#12[(var X#8)])
        ............................
    Delta4:
    {E#18;E#20} =?= {EE#16[X#8,(var X#15)]}

================================================================================
Critical Pair:

  (
     A#11[(app (letrec {E#7} in T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#8)]
    ,
     A#11[(letrec {E#7} in (app T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#8))]
  )

where

   Delta1 = {T#13,T#12,A#10,T#6,A#11}
   Delta2 = {E#2,E#7}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.]))}


and found solution:

    Sol = {A#10  |->  A#11,
           T#6   |->  A#11[(app (letrec {E#7} in T#14) S#8)],
           T#12  |->  (app (letrec {E#7} in T#14) S#8),
           T#13  |->  (letrec {E#7} in T#14),
           S#9   |->  T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  A#11[(app (letrec {E#7} in T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#8)]
    -llet-e1->                    A#11[(app (letrec {E#7} in T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#8)]
    ................................................................................
                                  A#11[(app (letrec {E#7} in T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#8)]
    -SR,lapp1->                   A#11[(letrec {E#7} in (app T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#8))]
    

================================================================================
Critical Pair:

  (
     A#11[(app (letrec
                   X#15= T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
                  ;E#17
                in
                   S#9
                ) S#8)]
    ,
     A#11[(letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17} in (app S#9 S#8))]
  )

where

   Delta1 = {T#13,T#12,A#10,T#6,A#11}
   Delta2 = {E#2,E#7}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#8,(letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.]))}


and found solution:

    Sol = {A#10  |->  A#11,
           T#6   |->  A#11[(app (letrec {X#15=T#14;E#17} in S#9) S#8)],
           T#12  |->  (app (letrec {X#15=T#14;E#17} in S#9) S#8),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#9),
           E#7   |->  {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  A#11[(app (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17} in S#9) S#8)]
    -llet-e1->                    A#11[(app (letrec {X#15=T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#17} in S#9) S#8)]
    ................................................................................
                                  A#11[(app (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17} in S#9) S#8)]
    -SR,lapp1->                   A#11[(letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17} in (app S#9 S#8))]
    

================================================================================
Critical Pair:

  (
     A#11[(app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#9) S#8)]
    ,
     A#11[(letrec {X#1=S#4;E#2;E#3} in (app S#9 S#8))]
  )

where

   Delta1 = {T#12,A#10,T#6,A#11}
   Delta2 = {E#2,E#7}
   Delta3 = {(S#9,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#8,(letrec {X#1=S#4;E#2;E#3} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.]))}


and found solution:

    Sol = {A#10  |->  A#11,
           T#6   |->  A#11[(app [.] S#8)],
           T#12  |->  (app [.] S#8),
           T#13  |->  [.],
           S#5   |->  S#9,
           E#7   |->  {X#1=S#4;E#2;E#3},
           E#14  |->  {E#2;E#3}}

and instantiated rules:

                                  A#11[(app (letrec {X#1=S#4;E#2;E#3} in S#9) S#8)]
    -llet-e1->                    A#11[(app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#9) S#8)]
    ................................................................................
                                  A#11[(app (letrec {X#1=S#4;E#2;E#3} in S#9) S#8)]
    -SR,lapp1->                   A#11[(letrec {X#1=S#4;E#2;E#3} in (app S#9 S#8))]
    

================================================================================
Critical Pair:

  (
     A#11[(app (letrec {E#7} in S#9) T#13[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
    ,
     A#11[(letrec {E#7} in (app S#9 T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)]))]
  )

where

   Delta1 = {T#12,A#10,T#6,A#11}
   Delta2 = {E#2,E#7}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {E#7} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.]))}


and found solution:

    Sol = {A#10  |->  A#11,
           T#6   |->  A#11[(app (letrec {E#7} in S#9) T#13)],
           T#12  |->  (app (letrec {E#7} in S#9) T#13),
           S#8   |->  T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  A#11[(app (letrec {E#7} in S#9) T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
    -llet-e1->                    A#11[(app (letrec {E#7} in S#9) T#13[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
    ................................................................................
                                  A#11[(app (letrec {E#7} in S#9) T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
    -SR,lapp1->                   A#11[(letrec {E#7} in (app S#9 T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)]))]
    

================================================================================
Critical Pair:

  (
     A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
    ,
     A#11[(app A#12[(letrec {E#7} in (app S#9 S#8))] T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
  )

where

   Delta1 = {A#10,T#6}
   Delta2 = {E#2,E#7}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.]))}


and found solution:

    Sol = {T#6   |->  A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13)],
           A#10  |->  A#11[(app A#12 T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
    -llet-e1->                    A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
    ................................................................................
                                  A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
    -SR,lapp1->                   A#11[(app A#12[(letrec {E#7} in (app S#9 S#8))] T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#7} in T#12[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#8)
    ,
     (letrec {E#7} in (app T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#8))
  )

where

   Delta1 = {T#11,T#6}
   Delta2 = {E#2,E#7}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.]))}


and found solution:

    Sol = {A#10  |->  [.],
           T#6   |->  (app (letrec {E#7} in T#12) S#8),
           T#11  |->  (letrec {E#7} in T#12),
           S#9   |->  T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (app (letrec {E#7} in T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#8)
    -llet-e1->                    (app (letrec {E#7} in T#12[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#8)
    ................................................................................
                                  (app (letrec {E#7} in T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#8)
    -SR,lapp1->                   (letrec {E#7} in (app T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#8))
    

================================================================================
Critical Pair:

  (
     (app (letrec
             X#13= T#12[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
            ;E#15
          in
             S#9
          ) S#8)
    ,
     (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15} in (app S#9 S#8))
  )

where

   Delta1 = {T#11,T#6}
   Delta2 = {E#2,E#7}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#8,(letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.]))}


and found solution:

    Sol = {A#10  |->  [.],
           T#6   |->  (app (letrec {X#13=T#12;E#15} in S#9) S#8),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#9),
           E#7   |->  {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (app (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15} in S#9) S#8)
    -llet-e1->                    (app (letrec {X#13=T#12[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#15} in S#9) S#8)
    ................................................................................
                                  (app (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15} in S#9) S#8)
    -SR,lapp1->                   (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15} in (app S#9 S#8))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#9) S#8)
    ,
     (letrec {X#1=S#4;E#2;E#3} in (app S#9 S#8))
  )

where

   Delta1 = {T#6}
   Delta2 = {E#2,E#7}
   Delta3 = {(S#9,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#8,(letrec {X#1=S#4;E#2;E#3} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.]))}


and found solution:

    Sol = {A#10  |->  [.],
           T#6   |->  (app [.] S#8),
           T#11  |->  [.],
           S#5   |->  S#9,
           E#7   |->  {X#1=S#4;E#2;E#3},
           E#12  |->  {E#2;E#3}}

and instantiated rules:

                                  (app (letrec {X#1=S#4;E#2;E#3} in S#9) S#8)
    -llet-e1->                    (app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#9) S#8)
    ................................................................................
                                  (app (letrec {X#1=S#4;E#2;E#3} in S#9) S#8)
    -SR,lapp1->                   (letrec {X#1=S#4;E#2;E#3} in (app S#9 S#8))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#7} in S#9) T#11[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])
    ,
     (letrec {E#7} in (app S#9 T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)]))
  )

where

   Delta1 = {T#6}
   Delta2 = {E#2,E#7}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {E#7} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.]))}


and found solution:

    Sol = {A#10  |->  [.],
           T#6   |->  (app (letrec {E#7} in S#9) T#11),
           S#8   |->  T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (app (letrec {E#7} in S#9) T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)])
    -llet-e1->                    (app (letrec {E#7} in S#9) T#11[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])
    ................................................................................
                                  (app (letrec {E#7} in S#9) T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)])
    -SR,lapp1->                   (letrec {E#7} in (app S#9 T#11[(letrec {X#1=S#4;E#2;E#3} in S#5)]))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#13[(app (letrec {E#8} in T#16[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#9)]
     )
    ,
     (letrec
        E#7
     in
        A#13[(letrec {E#8} in (app T#16[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#9))]
     )
  )

where

   Delta1 = {T#15,T#14,A#11,T#12,T#6,A#13}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#9,(letrec {E#8} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(letrec {E#8} in [.]))}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in A#13[(app (letrec {E#8} in T#16) S#9)]),
           A#11  |->  A#13,
           T#12  |->  A#13[(app (letrec {E#8} in T#16) S#9)],
           T#14  |->  (app (letrec {E#8} in T#16) S#9),
           T#15  |->  (letrec {E#8} in T#16),
           S#10  |->  T#16[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#7} in A#13[(app (letrec {E#8} in T#16[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#9)])
    -llet-e1->                    (letrec {E#7} in A#13[(app (letrec {E#8} in T#16[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#9)])
    ................................................................................
                                  (letrec {E#7} in A#13[(app (letrec {E#8} in T#16[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#13[(letrec {E#8} in (app T#16[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#13[(app (letrec
                      X#17= T#16[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
                     ;E#19
                   in
                      S#10
                   ) S#9)]
     )
    ,
     (letrec
        E#7
     in
        A#13[(letrec {X#17=T#16[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#19} in (app S#10 S#9))]
     )
  )

where

   Delta1 = {T#15,T#14,A#11,T#12,T#6,A#13}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#9,(letrec {X#17=T#16[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#19} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(letrec {E#8} in [.]))}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in A#13[(app (letrec {X#17=T#16;E#19} in S#10) S#9)]),
           A#11  |->  A#13,
           T#12  |->  A#13[(app (letrec {X#17=T#16;E#19} in S#10) S#9)],
           T#14  |->  (app (letrec {X#17=T#16;E#19} in S#10) S#9),
           T#15  |->  (letrec {X#17=T#16;E#19} in S#10),
           E#8   |->  {X#17=T#16[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#19},
           E#18  |->  {E#19}}

and instantiated rules:

                                  (letrec {E#7} in A#13[(app (letrec {X#17=T#16[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#19} in S#10) S#9)])
    -llet-e1->                    (letrec {E#7} in A#13[(app (letrec {X#17=T#16[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#19} in S#10) S#9)])
    ................................................................................
                                  (letrec {E#7} in A#13[(app (letrec {X#17=T#16[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#19} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#13[(letrec {X#17=T#16[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#19} in (app S#10 S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#13[(app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#10) S#9)]
     )
    ,
     (letrec {E#7} in A#13[(letrec {X#1=S#4;E#2;E#3} in (app S#10 S#9))])
  )

where

   Delta1 = {T#14,A#11,T#12,T#6,A#13}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {(S#10,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#9,(letrec {X#1=S#4;E#2;E#3} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(letrec {E#8} in [.]))}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in A#13[(app [.] S#9)]),
           A#11  |->  A#13,
           T#12  |->  A#13[(app [.] S#9)],
           T#14  |->  (app [.] S#9),
           T#15  |->  [.],
           S#5   |->  S#10,
           E#8   |->  {X#1=S#4;E#2;E#3},
           E#16  |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {E#7} in A#13[(app (letrec {X#1=S#4;E#2;E#3} in S#10) S#9)])
    -llet-e1->                    (letrec {E#7} in A#13[(app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#10) S#9)])
    ................................................................................
                                  (letrec {E#7} in A#13[(app (letrec {X#1=S#4;E#2;E#3} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#13[(letrec {X#1=S#4;E#2;E#3} in (app S#10 S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#13[(app (letrec {E#8} in S#10) T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
     )
    ,
     (letrec
        E#7
     in
        A#13[(letrec {E#8} in (app S#10 T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)]))]
     )
  )

where

   Delta1 = {T#14,A#11,T#12,T#6,A#13}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {E#8} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(letrec {E#8} in [.]))}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in A#13[(app (letrec {E#8} in S#10) T#15)]),
           A#11  |->  A#13,
           T#12  |->  A#13[(app (letrec {E#8} in S#10) T#15)],
           T#14  |->  (app (letrec {E#8} in S#10) T#15),
           S#9   |->  T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#7} in A#13[(app (letrec {E#8} in S#10) T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -llet-e1->                    (letrec {E#7} in A#13[(app (letrec {E#8} in S#10) T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#7} in A#13[(app (letrec {E#8} in S#10) T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -SR,lapp2->                   (letrec {E#7} in A#13[(letrec {E#8} in (app S#10 T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
     )
    ,
     (letrec
        E#7
     in
        A#13[(app A#14[(letrec {E#8} in (app S#10 S#9))] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#11,T#12,T#6}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#9,(letrec {E#8} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(letrec {E#8} in [.]))}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15)]),
           T#12  |->  A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {E#7} in A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -llet-e1->                    (letrec {E#7} in A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#7} in A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -SR,lapp2->                   (letrec {E#7} in A#13[(app A#14[(letrec {E#8} in (app S#10 S#9))] T#15[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (app (letrec {E#8} in T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#9)
     )
    ,
     (letrec
        E#7
     in
        (letrec {E#8} in (app T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#9))
     )
  )

where

   Delta1 = {T#13,T#12,T#6}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#9,(letrec {E#8} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(letrec {E#8} in [.]))}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in (app (letrec {E#8} in T#14) S#9)),
           A#11  |->  [.],
           T#12  |->  (app (letrec {E#8} in T#14) S#9),
           T#13  |->  (letrec {E#8} in T#14),
           S#10  |->  T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#7} in (app (letrec {E#8} in T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#9))
    -llet-e1->                    (letrec {E#7} in (app (letrec {E#8} in T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#9))
    ................................................................................
                                  (letrec {E#7} in (app (letrec {E#8} in T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#9))
    -SR,lapp2->                   (letrec {E#7} in (letrec {E#8} in (app T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#9)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (app (letrec
                X#15= T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
               ;E#17
             in
                S#10
             ) S#9)
     )
    ,
     (letrec
        E#7
     in
        (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17} in (app S#10 S#9))
     )
  )

where

   Delta1 = {T#13,T#12,T#6}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#9,(letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(letrec {E#8} in [.]))}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in (app (letrec {X#15=T#14;E#17} in S#10) S#9)),
           A#11  |->  [.],
           T#12  |->  (app (letrec {X#15=T#14;E#17} in S#10) S#9),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#10),
           E#8   |->  {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {E#7} in (app (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17} in S#10) S#9))
    -llet-e1->                    (letrec {E#7} in (app (letrec {X#15=T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#17} in S#10) S#9))
    ................................................................................
                                  (letrec {E#7} in (app (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17} in S#10) S#9))
    -SR,lapp2->                   (letrec {E#7} in (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17} in (app S#10 S#9)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#7} in (app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#10) S#9))
    ,
     (letrec {E#7} in (letrec {X#1=S#4;E#2;E#3} in (app S#10 S#9)))
  )

where

   Delta1 = {T#12,T#6}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {(S#10,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#9,(letrec {X#1=S#4;E#2;E#3} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(letrec {E#8} in [.]))}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in (app [.] S#9)),
           A#11  |->  [.],
           T#12  |->  (app [.] S#9),
           T#13  |->  [.],
           S#5   |->  S#10,
           E#8   |->  {X#1=S#4;E#2;E#3},
           E#14  |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {E#7} in (app (letrec {X#1=S#4;E#2;E#3} in S#10) S#9))
    -llet-e1->                    (letrec {E#7} in (app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#10) S#9))
    ................................................................................
                                  (letrec {E#7} in (app (letrec {X#1=S#4;E#2;E#3} in S#10) S#9))
    -SR,lapp2->                   (letrec {E#7} in (letrec {X#1=S#4;E#2;E#3} in (app S#10 S#9)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (app (letrec {E#8} in S#10) T#13[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])
     )
    ,
     (letrec
        E#7
     in
        (letrec {E#8} in (app S#10 T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)]))
     )
  )

where

   Delta1 = {T#12,T#6}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {E#8} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(letrec {E#8} in [.]))}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in (app (letrec {E#8} in S#10) T#13)),
           A#11  |->  [.],
           T#12  |->  (app (letrec {E#8} in S#10) T#13),
           S#9   |->  T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#7} in (app (letrec {E#8} in S#10) T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)]))
    -llet-e1->                    (letrec {E#7} in (app (letrec {E#8} in S#10) T#13[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]))
    ................................................................................
                                  (letrec {E#7} in (app (letrec {E#8} in S#10) T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)]))
    -SR,lapp2->                   (letrec {E#7} in (letrec {E#8} in (app S#10 T#13[(letrec {X#1=S#4;E#2;E#3} in S#5)])))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
       ;E#15
     in
        A#11[(app (letrec {E#8} in S#10) S#9)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)]
       ;E#15
     in
        A#11[(letrec {E#8} in (app S#10 S#9))]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#9,(letrec {E#8} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(letrec {E#8} in [.]))}


and found solution:

    Sol = {T#6   |->  (letrec {X#13=T#12;E#15} in A#11[(app (letrec {E#8} in S#10) S#9)]),
           E#7   |->  {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -llet-e1->                    (letrec {X#13=T#12[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#15} in A#11[(app (letrec {E#8} in S#10) S#9)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {X#13=T#12[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#15} in A#11[(letrec {E#8} in (app S#10 S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#2} in S#4)
       ;E#3
     in
        A#11[(app (letrec {E#8} in S#10) S#9)]
     )
    ,
     (letrec {X#1=S#4;E#2;E#3} in A#11[(letrec {E#8} in (app S#10 S#9))])
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#7,E#8}
   Delta3 = {(A#11[(app (letrec {E#8} in S#10) S#9)],(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#9,(letrec {E#8} in [.]))}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#2,E#7,E#8}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#9,(letrec {E#8} in [.]))}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#11[(app (letrec {E#8} in S#10) S#9)],
           E#7   |->  {X#1=S#4;E#2;E#3},
           E#12  |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {X#1=S#4;E#2;E#3} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -llet-e1->                    (letrec {X#1=(letrec {E#2} in S#4);E#3} in A#11[(app (letrec {E#8} in S#10) S#9)])
    ................................................................................
                                  (letrec {X#1=S#4;E#2;E#3} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {X#1=S#4;E#2;E#3} in A#11[(letrec {E#8} in (app S#10 S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
       ;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]
     in
        A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
     )
    ,
     (letrec
        E#8
       ;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]
     in
        A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#15[(app A#16[[.]] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])]),
             ((var X#7),A#15[(app A#16[[.]] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#7)] T#17)],
           A#12  |->  A#15[(app A#16 T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -llet-e1->                    (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=S#4;E#2;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
       ;E#17
       ;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)]
       ;E#17
       ;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#15=T#14;E#17;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)]),
           E#8   |->  {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17},
           E#16  |->  {E#17;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#15=T#14[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#17;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#15=T#14[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#17;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app (letrec {E#9} in T#21[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#10)]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(letrec {E#9} in (app T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#10))]
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,T#19,A#17,T#14,T#6,A#18}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#18[(app (letrec {E#9} in T#21) S#10)];E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  A#18,
           T#14         |->  A#18[(app (letrec {E#9} in T#21) S#10)],
           T#19         |->  (app (letrec {E#9} in T#21) S#10),
           T#20         |->  (letrec {E#9} in T#21),
           S#11         |->  T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=A#18[(app (letrec {E#9} in T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#10)];E#8} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=A#18[(app (letrec {E#9} in T#21[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#10)];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app (letrec {E#9} in T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#10)];E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#18[(letrec {E#9} in (app T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#10))];E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app (letrec
                           X#22= T#21[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
                          ;E#24
                        in
                           S#11
                        ) S#10)]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(letrec {X#22=T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#24} in (app S#11 S#10))]
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,T#19,A#17,T#14,T#6,A#18}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {X#22=T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#24} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#18[(app (letrec {X#22=T#21;E#24} in S#11) S#10)];E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  A#18,
           T#14         |->  A#18[(app (letrec {X#22=T#21;E#24} in S#11) S#10)],
           T#19         |->  (app (letrec {X#22=T#21;E#24} in S#11) S#10),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#11),
           E#9          |->  {X#22=T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#7=A#18[(app (letrec {X#22=T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#24} in S#11) S#10)];E#8} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=A#18[(app (letrec {X#22=T#21[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#24} in S#11) S#10)];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app (letrec {X#22=T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#24} in S#11) S#10)];E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#18[(letrec {X#22=T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#24} in (app S#11 S#10))];E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#11) S#10)]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(letrec {X#1=S#4;E#2;E#3} in (app S#11 S#10))]
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#19,A#17,T#14,T#6,A#18}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#11,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {X#1=S#4;E#2;E#3} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#18[(app [.] S#10)];E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  A#18,
           T#14         |->  A#18[(app [.] S#10)],
           T#19         |->  (app [.] S#10),
           T#20         |->  [.],
           S#5          |->  S#11,
           E#9          |->  {X#1=S#4;E#2;E#3},
           E#21         |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {X#7=A#18[(app (letrec {X#1=S#4;E#2;E#3} in S#11) S#10)];E#8} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=A#18[(app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#11) S#10)];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app (letrec {X#1=S#4;E#2;E#3} in S#11) S#10)];E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#18[(letrec {X#1=S#4;E#2;E#3} in (app S#11 S#10))];E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app (letrec {E#9} in S#11) T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(letrec {E#9} in (app S#11 T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]))]
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#19,A#17,T#14,T#6,A#18}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#18[(app (letrec {E#9} in S#11) T#20)];E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  A#18,
           T#14         |->  A#18[(app (letrec {E#9} in S#11) T#20)],
           T#19         |->  (app (letrec {E#9} in S#11) T#20),
           S#10         |->  T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=A#18[(app (letrec {E#9} in S#11) T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=A#18[(app (letrec {E#9} in S#11) T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app (letrec {E#9} in S#11) T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#18[(letrec {E#9} in (app S#11 T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]))];E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(app A#19[(letrec {E#9} in (app S#11 S#10))] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20)];E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           T#14         |->  A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20)],
           A#17         |->  A#18[(app A#19 T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#18[(app A#19[(letrec {E#9} in (app S#11 S#10))] T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (app (letrec {E#9} in T#19[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#10)
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= (letrec {E#9} in (app T#19[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#10))
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#18,T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(app (letrec {E#9} in T#19) S#10);E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  [.],
           T#14         |->  (app (letrec {E#9} in T#19) S#10),
           T#18         |->  (letrec {E#9} in T#19),
           S#11         |->  T#19[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=(app (letrec {E#9} in T#19[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#10);E#8} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=(app (letrec {E#9} in T#19[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#10);E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(app (letrec {E#9} in T#19[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#10);E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=(letrec {E#9} in (app T#19[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#10));E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (app (letrec
                     X#20= T#19[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
                    ;E#22
                  in
                     S#11
                  ) S#10)
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= (letrec {X#20=T#19[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#22} in (app S#11 S#10))
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#18,T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {X#20=T#19[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#22} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(app (letrec {X#20=T#19;E#22} in S#11) S#10);E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  [.],
           T#14         |->  (app (letrec {X#20=T#19;E#22} in S#11) S#10),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#11),
           E#9          |->  {X#20=T#19[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#7=(app (letrec {X#20=T#19[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#22} in S#11) S#10);E#8} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=(app (letrec {X#20=T#19[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#22} in S#11) S#10);E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(app (letrec {X#20=T#19[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#22} in S#11) S#10);E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=(letrec {X#20=T#19[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#22} in (app S#11 S#10));E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#11) S#10)
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= (letrec {X#1=S#4;E#2;E#3} in (app S#11 S#10))
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#11,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {X#1=S#4;E#2;E#3} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(app [.] S#10);E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  [.],
           T#14         |->  (app [.] S#10),
           T#18         |->  [.],
           S#5          |->  S#11,
           E#9          |->  {X#1=S#4;E#2;E#3},
           E#19         |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {X#7=(app (letrec {X#1=S#4;E#2;E#3} in S#11) S#10);E#8} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=(app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#11) S#10);E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(app (letrec {X#1=S#4;E#2;E#3} in S#11) S#10);E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=(letrec {X#1=S#4;E#2;E#3} in (app S#11 S#10));E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (app (letrec {E#9} in S#11) T#18[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= (letrec {E#9} in (app S#11 T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)]))
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(app (letrec {E#9} in S#11) T#18);E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  [.],
           T#14         |->  (app (letrec {E#9} in S#11) T#18),
           S#10         |->  T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=(app (letrec {E#9} in S#11) T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)]);E#8} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=(app (letrec {E#9} in S#11) T#18[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]);E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(app (letrec {E#9} in S#11) T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)]);E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=(letrec {E#9} in (app S#11 T#18[(letrec {X#1=S#4;E#2;E#3} in S#5)]));E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#8
       ;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#8
       ;EE#19[X#18,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22)];E#8;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];EE#19[X#18,[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#8;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]},
           T#14         |->  A#20[(app A#21[(var X#18)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#8;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8;EE#19[X#18,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#8
       ;EE#20[X#7,(var X#18)]
       ;EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#8
       ;EE#20[X#7,(var X#18)]
       ;EE#21[X#19,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24)];E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]},
           T#14         |->  A#22[(app A#23[(var X#19)] T#24)],
           A#17         |->  A#22[(app A#23 T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (letrec {E#9} in T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#10)]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {E#9} in (app T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#10))]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,T#21,A#17,T#14,T#6,A#20}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app (letrec {E#9} in T#23) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[(app (letrec {E#9} in T#23) S#10)],
           T#21         |->  (app (letrec {E#9} in T#23) S#10),
           T#22         |->  (letrec {E#9} in T#23),
           S#11         |->  T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (letrec {E#9} in T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#18=A#20[(app (letrec {E#9} in T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (letrec {E#9} in T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#20[(letrec {E#9} in (app T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#10))];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (letrec
                            X#24= T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
                           ;E#26
                         in
                            S#11
                         ) S#10)]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {X#24=T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#26} in (app S#11 S#10))]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,T#21,A#17,T#14,T#6,A#20}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {X#24=T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#26} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app (letrec {X#24=T#23;E#26} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[(app (letrec {X#24=T#23;E#26} in S#11) S#10)],
           T#21         |->  (app (letrec {X#24=T#23;E#26} in S#11) S#10),
           T#22         |->  (letrec {X#24=T#23;E#26} in S#11),
           E#9          |->  {X#24=T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#26},
           E#25         |->  {E#26}}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (letrec {X#24=T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#26} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#18=A#20[(app (letrec {X#24=T#23[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#26} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (letrec {X#24=T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#26} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#20[(letrec {X#24=T#23[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#26} in (app S#11 S#10))];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#11) S#10)]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {X#1=S#4;E#2;E#3} in (app S#11 S#10))]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#21,A#17,T#14,T#6,A#20}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#11,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {X#1=S#4;E#2;E#3} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app [.] S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[(app [.] S#10)],
           T#21         |->  (app [.] S#10),
           T#22         |->  [.],
           S#5          |->  S#11,
           E#9          |->  {X#1=S#4;E#2;E#3},
           E#23         |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (letrec {X#1=S#4;E#2;E#3} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#18=A#20[(app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (letrec {X#1=S#4;E#2;E#3} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#20[(letrec {X#1=S#4;E#2;E#3} in (app S#11 S#10))];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (letrec {E#9} in S#11) T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {E#9} in (app S#11 T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)]))]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#21,A#17,T#14,T#6,A#20}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app (letrec {E#9} in S#11) T#22)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[(app (letrec {E#9} in S#11) T#22)],
           T#21         |->  (app (letrec {E#9} in S#11) T#22),
           S#10         |->  T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (letrec {E#9} in S#11) T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#18=A#20[(app (letrec {E#9} in S#11) T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (letrec {E#9} in S#11) T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#20[(letrec {E#9} in (app S#11 T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)]))];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(letrec {E#9} in (app S#11 S#10))] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           T#14         |->  A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#18=A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#20[(app A#21[(letrec {E#9} in (app S#11 S#10))] T#22[(letrec {X#1=S#4;E#2;E#3} in S#5)])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (letrec {E#9} in T#21[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#10)
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= (letrec {E#9} in (app T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#10))
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=(app (letrec {E#9} in T#21) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  (app (letrec {E#9} in T#21) S#10),
           T#20         |->  (letrec {E#9} in T#21),
           S#11         |->  T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#18=(app (letrec {E#9} in T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#18=(app (letrec {E#9} in T#21[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=(app (letrec {E#9} in T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)]) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=(letrec {E#9} in (app T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)] S#10));E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (letrec
                      X#22= T#21[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
                     ;E#24
                   in
                      S#11
                   ) S#10)
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= (letrec {X#22=T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#24} in (app S#11 S#10))
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {X#22=T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#24} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=(app (letrec {X#22=T#21;E#24} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  (app (letrec {X#22=T#21;E#24} in S#11) S#10),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#11),
           E#9          |->  {X#22=T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#18=(app (letrec {X#22=T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#24} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#18=(app (letrec {X#22=T#21[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)];E#24} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=(app (letrec {X#22=T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#24} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=(letrec {X#22=T#21[(letrec {X#1=S#4;E#2;E#3} in S#5)];E#24} in (app S#11 S#10));E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#11) S#10)
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= (letrec {X#1=S#4;E#2;E#3} in (app S#11 S#10))
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#11,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {X#1=S#4;E#2;E#3} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=(app [.] S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  (app [.] S#10),
           T#20         |->  [.],
           S#5          |->  S#11,
           E#9          |->  {X#1=S#4;E#2;E#3},
           E#21         |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {X#18=(app (letrec {X#1=S#4;E#2;E#3} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#18=(app (letrec {X#1=(letrec {E#2} in S#4);E#3} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=(app (letrec {X#1=S#4;E#2;E#3} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=(letrec {X#1=S#4;E#2;E#3} in (app S#11 S#10));E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (letrec {E#9} in S#11) T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)])
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= (letrec {E#9} in (app S#11 T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]))
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {E#2,E#9}
   Delta3 = {(S#5,(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)],(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=(app (letrec {E#9} in S#11) T#20);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  (app (letrec {E#9} in S#11) T#20),
           S#10         |->  T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#18=(app (letrec {E#9} in S#11) T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#18=(app (letrec {E#9} in S#11) T#20[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=(app (letrec {E#9} in S#11) T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=(letrec {E#9} in (app S#11 T#20[(letrec {X#1=S#4;E#2;E#3} in S#5)]));E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {E#17;E#18} in S#4);E#15;E#16} in A#12[(var X#7)])
    ,
     (letrec
        X#1= S#4
       ;E#16
       ;E#18
       ;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#15,E#18}
   Delta3 = {(A#12[(var X#7)],(letrec {E#17;E#18} in [.])),
             [{E#15;E#16},(letrec {E#17;E#18} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#15;E#17} =?= {EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]}}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#7)],
           E#8   |->  {X#1=S#4;E#16;E#18},
           E#14  |->  {E#16;E#18},
           E#2   |->  {E#17;E#18},
           E#3   |->  {E#15;E#16}}

and instantiated rules:

                                  (letrec {X#1=S#4;E#15;E#16;E#17;E#18} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#1=(letrec {E#17;E#18} in S#4);E#15;E#16} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#1=S#4;E#16;E#18;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#1=S#4;E#16;E#18;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#15;E#17} =?= {EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#2} in A#14[(app (letrec {E#9} in S#11) S#10)])
       ;E#3
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#14[(letrec {E#9} in (app S#11 S#10))]
       ;E#2
       ;E#3
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9}
   Delta3 = {(A#12[(var X#7)],(letrec {E#2} in [.])),
             [{E#3},(letrec {E#2} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {[.1]=A#14[[.2]]},
           X#1          |->  X#7,
           S#4          |->  A#14[(app (letrec {E#9} in S#11) S#10)],
           E#8          |->  {E#2;E#3}}

and instantiated rules:

                                  (letrec {X#7=A#14[(app (letrec {E#9} in S#11) S#10)];E#2;E#3} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=(letrec {E#2} in A#14[(app (letrec {E#9} in S#11) S#10)]);E#3} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#14[(app (letrec {E#9} in S#11) S#10)];E#2;E#3} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#14[(letrec {E#9} in (app S#11 S#10))];E#2;E#3} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#19;E#20} in A#14[(var X#15)])
       ;E#17
       ;E#18
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#14[(var X#15)]
       ;E#18
       ;E#20
       ;EE#16[X#15,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#17,E#20}
   Delta3 = {(A#12[(var X#7)],(letrec {E#19;E#20} in [.])),
             [{E#17;E#18},(letrec {E#19;E#20} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#17;E#19} =?= {EE#16[X#15,(app (letrec {E#9} in S#11) S#10)]}}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {[.1]=A#14[(var X#15)];EE#16[X#15,[.2]]},
           X#1          |->  X#7,
           S#4          |->  A#14[(var X#15)],
           E#8          |->  {E#18;E#20},
           E#2          |->  {E#19;E#20},
           E#3          |->  {E#17;E#18}}

and instantiated rules:

                                  (letrec {X#7=A#14[(var X#15)];E#17;E#18;E#19;E#20} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=(letrec {E#19;E#20} in A#14[(var X#15)]);E#17;E#18} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#14[(var X#15)];E#18;E#20;EE#16[X#15,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#14[(var X#15)];E#18;E#20;EE#16[X#15,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#17;E#19} =?= {EE#16[X#15,(app (letrec {E#9} in S#11) S#10)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#19;E#20} in A#14[(var X#15)])
       ;E#17
       ;E#18
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#14[(var X#15)]
       ;E#18
       ;E#20
       ;EE#16[X#15,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#19}
   Delta3 = {(A#12[(var X#7)],(letrec {E#19;E#20} in [.])),
             [{E#17;E#18},(letrec {E#19;E#20} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#17;E#19} =?= {EE#16[X#15,(app (letrec {E#9} in S#11) S#10)]}}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {[.1]=A#14[(var X#15)];EE#16[X#15,[.2]]},
           X#1          |->  X#7,
           S#4          |->  A#14[(var X#15)],
           E#8          |->  {E#18;E#20},
           E#2          |->  {E#19;E#20},
           E#3          |->  {E#17;E#18}}

and instantiated rules:

                                  (letrec {X#7=A#14[(var X#15)];E#17;E#18;E#19;E#20} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#7=(letrec {E#19;E#20} in A#14[(var X#15)]);E#17;E#18} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#14[(var X#15)];E#18;E#20;EE#16[X#15,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#14[(var X#15)];E#18;E#20;EE#16[X#15,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#17;E#19} =?= {EE#16[X#15,(app (letrec {E#9} in S#11) S#10)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#22;E#23;E#24} in A#14[(var X#16)])
       ;E#19
       ;E#20
       ;E#21
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;E#21
       ;E#24
       ;EE#17[X#7,(var X#15)]
       ;EE#18[X#16,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#19,E#20,E#24}
   Delta3 = {(A#12[(var X#7)],(letrec {E#22;E#23;E#24} in [.])),
             [{E#19;E#20;E#21},(letrec {E#22;E#23;E#24} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#19;E#22} =?= {EE#17[X#7,(var X#15)]},
             {E#20;E#23} =?= {EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]}}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#1          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           E#8          |->  {E#21;E#24},
           E#2          |->  {E#22;E#23;E#24},
           E#3          |->  {E#19;E#20;E#21}}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];E#19;E#20;E#21;E#22;E#23;E#24} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#15=(letrec {E#22;E#23;E#24} in A#14[(var X#16)]);E#19;E#20;E#21} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];E#21;E#24;EE#17[X#7,(var X#15)];EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#15=A#14[(var X#16)];E#21;E#24;EE#17[X#7,(var X#15)];EE#18[X#16,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#19;E#22} =?= {EE#17[X#7,(var X#15)]},
    {E#20;E#23} =?= {EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#22;E#23;E#24} in A#14[(var X#16)])
       ;E#19
       ;E#20
       ;E#21
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;E#21
       ;E#24
       ;EE#17[X#7,(var X#15)]
       ;EE#18[X#16,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#19,E#23}
   Delta3 = {(A#12[(var X#7)],(letrec {E#22;E#23;E#24} in [.])),
             [{E#19;E#20;E#21},(letrec {E#22;E#23;E#24} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#19;E#22} =?= {EE#17[X#7,(var X#15)]},
             {E#20;E#23} =?= {EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]}}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#1          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           E#8          |->  {E#21;E#24},
           E#2          |->  {E#22;E#23;E#24},
           E#3          |->  {E#19;E#20;E#21}}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];E#19;E#20;E#21;E#22;E#23;E#24} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#15=(letrec {E#22;E#23;E#24} in A#14[(var X#16)]);E#19;E#20;E#21} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];E#21;E#24;EE#17[X#7,(var X#15)];EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#15=A#14[(var X#16)];E#21;E#24;EE#17[X#7,(var X#15)];EE#18[X#16,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#19;E#22} =?= {EE#17[X#7,(var X#15)]},
    {E#20;E#23} =?= {EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]}

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#19;E#20} in A#14[(app (letrec {E#9} in S#11) S#10)])
       ;E#17
       ;E#18
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= A#14[(letrec {E#9} in (app S#11 S#10))]
       ;E#18
       ;E#20
       ;EE#16[X#7,(var X#15)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#9,E#17,E#20}
   Delta3 = {(A#12[(var X#7)],(letrec {E#19;E#20} in [.])),
             [{E#17;E#18},(letrec {E#19;E#20} in [.])],
             (S#10,(letrec {E#9} in [.])),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {
             {E#17;E#19} =?= {EE#16[X#7,(var X#15)]}}

from overlapping -llet-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
    -llet-e1->                    T#6[(letrec {X#1=(letrec {E#2} in S#4);E#3} in S#5)]
    and constraints: E#2/= {}, (S#5,(letrec {E#2} in [.])), ({E#3},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=S#4;E#2;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#9}
      Delta3=  {(S#5,(letrec {E#2} in [.])),[{E#3},(letrec {E#2} in [.])],(S#10,(letrec {E#9} in [.])),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[[.2]];EE#16[[.1],(var X#15)]},
           X#1          |->  X#15,
           S#4          |->  A#14[(app (letrec {E#9} in S#11) S#10)],
           E#8          |->  {E#18;E#20},
           E#2          |->  {E#19;E#20},
           E#3          |->  {E#17;E#18}}

and instantiated rules:

                                  (letrec {X#15=A#14[(app (letrec {E#9} in S#11) S#10)];E#17;E#18;E#19;E#20} in A#12[(var X#7)])
    -llet-e1->                    (letrec {X#15=(letrec {E#19;E#20} in A#14[(app (letrec {E#9} in S#11) S#10)]);E#17;E#18} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=A#14[(app (letrec {E#9} in S#11) S#10)];E#18;E#20;EE#16[X#7,(var X#15)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#15=A#14[(letrec {E#9} in (app S#11 S#10))];E#18;E#20;EE#16[X#7,(var X#15)]} in A#12[(var X#7)])
        ............................
    Delta4:
    {E#17;E#19} =?= {EE#16[X#7,(var X#15)]}

================================================================================
Critical Pair:

  (
     A#13[(app (\ X#9.S#11) T#15[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    ,
     A#13[(letrec
              X#9= T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
           in
              S#11
           )]
  )

where

   Delta1 = {T#14,A#12,T#7,A#13}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(\ X#9.[.])),
             (T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {X#9=[.]} in S#11)),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  A#12[(app (\ X#9.S#11) S#10)]
    -SR,lbeta1->                  A#12[(letrec {X#9=S#10} in S#11)]
    and constraints: (S#10,(\ X#9.[.])), (S#10,(letrec {X#9=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        A#12[(app (\ X#9.S#11) S#10)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#10,(\ X#9.[.])),(S#10,(letrec {X#9=[.]} in S#11)),((var X#2),C#8[[.]])}


and found solution:

    Sol = {A#12  |->  A#13,
           T#7   |->  A#13[(app (\ X#9.S#11) T#15)],
           T#14  |->  (app (\ X#9.S#11) T#15),
           S#10  |->  T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  A#13[(app (\ X#9.S#11) T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    -cp-e1->                      A#13[(app (\ X#9.S#11) T#15[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    ................................................................................
                                  A#13[(app (\ X#9.S#11) T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    -SR,lbeta1->                  A#13[(letrec {X#9=T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]} in S#11)]
    

================================================================================
Critical Pair:

  (
     A#13[(app A#14[(app (\ X#9.S#11) S#10)] T#15[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    ,
     A#13[(app A#14[(letrec {X#9=S#10} in S#11)] T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
  )

where

   Delta1 = {A#12,T#7}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#10,(\ X#9.[.])),
             (S#10,(letrec {X#9=[.]} in S#11)),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  A#12[(app (\ X#9.S#11) S#10)]
    -SR,lbeta1->                  A#12[(letrec {X#9=S#10} in S#11)]
    and constraints: (S#10,(\ X#9.[.])), (S#10,(letrec {X#9=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        A#12[(app (\ X#9.S#11) S#10)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#10,(\ X#9.[.])),(S#10,(letrec {X#9=[.]} in S#11)),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  A#13[(app A#14[(app (\ X#9.S#11) S#10)] T#15)],
           A#12  |->  A#13[(app A#14 T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  A#13[(app A#14[(app (\ X#9.S#11) S#10)] T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    -cp-e1->                      A#13[(app A#14[(app (\ X#9.S#11) S#10)] T#15[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    ................................................................................
                                  A#13[(app A#14[(app (\ X#9.S#11) S#10)] T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    -SR,lbeta1->                  A#13[(app A#14[(letrec {X#9=S#10} in S#11)] T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    

================================================================================
Critical Pair:

  (
     (app (\ X#9.S#11) T#13[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])
    ,
     (letrec
        X#9= T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
     in
        S#11
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(\ X#9.[.])),
             (T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {X#9=[.]} in S#11)),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  A#12[(app (\ X#9.S#11) S#10)]
    -SR,lbeta1->                  A#12[(letrec {X#9=S#10} in S#11)]
    and constraints: (S#10,(\ X#9.[.])), (S#10,(letrec {X#9=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        A#12[(app (\ X#9.S#11) S#10)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#10,(\ X#9.[.])),(S#10,(letrec {X#9=[.]} in S#11)),((var X#2),C#8[[.]])}


and found solution:

    Sol = {A#12  |->  [.],
           T#7   |->  (app (\ X#9.S#11) T#13),
           S#10  |->  T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (app (\ X#9.S#11) T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])
    -cp-e1->                      (app (\ X#9.S#11) T#13[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])
    ................................................................................
                                  (app (\ X#9.S#11) T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])
    -SR,lbeta1->                  (letrec {X#9=T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]} in S#11)
    

================================================================================
Critical Pair:

  (
     (letrec
        E#10
     in
        A#15[(app (\ X#9.S#12) T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
    ,
     (letrec
        E#10
     in
        A#15[(letrec
                 X#9= T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
              in
                 S#12
              )]
     )
  )

where

   Delta1 = {T#16,A#13,T#14,T#7,A#15}
   Delta2 = {E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(\ X#9.[.])),
             (T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10} in A#13[(app (\ X#9.S#12) S#11)])
    -SR,lbeta2->                  (letrec {E#10} in A#13[(letrec {X#9=S#11} in S#12)])
    and constraints: E#10/= {}, (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10} in A#13[(app (\ X#9.S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#10} in A#15[(app (\ X#9.S#12) T#17)]),
           A#13  |->  A#15,
           T#14  |->  A#15[(app (\ X#9.S#12) T#17)],
           T#16  |->  (app (\ X#9.S#12) T#17),
           S#11  |->  T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {E#10} in A#15[(app (\ X#9.S#12) T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -cp-e1->                      (letrec {E#10} in A#15[(app (\ X#9.S#12) T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    ................................................................................
                                  (letrec {E#10} in A#15[(app (\ X#9.S#12) T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -SR,lbeta2->                  (letrec {E#10} in A#15[(letrec {X#9=T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]} in S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#10
     in
        A#15[(app A#16[(app (\ X#9.S#12) S#11)] T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
    ,
     (letrec
        E#10
     in
        A#15[(app A#16[(letrec {X#9=S#11} in S#12)] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
  )

where

   Delta1 = {A#13,T#14,T#7}
   Delta2 = {E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10} in A#13[(app (\ X#9.S#12) S#11)])
    -SR,lbeta2->                  (letrec {E#10} in A#13[(letrec {X#9=S#11} in S#12)])
    and constraints: E#10/= {}, (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10} in A#13[(app (\ X#9.S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#10} in A#15[(app A#16[(app (\ X#9.S#12) S#11)] T#17)]),
           T#14  |->  A#15[(app A#16[(app (\ X#9.S#12) S#11)] T#17)],
           A#13  |->  A#15[(app A#16 T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {E#10} in A#15[(app A#16[(app (\ X#9.S#12) S#11)] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -cp-e1->                      (letrec {E#10} in A#15[(app A#16[(app (\ X#9.S#12) S#11)] T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    ................................................................................
                                  (letrec {E#10} in A#15[(app A#16[(app (\ X#9.S#12) S#11)] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -SR,lbeta2->                  (letrec {E#10} in A#15[(app A#16[(letrec {X#9=S#11} in S#12)] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#10
     in
        (app (\ X#9.S#12) T#15[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])
     )
    ,
     (letrec
        E#10
     in
        (letrec
           X#9= T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        in
           S#12
        )
     )
  )

where

   Delta1 = {T#14,T#7}
   Delta2 = {E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(\ X#9.[.])),
             (T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10} in A#13[(app (\ X#9.S#12) S#11)])
    -SR,lbeta2->                  (letrec {E#10} in A#13[(letrec {X#9=S#11} in S#12)])
    and constraints: E#10/= {}, (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10} in A#13[(app (\ X#9.S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#10} in (app (\ X#9.S#12) T#15)),
           A#13  |->  [.],
           T#14  |->  (app (\ X#9.S#12) T#15),
           S#11  |->  T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {E#10} in (app (\ X#9.S#12) T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]))
    -cp-e1->                      (letrec {E#10} in (app (\ X#9.S#12) T#15[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]))
    ................................................................................
                                  (letrec {E#10} in (app (\ X#9.S#12) T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]))
    -SR,lbeta2->                  (letrec {E#10} in (letrec {X#9=T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]} in S#12))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;E#17
     in
        A#13[(app (\ X#9.S#12) S#11)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;E#17
     in
        A#13[(letrec {X#9=S#11} in S#12)]
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10} in A#13[(app (\ X#9.S#12) S#11)])
    -SR,lbeta2->                  (letrec {E#10} in A#13[(letrec {X#9=S#11} in S#12)])
    and constraints: E#10/= {}, (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10} in A#13[(app (\ X#9.S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#15=T#14;E#17} in A#13[(app (\ X#9.S#12) S#11)]),
           E#10  |->  {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17} in A#13[(app (\ X#9.S#12) S#11)])
    -cp-e1->                      (letrec {X#15=T#14[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17} in A#13[(app (\ X#9.S#12) S#11)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17} in A#13[(app (\ X#9.S#12) S#11)])
    -SR,lbeta2->                  (letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17} in A#13[(letrec {X#9=S#11} in S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#8[(var X#2)]
       ;X#2= (\ X#3.S#5)
       ;E#15
     in
        A#13[(app (\ X#9.S#12) S#11)]
     )
    ,
     (letrec
        X#1= C#8[(\ X#3.S#5)]
       ;X#2= (\ X#3.S#5)
       ;E#15
     in
        A#13[(letrec {X#9=S#11} in S#12)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10} in A#13[(app (\ X#9.S#12) S#11)])
    -SR,lbeta2->                  (letrec {E#10} in A#13[(letrec {X#9=S#11} in S#12)])
    and constraints: E#10/= {}, (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10} in A#13[(app (\ X#9.S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#13[(app (\ X#9.S#12) S#11)],
           E#10  |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15},
           E#14  |->  {X#1=C#8[(\ X#3.S#5)];E#15},
           E#4   |->  {E#15}}

and instantiated rules:

                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15} in A#13[(app (\ X#9.S#12) S#11)])
    -cp-e1->                      (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#15} in A#13[(app (\ X#9.S#12) S#11)])
    ................................................................................
                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15} in A#13[(app (\ X#9.S#12) S#11)])
    -SR,lbeta2->                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15} in A#13[(letrec {X#9=S#11} in S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#11
       ;EE#15[X#9,(app (\ X#10.S#13) S#12)]
     in
        A#17[(app A#18[(var X#9)] T#19[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
    ,
     (letrec
        E#11
       ;EE#15[X#9,(letrec {X#10=S#12} in S#13)]
     in
        A#17[(app A#18[(var X#9)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
  )

where

   Delta1 = {A#14,T#16,T#7}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in S#13)),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#17[(app A#18[[.]] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]),
             ((var X#9),A#17[(app A#18[[.]] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#17[(app A#18[(var X#9)] T#19)]),
           T#16  |->  A#17[(app A#18[(var X#9)] T#19)],
           A#14  |->  A#17[(app A#18 T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#17[(app A#18[(var X#9)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -cp-e1->                      (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#17[(app A#18[(var X#9)] T#19[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#17[(app A#18[(var X#9)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#17[(app A#18[(var X#9)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;E#19
       ;EE#15[X#9,(app (\ X#10.S#13) S#12)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#17= T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;E#19
       ;EE#15[X#9,(letrec {X#10=S#12} in S#13)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in S#13)),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#17=T#16;E#19;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)]),
           E#11  |->  {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19},
           E#18  |->  {E#19;EE#15[X#9,(app (\ X#10.S#13) S#12)]}}

and instantiated rules:

                                  (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#17=T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= A#20[(app (\ X#10.S#13) T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#11
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#9= A#20[(letrec
                      X#10= T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
                   in
                      S#13
                   )]
       ;E#11
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#21,A#19,T#16,T#7,A#20}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(\ X#10.[.])),
             (T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {X#10=[.]} in S#13)),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#9=A#20[(app (\ X#10.S#13) T#22)];E#11} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#20[[.2]]},
           X#17         |->  X#9,
           E#18         |->  {E#11},
           A#19         |->  A#20,
           T#16         |->  A#20[(app (\ X#10.S#13) T#22)],
           T#21         |->  (app (\ X#10.S#13) T#22),
           S#12         |->  T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {X#9=A#20[(app (\ X#10.S#13) T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#9=A#20[(app (\ X#10.S#13) T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#9=A#20[(app (\ X#10.S#13) T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#9=A#20[(letrec {X#10=T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]} in S#13)];E#11} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= A#20[(app A#21[(app (\ X#10.S#13) S#12)] T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#11
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#9= A#20[(app A#21[(letrec {X#10=S#12} in S#13)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#11
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#19,T#16,T#7}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in S#13)),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#9=A#20[(app A#21[(app (\ X#10.S#13) S#12)] T#22)];E#11} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#20[(app A#21[[.2]] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]},
           X#17         |->  X#9,
           E#18         |->  {E#11},
           T#16         |->  A#20[(app A#21[(app (\ X#10.S#13) S#12)] T#22)],
           A#19         |->  A#20[(app A#21 T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#9=A#20[(app A#21[(app (\ X#10.S#13) S#12)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#9=A#20[(app A#21[(app (\ X#10.S#13) S#12)] T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#9=A#20[(app A#21[(app (\ X#10.S#13) S#12)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#9=A#20[(app A#21[(letrec {X#10=S#12} in S#13)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (app (\ X#10.S#13) T#20[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])
       ;E#11
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#9= (letrec
                X#10= T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
             in
                S#13
             )
       ;E#11
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#16,T#7}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(\ X#10.[.])),
             (T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {X#10=[.]} in S#13)),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#9=(app (\ X#10.S#13) T#20);E#11} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#17         |->  X#9,
           E#18         |->  {E#11},
           A#19         |->  [.],
           T#16         |->  (app (\ X#10.S#13) T#20),
           S#12         |->  T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {X#9=(app (\ X#10.S#13) T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#11} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#9=(app (\ X#10.S#13) T#20[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#11} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#9=(app (\ X#10.S#13) T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#11} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#9=(letrec {X#10=T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]} in S#13);E#11} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#11
       ;EE#21[X#20,(app (\ X#10.S#13) S#12)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#9= A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#11
       ;EE#21[X#20,(letrec {X#10=S#12} in S#13)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#19,T#16,T#7}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in S#13)),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#9=A#22[(app A#23[(var X#20)] T#24)];E#11;EE#21[X#20,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];EE#21[X#20,[.2]]},
           X#17         |->  X#9,
           E#18         |->  {E#11;EE#21[X#20,(app (\ X#10.S#13) S#12)]},
           T#16         |->  A#22[(app A#23[(var X#20)] T#24)],
           A#19         |->  A#22[(app A#23 T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#9=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;EE#21[X#20,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#9=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;EE#21[X#20,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#9=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;EE#21[X#20,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#9=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;EE#21[X#20,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#11
       ;EE#22[X#9,(var X#20)]
       ;EE#23[X#21,(app (\ X#10.S#13) S#12)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#20= A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#11
       ;EE#22[X#9,(var X#20)]
       ;EE#23[X#21,(letrec {X#10=S#12} in S#13)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#19,T#16,T#7}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in S#13)),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26)];E#11;EE#22[X#9,(var X#20)];EE#23[X#21,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];EE#22[[.1],(var X#20)];EE#23[X#21,[.2]]},
           X#17         |->  X#20,
           E#18         |->  {E#11;EE#22[X#9,(var X#20)];EE#23[X#21,(app (\ X#10.S#13) S#12)]},
           T#16         |->  A#24[(app A#25[(var X#21)] T#26)],
           A#19         |->  A#24[(app A#25 T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;EE#22[X#9,(var X#20)];EE#23[X#21,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;EE#22[X#9,(var X#20)];EE#23[X#21,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;EE#22[X#9,(var X#20)];EE#23[X#21,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;EE#22[X#9,(var X#20)];EE#23[X#21,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app (\ X#10.S#13) T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#11
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#20= A#22[(letrec
                       X#10= T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
                    in
                       S#13
                    )]
       ;E#11
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#23,A#19,T#16,T#7,A#22}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(\ X#10.[.])),
             (T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {X#10=[.]} in S#13)),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=A#22[(app (\ X#10.S#13) T#24)];E#11;EE#21[X#9,(var X#20)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#20=A#22[[.2]];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {E#11;EE#21[X#9,(var X#20)]},
           A#19         |->  A#22,
           T#16         |->  A#22[(app (\ X#10.S#13) T#24)],
           T#23         |->  (app (\ X#10.S#13) T#24),
           S#12         |->  T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app (\ X#10.S#13) T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#20=A#22[(app (\ X#10.S#13) T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#20=A#22[(app (\ X#10.S#13) T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#20=A#22[(letrec {X#10=T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]} in S#13)];E#11;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app A#23[(app (\ X#10.S#13) S#12)] T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#11
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#20= A#22[(app A#23[(letrec {X#10=S#12} in S#13)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#11
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#19,T#16,T#7}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in S#13)),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=A#22[(app A#23[(app (\ X#10.S#13) S#12)] T#24)];E#11;EE#21[X#9,(var X#20)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#20=A#22[(app A#23[[.2]] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {E#11;EE#21[X#9,(var X#20)]},
           T#16         |->  A#22[(app A#23[(app (\ X#10.S#13) S#12)] T#24)],
           A#19         |->  A#22[(app A#23 T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app A#23[(app (\ X#10.S#13) S#12)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#20=A#22[(app A#23[(app (\ X#10.S#13) S#12)] T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#20=A#22[(app A#23[(app (\ X#10.S#13) S#12)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#20=A#22[(app A#23[(letrec {X#10=S#12} in S#13)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= (app (\ X#10.S#13) T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])
       ;E#11
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#20= (letrec
                 X#10= T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
              in
                 S#13
              )
       ;E#11
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#16,T#7}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(\ X#10.[.])),
             (T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {X#10=[.]} in S#13)),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=(app (\ X#10.S#13) T#22);E#11;EE#21[X#9,(var X#20)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {E#11;EE#21[X#9,(var X#20)]},
           A#19         |->  [.],
           T#16         |->  (app (\ X#10.S#13) T#22),
           S#12         |->  T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {X#20=(app (\ X#10.S#13) T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#11;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#20=(app (\ X#10.S#13) T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#11;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#20=(app (\ X#10.S#13) T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#11;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#20=(letrec {X#10=T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]} in S#13);E#11;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#8[(var X#2)]
       ;X#2= (\ X#3.S#5)
       ;E#17
       ;EE#15[X#9,(app (\ X#10.S#13) S#12)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#1= C#8[(\ X#3.S#5)]
       ;X#2= (\ X#3.S#5)
       ;E#17
       ;EE#15[X#9,(letrec {X#10=S#12} in S#13)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in S#13)),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#14[(var X#9)],
           E#11  |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17},
           E#16  |->  {X#1=C#8[(\ X#3.S#5)];E#17},
           E#4   |->  {E#17;EE#15[X#9,(app (\ X#10.S#13) S#12)]}}

and instantiated rules:

                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#17;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#18[(app (\ X#10.C#21[(var X#2)]) S#12)]
       ;E#16
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#18[(letrec {X#10=S#12} in C#21[(\ X#3.S#5)])]
       ;E#16
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#20,C#19,A#17,C#8,A#18}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#18[(app (\ X#10.C#21) S#12)]),
             ((var X#2),A#18[(app (\ X#10.C#21) S#12)]),
             (S#5,A#18[(app (\ X#10.C#21) S#12)]),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in C#21[(\ X#3.S#5)])),
             ((var X#2),A#18[(app (\ X#10.C#21[[.]]) S#12)]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#1          |->  X#9,
           E#4          |->  {E#16},
           A#17         |->  A#18,
           C#8          |->  A#18[(app (\ X#10.C#21) S#12)],
           C#19         |->  (app (\ X#10.C#21) S#12),
           C#20         |->  (\ X#10.C#21),
           S#13         |->  C#21[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app (\ X#10.C#21[(\ X#3.S#5)]) S#12)];E#16} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app (\ X#10.C#21[(var X#2)]) S#12)];E#16} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app (\ X#10.C#21[(\ X#3.S#5)]) S#12)];E#16} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(letrec {X#10=S#12} in C#21[(\ X#3.S#5)])];E#16} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#10.S#13)
       ;X#9= A#18[(app (var X#2) S#12)]
       ;E#16
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#2= (\ X#10.S#13)
       ;X#9= A#18[(letrec {X#10=S#12} in S#13)]
       ;E#16
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#19,A#17,C#8,A#18}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),A#18[(app [.] S#12)]),
             ((var X#2),A#18[(app [.] S#12)]),
             (S#13,A#18[(app [.] S#12)]),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in S#13)),
             ((var X#2),A#18[(app [.] S#12)]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#10.S#13);E#16},
           EE#15[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#1          |->  X#9,
           E#4          |->  {E#16},
           A#17         |->  A#18,
           C#8          |->  A#18[(app [.] S#12)],
           C#19         |->  (app [.] S#12),
           C#20         |->  [.],
           X#3          |->  X#10,
           S#5          |->  S#13}

and instantiated rules:

                                  (letrec {X#2=(\ X#10.S#13);X#9=A#18[(app (\ X#10.S#13) S#12)];E#16} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#10.S#13);X#9=A#18[(app (var X#2) S#12)];E#16} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#10.S#13);X#9=A#18[(app (\ X#10.S#13) S#12)];E#16} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#2=(\ X#10.S#13);X#9=A#18[(letrec {X#10=S#12} in S#13)];E#16} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#18[(app (\ X#10.S#13) C#20[(var X#2)])]
       ;E#16
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#18[(letrec {X#10=C#20[(\ X#3.S#5)]} in S#13)]
       ;E#16
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#19,A#17,C#8,A#18}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#18[(app (\ X#10.S#13) C#20)]),
             ((var X#2),A#18[(app (\ X#10.S#13) C#20)]),
             (S#5,A#18[(app (\ X#10.S#13) C#20)]),
             (C#20[(\ X#3.S#5)],(\ X#10.[.])),
             (C#20[(\ X#3.S#5)],(letrec {X#10=[.]} in S#13)),
             ((var X#2),A#18[(app (\ X#10.S#13) C#20[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#1          |->  X#9,
           E#4          |->  {E#16},
           A#17         |->  A#18,
           C#8          |->  A#18[(app (\ X#10.S#13) C#20)],
           C#19         |->  (app (\ X#10.S#13) C#20),
           S#12         |->  C#20[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app (\ X#10.S#13) C#20[(\ X#3.S#5)])];E#16} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app (\ X#10.S#13) C#20[(var X#2)])];E#16} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app (\ X#10.S#13) C#20[(\ X#3.S#5)])];E#16} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(letrec {X#10=C#20[(\ X#3.S#5)]} in S#13)];E#16} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#18[(app A#19[(app (\ X#10.S#13) S#12)] C#20[(var X#2)])]
       ;E#16
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#18[(app A#19[(letrec {X#10=S#12} in S#13)] C#20[(\ X#3.S#5)])]
       ;E#16
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#17,C#8}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#18[(app A#19[(app (\ X#10.S#13) S#12)] C#20)]),
             ((var X#2),A#18[(app A#19[(app (\ X#10.S#13) S#12)] C#20)]),
             (S#5,A#18[(app A#19[(app (\ X#10.S#13) S#12)] C#20)]),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in S#13)),
             ((var X#2),A#18[(app A#19[(app (\ X#10.S#13) S#12)] C#20[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] C#20[(\ X#3.S#5)])]},
           X#1          |->  X#9,
           E#4          |->  {E#16},
           C#8          |->  A#18[(app A#19[(app (\ X#10.S#13) S#12)] C#20)],
           A#17         |->  A#18[(app A#19 C#20[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app A#19[(app (\ X#10.S#13) S#12)] C#20[(\ X#3.S#5)])];E#16} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app A#19[(app (\ X#10.S#13) S#12)] C#20[(var X#2)])];E#16} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app A#19[(app (\ X#10.S#13) S#12)] C#20[(\ X#3.S#5)])];E#16} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app A#19[(letrec {X#10=S#12} in S#13)] C#20[(\ X#3.S#5)])];E#16} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (app (\ X#10.C#19[(var X#2)]) S#12)
       ;E#16
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (letrec {X#10=S#12} in C#19[(\ X#3.S#5)])
       ;E#16
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#18,C#8}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),(app (\ X#10.C#19) S#12)),
             ((var X#2),(app (\ X#10.C#19) S#12)),
             (S#5,(app (\ X#10.C#19) S#12)),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in C#19[(\ X#3.S#5)])),
             ((var X#2),(app (\ X#10.C#19[[.]]) S#12)),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#9,
           E#4          |->  {E#16},
           A#17         |->  [.],
           C#8          |->  (app (\ X#10.C#19) S#12),
           C#18         |->  (\ X#10.C#19),
           S#13         |->  C#19[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=(app (\ X#10.C#19[(\ X#3.S#5)]) S#12);E#16} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=(app (\ X#10.C#19[(var X#2)]) S#12);E#16} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=(app (\ X#10.C#19[(\ X#3.S#5)]) S#12);E#16} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#2=(\ X#3.S#5);X#9=(letrec {X#10=S#12} in C#19[(\ X#3.S#5)]);E#16} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#2=(\ X#10.S#13);X#9=(app (var X#2) S#12);E#16} in A#14[(var X#9)])
    ,
     (letrec
        X#2= (\ X#10.S#13)
       ;X#9= (letrec {X#10=S#12} in S#13)
       ;E#16
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#8}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),(app [.] S#12)),
             ((var X#2),(app [.] S#12)),
             (S#13,(app [.] S#12)),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in S#13)),
             ((var X#2),(app [.] S#12)),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#10.S#13);E#16},
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#9,
           E#4          |->  {E#16},
           A#17         |->  [.],
           C#8          |->  (app [.] S#12),
           C#18         |->  [.],
           X#3          |->  X#10,
           S#5          |->  S#13}

and instantiated rules:

                                  (letrec {X#2=(\ X#10.S#13);X#9=(app (\ X#10.S#13) S#12);E#16} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#10.S#13);X#9=(app (var X#2) S#12);E#16} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#10.S#13);X#9=(app (\ X#10.S#13) S#12);E#16} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#2=(\ X#10.S#13);X#9=(letrec {X#10=S#12} in S#13);E#16} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (app (\ X#10.S#13) C#18[(var X#2)])
       ;E#16
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (letrec {X#10=C#18[(\ X#3.S#5)]} in S#13)
       ;E#16
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#8}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),(app (\ X#10.S#13) C#18)),
             ((var X#2),(app (\ X#10.S#13) C#18)),
             (S#5,(app (\ X#10.S#13) C#18)),
             (C#18[(\ X#3.S#5)],(\ X#10.[.])),
             (C#18[(\ X#3.S#5)],(letrec {X#10=[.]} in S#13)),
             ((var X#2),(app (\ X#10.S#13) C#18[[.]])),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#9,
           E#4          |->  {E#16},
           A#17         |->  [.],
           C#8          |->  (app (\ X#10.S#13) C#18),
           S#12         |->  C#18[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=(app (\ X#10.S#13) C#18[(\ X#3.S#5)]);E#16} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=(app (\ X#10.S#13) C#18[(var X#2)]);E#16} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=(app (\ X#10.S#13) C#18[(\ X#3.S#5)]);E#16} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#2=(\ X#3.S#5);X#9=(letrec {X#10=C#18[(\ X#3.S#5)]} in S#13);E#16} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#20[(app A#21[(var X#18)] C#22[(var X#2)])]
       ;E#16
       ;EE#19[X#18,(app (\ X#10.S#13) S#12)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])]
       ;E#16
       ;EE#19[X#18,(letrec {X#10=S#12} in S#13)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#17,C#8}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#20[(app A#21[(var X#18)] C#22)]),
             ((var X#2),A#20[(app A#21[(var X#18)] C#22)]),
             (S#5,A#20[(app A#21[(var X#18)] C#22)]),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in S#13)),
             ((var X#2),A#20[(app A#21[(var X#18)] C#22[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])];EE#19[X#18,[.2]]},
           X#1          |->  X#9,
           E#4          |->  {E#16;EE#19[X#18,(app (\ X#10.S#13) S#12)]},
           C#8          |->  A#20[(app A#21[(var X#18)] C#22)],
           A#17         |->  A#20[(app A#21 C#22[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])];E#16;EE#19[X#18,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=A#20[(app A#21[(var X#18)] C#22[(var X#2)])];E#16;EE#19[X#18,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])];E#16;EE#19[X#18,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#2=(\ X#3.S#5);X#9=A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])];E#16;EE#19[X#18,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] C#24[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#20[X#9,(var X#18)]
       ;EE#21[X#19,(app (\ X#10.S#13) S#12)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#20[X#9,(var X#18)]
       ;EE#21[X#19,(letrec {X#10=S#12} in S#13)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#17,C#8}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#22[(app A#23[(var X#19)] C#24)]),
             ((var X#2),A#22[(app A#23[(var X#19)] C#24)]),
             (S#5,A#22[(app A#23[(var X#19)] C#24)]),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in S#13)),
             ((var X#2),A#22[(app A#23[(var X#19)] C#24[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#20[X#9,(var X#18)];EE#21[X#19,(app (\ X#10.S#13) S#12)]},
           C#8          |->  A#22[(app A#23[(var X#19)] C#24)],
           A#17         |->  A#22[(app A#23 C#24[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#20[X#9,(var X#18)];EE#21[X#19,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(var X#2)])];X#2=(\ X#3.S#5);E#16;EE#20[X#9,(var X#18)];EE#21[X#19,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#20[X#9,(var X#18)];EE#21[X#19,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#20[X#9,(var X#18)];EE#21[X#19,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (\ X#10.C#23[(var X#2)]) S#12)]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {X#10=S#12} in C#23[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#22,C#21,A#17,C#8,A#20}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#20[(app (\ X#10.C#23) S#12)]),
             ((var X#2),A#20[(app (\ X#10.C#23) S#12)]),
             (S#5,A#20[(app (\ X#10.C#23) S#12)]),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in C#23[(\ X#3.S#5)])),
             ((var X#2),A#20[(app (\ X#10.C#23[[.]]) S#12)]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#19[X#9,(var X#18)]},
           A#17         |->  A#20,
           C#8          |->  A#20[(app (\ X#10.C#23) S#12)],
           C#21         |->  (app (\ X#10.C#23) S#12),
           C#22         |->  (\ X#10.C#23),
           S#13         |->  C#23[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (\ X#10.C#23[(\ X#3.S#5)]) S#12)];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=A#20[(app (\ X#10.C#23[(var X#2)]) S#12)];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (\ X#10.C#23[(\ X#3.S#5)]) S#12)];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#18=A#20[(letrec {X#10=S#12} in C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (var X#2) S#12)]
       ;X#2= (\ X#10.S#13)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {X#10=S#12} in S#13)]
       ;X#2= (\ X#10.S#13)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#21,A#17,C#8,A#20}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),A#20[(app [.] S#12)]),
             ((var X#2),A#20[(app [.] S#12)]),
             (S#13,A#20[(app [.] S#12)]),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in S#13)),
             ((var X#2),A#20[(app [.] S#12)]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#10.S#13);E#16},
           EE#15[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#19[X#9,(var X#18)]},
           A#17         |->  A#20,
           C#8          |->  A#20[(app [.] S#12)],
           C#21         |->  (app [.] S#12),
           C#22         |->  [.],
           X#3          |->  X#10,
           S#5          |->  S#13}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (\ X#10.S#13) S#12)];X#2=(\ X#10.S#13);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=A#20[(app (var X#2) S#12)];X#2=(\ X#10.S#13);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (\ X#10.S#13) S#12)];X#2=(\ X#10.S#13);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#18=A#20[(letrec {X#10=S#12} in S#13)];X#2=(\ X#10.S#13);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (\ X#10.S#13) C#22[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {X#10=C#22[(\ X#3.S#5)]} in S#13)]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#21,A#17,C#8,A#20}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#20[(app (\ X#10.S#13) C#22)]),
             ((var X#2),A#20[(app (\ X#10.S#13) C#22)]),
             (S#5,A#20[(app (\ X#10.S#13) C#22)]),
             (C#22[(\ X#3.S#5)],(\ X#10.[.])),
             (C#22[(\ X#3.S#5)],(letrec {X#10=[.]} in S#13)),
             ((var X#2),A#20[(app (\ X#10.S#13) C#22[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#19[X#9,(var X#18)]},
           A#17         |->  A#20,
           C#8          |->  A#20[(app (\ X#10.S#13) C#22)],
           C#21         |->  (app (\ X#10.S#13) C#22),
           S#12         |->  C#22[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (\ X#10.S#13) C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=A#20[(app (\ X#10.S#13) C#22[(var X#2)])];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (\ X#10.S#13) C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#18=A#20[(letrec {X#10=C#22[(\ X#3.S#5)]} in S#13)];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(app (\ X#10.S#13) S#12)] C#22[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(letrec {X#10=S#12} in S#13)] C#22[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#17,C#8}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#20[(app A#21[(app (\ X#10.S#13) S#12)] C#22)]),
             ((var X#2),A#20[(app A#21[(app (\ X#10.S#13) S#12)] C#22)]),
             (S#5,A#20[(app A#21[(app (\ X#10.S#13) S#12)] C#22)]),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in S#13)),
             ((var X#2),A#20[(app A#21[(app (\ X#10.S#13) S#12)] C#22[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] C#22[(\ X#3.S#5)])];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#19[X#9,(var X#18)]},
           C#8          |->  A#20[(app A#21[(app (\ X#10.S#13) S#12)] C#22)],
           A#17         |->  A#20[(app A#21 C#22[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(app (\ X#10.S#13) S#12)] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=A#20[(app A#21[(app (\ X#10.S#13) S#12)] C#22[(var X#2)])];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(app (\ X#10.S#13) S#12)] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#18=A#20[(app A#21[(letrec {X#10=S#12} in S#13)] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (\ X#10.C#21[(var X#2)]) S#12)
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= (letrec {X#10=S#12} in C#21[(\ X#3.S#5)])
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#20,C#8}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),(app (\ X#10.C#21) S#12)),
             ((var X#2),(app (\ X#10.C#21) S#12)),
             (S#5,(app (\ X#10.C#21) S#12)),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in C#21[(\ X#3.S#5)])),
             ((var X#2),(app (\ X#10.C#21[[.]]) S#12)),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#19[X#9,(var X#18)]},
           A#17         |->  [.],
           C#8          |->  (app (\ X#10.C#21) S#12),
           C#20         |->  (\ X#10.C#21),
           S#13         |->  C#21[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#18=(app (\ X#10.C#21[(\ X#3.S#5)]) S#12);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=(app (\ X#10.C#21[(var X#2)]) S#12);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=(app (\ X#10.C#21[(\ X#3.S#5)]) S#12);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#18=(letrec {X#10=S#12} in C#21[(\ X#3.S#5)]);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (var X#2) S#12)
       ;X#2= (\ X#10.S#13)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= (letrec {X#10=S#12} in S#13)
       ;X#2= (\ X#10.S#13)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#8}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),(app [.] S#12)),
             ((var X#2),(app [.] S#12)),
             (S#13,(app [.] S#12)),
             (S#12,(\ X#10.[.])),
             (S#12,(letrec {X#10=[.]} in S#13)),
             ((var X#2),(app [.] S#12)),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#10.S#13);E#16},
           EE#15[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#19[X#9,(var X#18)]},
           A#17         |->  [.],
           C#8          |->  (app [.] S#12),
           C#20         |->  [.],
           X#3          |->  X#10,
           S#5          |->  S#13}

and instantiated rules:

                                  (letrec {X#18=(app (\ X#10.S#13) S#12);X#2=(\ X#10.S#13);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=(app (var X#2) S#12);X#2=(\ X#10.S#13);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=(app (\ X#10.S#13) S#12);X#2=(\ X#10.S#13);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#18=(letrec {X#10=S#12} in S#13);X#2=(\ X#10.S#13);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (\ X#10.S#13) C#20[(var X#2)])
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= (letrec {X#10=C#20[(\ X#3.S#5)]} in S#13)
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#8}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),(app (\ X#10.S#13) C#20)),
             ((var X#2),(app (\ X#10.S#13) C#20)),
             (S#5,(app (\ X#10.S#13) C#20)),
             (C#20[(\ X#3.S#5)],(\ X#10.[.])),
             (C#20[(\ X#3.S#5)],(letrec {X#10=[.]} in S#13)),
             ((var X#2),(app (\ X#10.S#13) C#20[[.]])),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lbeta3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {E#11;EE#15[X#9,(letrec {X#10=S#12} in S#13)]} in A#14[(var X#9)])
    and constraints: (S#12,(\ X#10.[.])), (S#12,(letrec {X#10=[.]} in S#13))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#11;EE#15[X#9,(app (\ X#10.S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(\ X#10.[.])),(S#12,(letrec {X#10=[.]} in S#13)),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#11         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#19[X#9,(var X#18)]},
           A#17         |->  [.],
           C#8          |->  (app (\ X#10.S#13) C#20),
           S#12         |->  C#20[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#18=(app (\ X#10.S#13) C#20[(\ X#3.S#5)]);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=(app (\ X#10.S#13) C#20[(var X#2)]);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=(app (\ X#10.S#13) C#20[(\ X#3.S#5)]);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -SR,lbeta3->                  (letrec {X#18=(letrec {X#10=C#20[(\ X#3.S#5)]} in S#13);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (\ X#10.S#12)
       ;E#11
     in
        A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
    ,
     (letrec
        X#9= (\ X#10.S#12)
       ;E#11
     in
        A#15[(app A#16[(\ X#10.S#12)] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
  )

where

   Delta1 = {A#13,T#14,T#7}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#15[(app A#16[[.]] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-in1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(var X#9)])
    -SR,cp-in1->                  (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(\ X#10.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#9=(\ X#10.S#12);E#11} in A#15[(app A#16[(var X#9)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#9)] T#17)],
           A#13  |->  A#15[(app A#16 T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#9=(\ X#10.S#12);E#11} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -cp-e1->                      (letrec {X#9=(\ X#10.S#12);E#11} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#12);E#11} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -SR,cp-in1->                  (letrec {X#9=(\ X#10.S#12);E#11} in A#15[(app A#16[(\ X#10.S#12)] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;X#9= (\ X#10.S#12)
       ;E#17
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;X#9= (\ X#10.S#12)
       ;E#17
     in
        A#13[(\ X#10.S#12)]
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-in1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(var X#9)])
    -SR,cp-in1->                  (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(\ X#10.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#15=T#14;X#9=(\ X#10.S#12);E#17} in A#13[(var X#9)]),
           E#11  |->  {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17},
           E#16  |->  {X#9=(\ X#10.S#12);E#17}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#12);E#17} in A#13[(var X#9)])
    -cp-e1->                      (letrec {X#15=T#14[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#12);E#17} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#12);E#17} in A#13[(var X#9)])
    -SR,cp-in1->                  (letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#12);E#17} in A#13[(\ X#10.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=C#8[(var X#9)];X#9=(\ X#10.S#12);E#14} in A#13[(var X#9)])
    ,
     (letrec {X#1=C#8[(\ X#10.S#12)];X#9=(\ X#10.S#12);E#14} in A#13[(\ X#10.S#12)])
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((\ X#10.S#12),C#8),
             ((var X#9),C#8),
             (S#12,C#8),
             ((var X#9),C#8[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-in1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(var X#9)])
    -SR,cp-in1->                  (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(\ X#10.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#13[(var X#9)],
           X#2   |->  X#9,
           X#3   |->  X#10,
           S#5   |->  S#12,
           E#11  |->  {X#1=C#8[(\ X#10.S#12)];E#14},
           E#4   |->  {E#14}}

and instantiated rules:

                                  (letrec {X#1=C#8[(\ X#10.S#12)];X#9=(\ X#10.S#12);E#14} in A#13[(var X#9)])
    -cp-e1->                      (letrec {X#1=C#8[(var X#9)];X#9=(\ X#10.S#12);E#14} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=C#8[(\ X#10.S#12)];X#9=(\ X#10.S#12);E#14} in A#13[(var X#9)])
    -SR,cp-in1->                  (letrec {X#1=C#8[(\ X#10.S#12)];X#9=(\ X#10.S#12);E#14} in A#13[(\ X#10.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#15[(var X#2)]);E#14} in A#13[(var X#9)])
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.C#15[(\ X#3.S#5)])
       ;E#14
     in
        A#13[(\ X#10.C#15[(\ X#3.S#5)])]
     )
  )

where

   Delta1 = {C#8}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),(\ X#10.C#15)),
             ((var X#2),(\ X#10.C#15)),
             (S#5,(\ X#10.C#15)),
             ((var X#2),(\ X#10.C#15[[.]])),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-in1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(var X#9)])
    -SR,cp-in1->                  (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(\ X#10.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#13[(var X#9)],
           E#11  |->  {X#2=(\ X#3.S#5);E#14},
           X#1   |->  X#9,
           E#4   |->  {E#14},
           C#8   |->  (\ X#10.C#15),
           S#12  |->  C#15[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#15[(\ X#3.S#5)]);E#14} in A#13[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#15[(var X#2)]);E#14} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#15[(\ X#3.S#5)]);E#14} in A#13[(var X#9)])
    -SR,cp-in1->                  (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#15[(\ X#3.S#5)]);E#14} in A#13[(\ X#10.C#15[(\ X#3.S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#2=(\ X#10.S#12);X#9=(var X#2);E#14} in A#13[(var X#9)])
    ,
     (letrec {X#2=(\ X#10.S#12);X#9=(\ X#10.S#12);E#14} in A#13[(\ X#10.S#12)])
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((\ X#10.S#12),[.]),
             ((var X#2),[.]),
             (S#12,[.]),
             ((var X#2),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-in1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(var X#9)])
    -SR,cp-in1->                  (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(\ X#10.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#13[(var X#9)],
           E#11  |->  {X#2=(\ X#10.S#12);E#14},
           X#1   |->  X#9,
           E#4   |->  {E#14},
           C#8   |->  [.],
           X#3   |->  X#10,
           S#5   |->  S#12}

and instantiated rules:

                                  (letrec {X#2=(\ X#10.S#12);X#9=(\ X#10.S#12);E#14} in A#13[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#10.S#12);X#9=(var X#2);E#14} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#10.S#12);X#9=(\ X#10.S#12);E#14} in A#13[(var X#9)])
    -SR,cp-in1->                  (letrec {X#2=(\ X#10.S#12);X#9=(\ X#10.S#12);E#14} in A#13[(\ X#10.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#8[(var X#2)]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#12)
       ;E#15
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= C#8[(\ X#3.S#5)]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#12)
       ;E#15
     in
        A#13[(\ X#10.S#12)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-in1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(var X#9)])
    -SR,cp-in1->                  (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(\ X#10.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#12);E#11} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#13[(var X#9)],
           E#11  |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15},
           E#14  |->  {X#1=C#8[(\ X#3.S#5)];E#15},
           E#4   |->  {X#9=(\ X#10.S#12);E#15}}

and instantiated rules:

                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#12);E#15} in A#13[(var X#9)])
    -cp-e1->                      (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#12);E#15} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#12);E#15} in A#13[(var X#9)])
    -SR,cp-in1->                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#12);E#15} in A#13[(\ X#10.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (\ X#10.S#13)
       ;E#12
       ;VV#15|X#11,(var X#9)|
     in
        A#17[(app A#18[(var X#11)] T#19[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
    ,
     (letrec
        X#9= (\ X#10.S#13)
       ;E#12
       ;VV#15|X#11,(var X#9)|
     in
        A#17[(app A#18[(\ X#10.S#13)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
  )

where

   Delta1 = {A#14,T#16,T#7}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#17[(app A#18[[.]] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]),
             ((var X#9),[.])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-in2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -SR,cp-in2->                  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(\ X#10.S#13)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#14[[.]]),((var X#9),[.])}


and found solution:

    Sol = {T#7   |->  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#17[(app A#18[(var X#11)] T#19)]),
           T#16  |->  A#17[(app A#18[(var X#11)] T#19)],
           A#14  |->  A#17[(app A#18 T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#17[(app A#18[(var X#11)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -cp-e1->                      (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#17[(app A#18[(var X#11)] T#19[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#17[(app A#18[(var X#11)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -SR,cp-in2->                  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#17[(app A#18[(\ X#10.S#13)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;X#9= (\ X#10.S#13)
       ;E#19
       ;VV#15|X#11,(var X#9)|
     in
        A#14[(var X#11)]
     )
    ,
     (letrec
        X#17= T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;X#9= (\ X#10.S#13)
       ;E#19
       ;VV#15|X#11,(var X#9)|
     in
        A#14[(\ X#10.S#13)]
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#14[[.]]),
             ((var X#9),[.])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-in2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -SR,cp-in2->                  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(\ X#10.S#13)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#14[[.]]),((var X#9),[.])}


and found solution:

    Sol = {T#7   |->  (letrec {X#17=T#16;X#9=(\ X#10.S#13);E#19;VV#15|X#11,(var X#9)|} in A#14[(var X#11)]),
           E#12  |->  {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19},
           E#18  |->  {X#9=(\ X#10.S#13);E#19;VV#15|X#11,(var X#9)|}}

and instantiated rules:

                                  (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#13);E#19;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -cp-e1->                      (letrec {X#17=T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#13);E#19;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    ................................................................................
                                  (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#13);E#19;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -SR,cp-in2->                  (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#13);E#19;VV#15|X#11,(var X#9)|} in A#14[(\ X#10.S#13)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#8[(var X#9)]
       ;X#9= (\ X#10.S#13)
       ;E#16
       ;VV#15|X#11,(var X#9)|
     in
        A#14[(var X#11)]
     )
    ,
     (letrec
        X#1= C#8[(\ X#10.S#13)]
       ;X#9= (\ X#10.S#13)
       ;E#16
       ;VV#15|X#11,(var X#9)|
     in
        A#14[(\ X#10.S#13)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),C#8),
             ((var X#9),C#8),
             (S#13,C#8),
             ((var X#9),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#14[[.]]),
             ((var X#9),[.])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-in2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -SR,cp-in2->                  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(\ X#10.S#13)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#14[[.]]),((var X#9),[.])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#14[(var X#11)],
           X#2   |->  X#9,
           X#3   |->  X#10,
           S#5   |->  S#13,
           E#12  |->  {X#1=C#8[(\ X#10.S#13)];E#16},
           E#4   |->  {E#16;VV#15|X#11,(var X#9)|}}

and instantiated rules:

                                  (letrec {X#1=C#8[(\ X#10.S#13)];X#9=(\ X#10.S#13);E#16;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -cp-e1->                      (letrec {X#1=C#8[(var X#9)];X#9=(\ X#10.S#13);E#16;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    ................................................................................
                                  (letrec {X#1=C#8[(\ X#10.S#13)];X#9=(\ X#10.S#13);E#16;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -SR,cp-in2->                  (letrec {X#1=C#8[(\ X#10.S#13)];X#9=(\ X#10.S#13);E#16;VV#15|X#11,(var X#9)|} in A#14[(\ X#10.S#13)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.C#17[(var X#2)])
       ;E#16
       ;VV#15|X#11,(var X#9)|
     in
        A#14[(var X#11)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.C#17[(\ X#3.S#5)])
       ;E#16
       ;VV#15|X#11,(var X#9)|
     in
        A#14[(\ X#10.C#17[(\ X#3.S#5)])]
     )
  )

where

   Delta1 = {C#8}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),(\ X#10.C#17)),
             ((var X#2),(\ X#10.C#17)),
             (S#5,(\ X#10.C#17)),
             ((var X#2),(\ X#10.C#17[[.]])),
             ((var X#9),[.]),
             ((var X#11),A#14[[.]]),
             ((var X#9),[.])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-in2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -SR,cp-in2->                  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(\ X#10.S#13)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#14[[.]]),((var X#9),[.])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#14[(var X#11)],
           E#12  |->  {X#2=(\ X#3.S#5);E#16},
           X#1   |->  X#9,
           E#4   |->  {E#16;VV#15|X#11,(var X#9)|},
           C#8   |->  (\ X#10.C#17),
           S#13  |->  C#17[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#17[(\ X#3.S#5)]);E#16;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#17[(var X#2)]);E#16;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#17[(\ X#3.S#5)]);E#16;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -SR,cp-in2->                  (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#17[(\ X#3.S#5)]);E#16;VV#15|X#11,(var X#9)|} in A#14[(\ X#10.C#17[(\ X#3.S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#10.S#13)
       ;X#9= (var X#2)
       ;E#16
       ;VV#15|X#11,(var X#9)|
     in
        A#14[(var X#11)]
     )
    ,
     (letrec
        X#2= (\ X#10.S#13)
       ;X#9= (\ X#10.S#13)
       ;E#16
       ;VV#15|X#11,(var X#9)|
     in
        A#14[(\ X#10.S#13)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),[.]),
             ((var X#2),[.]),
             (S#13,[.]),
             ((var X#2),[.]),
             ((var X#9),[.]),
             ((var X#11),A#14[[.]]),
             ((var X#9),[.])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-in2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -SR,cp-in2->                  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(\ X#10.S#13)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#14[[.]]),((var X#9),[.])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#14[(var X#11)],
           E#12  |->  {X#2=(\ X#10.S#13);E#16},
           X#1   |->  X#9,
           E#4   |->  {E#16;VV#15|X#11,(var X#9)|},
           C#8   |->  [.],
           X#3   |->  X#10,
           S#5   |->  S#13}

and instantiated rules:

                                  (letrec {X#2=(\ X#10.S#13);X#9=(\ X#10.S#13);E#16;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -cp-e1->                      (letrec {X#2=(\ X#10.S#13);X#9=(var X#2);E#16;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    ................................................................................
                                  (letrec {X#2=(\ X#10.S#13);X#9=(\ X#10.S#13);E#16;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -SR,cp-in2->                  (letrec {X#2=(\ X#10.S#13);X#9=(\ X#10.S#13);E#16;VV#15|X#11,(var X#9)|} in A#14[(\ X#10.S#13)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#8[(var X#2)]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
       ;VV#15|X#11,(var X#9)|
     in
        A#14[(var X#11)]
     )
    ,
     (letrec
        X#1= C#8[(\ X#3.S#5)]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
       ;VV#15|X#11,(var X#9)|
     in
        A#14[(\ X#10.S#13)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#14[[.]]),
             ((var X#9),[.])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-in2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -SR,cp-in2->                  (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(\ X#10.S#13)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#14[[.]]),((var X#9),[.])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#14[(var X#11)],
           E#12  |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17},
           E#16  |->  {X#1=C#8[(\ X#3.S#5)];E#17},
           E#4   |->  {X#9=(\ X#10.S#13);E#17;VV#15|X#11,(var X#9)|}}

and instantiated rules:

                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -cp-e1->                      (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    ................................................................................
                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;VV#15|X#11,(var X#9)|} in A#14[(var X#11)])
    -SR,cp-in2->                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;VV#15|X#11,(var X#9)|} in A#14[(\ X#10.S#13)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (\ X#10.S#13)
       ;E#12
       ;EE#16[X#11,A#14[(var X#9)]]
     in
        A#18[(app A#19[(var X#11)] T#20[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
    ,
     (letrec
        X#9= (\ X#10.S#13)
       ;E#12
       ;EE#16[X#11,A#14[(\ X#10.S#13)]]
     in
        A#18[(app A#19[(var X#11)] T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
  )

where

   Delta1 = {A#15,T#17,T#7,A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#18[(app A#19[[.]] T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]),
             ((var X#11),A#18[(app A#19[[.]] T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#18[(app A#19[(var X#11)] T#20)]),
           T#17  |->  A#18[(app A#19[(var X#11)] T#20)],
           A#15  |->  A#18[(app A#19 T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#18[(app A#19[(var X#11)] T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -cp-e1->                      (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#18[(app A#19[(var X#11)] T#20[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#18[(app A#19[(var X#11)] T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#18[(app A#19[(var X#11)] T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;X#9= (\ X#10.S#13)
       ;E#20
       ;EE#16[X#11,A#14[(var X#9)]]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#18= T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;X#9= (\ X#10.S#13)
       ;E#20
       ;EE#16[X#11,A#14[(\ X#10.S#13)]]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {T#7,A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#18=T#17;X#9=(\ X#10.S#13);E#20;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)]),
           E#12  |->  {X#18=T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#20},
           E#19  |->  {X#9=(\ X#10.S#13);E#20;EE#16[X#11,A#14[(var X#9)]]}}

and instantiated rules:

                                  (letrec {X#18=T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#13);E#20;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#18=T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#13);E#20;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#18=T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#13);E#20;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#18=T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#13);E#20;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#21[A#23[(app A#24[(var X#9)] T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]]
       ;X#9= (\ X#10.S#13)
       ;E#12
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#11= A#21[A#23[(app A#24[(\ X#10.S#13)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]]
       ;X#9= (\ X#10.S#13)
       ;E#12
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {T#22,A#20,T#17,T#7,A#14,A#21}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#23[(app A#24[[.]] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#11=A#21[A#23[(app A#24[(var X#9)] T#25)]];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)]),
           EE#16[.1,.2] |-> {[.1]=A#21[[.2]]},
           X#18         |->  X#11,
           E#19         |->  {X#9=(\ X#10.S#13);E#12},
           A#20         |->  A#21,
           T#17         |->  A#21[A#23[(app A#24[(var X#9)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#9)] T#25)],
           A#14         |->  A#23[(app A#24 T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#11=A#21[A#23[(app A#24[(var X#9)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#21[A#23[(app A#24[(var X#9)] T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#21[A#23[(app A#24[(var X#9)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#11=A#21[A#23[(app A#24[(\ X#10.S#13)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#21[(app A#22[A#14[(var X#9)]] T#23[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#11= A#21[(app A#22[A#14[(\ X#10.S#13)]] T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {A#20,T#17,T#7,A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#11=A#21[(app A#22[A#14[(var X#9)]] T#23)];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)]),
           EE#16[.1,.2] |-> {[.1]=A#21[(app A#22[[.2]] T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]},
           X#18         |->  X#11,
           E#19         |->  {X#9=(\ X#10.S#13);E#12},
           T#17         |->  A#21[(app A#22[A#14[(var X#9)]] T#23)],
           A#20         |->  A#21[(app A#22 T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#11=A#21[(app A#22[A#14[(var X#9)]] T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#21[(app A#22[A#14[(var X#9)]] T#23[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#21[(app A#22[A#14[(var X#9)]] T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#11=A#21[(app A#22[A#14[(\ X#10.S#13)]] T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#21[(app A#22[(var X#9)] T#23[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#11= A#21[(app A#22[(\ X#10.S#13)] T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {T#17,T#7,A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#21[(app A#22[[.]] T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#11=A#21[(app A#22[(var X#9)] T#23)];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)]),
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#18         |->  X#11,
           E#19         |->  {X#9=(\ X#10.S#13);E#12},
           A#20         |->  [.],
           T#17         |->  A#21[(app A#22[(var X#9)] T#23)],
           A#14         |->  A#21[(app A#22 T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#11=A#21[(app A#22[(var X#9)] T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#21[(app A#22[(var X#9)] T#23[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#21[(app A#22[(var X#9)] T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#11=A#21[(app A#22[(\ X#10.S#13)] T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#22[X#21,A#14[(var X#9)]]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#11= A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#22[X#21,A#14[(\ X#10.S#13)]]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {A#20,T#17,T#7,A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#11=A#23[(app A#24[(var X#21)] T#25)];X#9=(\ X#10.S#13);E#12;EE#22[X#21,A#14[(var X#9)]]} in A#15[(var X#11)]),
           EE#16[.1,.2] |-> {[.1]=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];EE#22[X#21,[.2]]},
           X#18         |->  X#11,
           E#19         |->  {X#9=(\ X#10.S#13);E#12;EE#22[X#21,A#14[(var X#9)]]},
           T#17         |->  A#23[(app A#24[(var X#21)] T#25)],
           A#20         |->  A#23[(app A#24 T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#11=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#22[X#21,A#14[(var X#9)]]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#22[X#21,A#14[(var X#9)]]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#22[X#21,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#11=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#22[X#21,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#23[X#11,(var X#21)]
       ;EE#24[X#22,A#14[(var X#9)]]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#21= A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#23[X#11,(var X#21)]
       ;EE#24[X#22,A#14[(\ X#10.S#13)]]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {A#20,T#17,T#7,A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#21=A#25[(app A#26[(var X#22)] T#27)];X#9=(\ X#10.S#13);E#12;EE#23[X#11,(var X#21)];EE#24[X#22,A#14[(var X#9)]]} in A#15[(var X#11)]),
           EE#16[.1,.2] |-> {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];EE#23[[.1],(var X#21)];EE#24[X#22,[.2]]},
           X#18         |->  X#21,
           E#19         |->  {X#9=(\ X#10.S#13);E#12;EE#23[X#11,(var X#21)];EE#24[X#22,A#14[(var X#9)]]},
           T#17         |->  A#25[(app A#26[(var X#22)] T#27)],
           A#20         |->  A#25[(app A#26 T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#23[X#11,(var X#21)];EE#24[X#22,A#14[(var X#9)]]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#23[X#11,(var X#21)];EE#24[X#22,A#14[(var X#9)]]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#23[X#11,(var X#21)];EE#24[X#22,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#23[X#11,(var X#21)];EE#24[X#22,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#23[A#25[(app A#26[(var X#9)] T#27[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#22[X#11,(var X#21)]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#21= A#23[A#25[(app A#26[(\ X#10.S#13)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#22[X#11,(var X#21)]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {T#24,A#20,T#17,T#7,A#14,A#23}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#25[(app A#26[[.]] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#21=A#23[A#25[(app A#26[(var X#9)] T#27)]];X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]} in A#15[(var X#11)]),
           EE#16[.1,.2] |-> {X#21=A#23[[.2]];EE#22[[.1],(var X#21)]},
           X#18         |->  X#21,
           E#19         |->  {X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]},
           A#20         |->  A#23,
           T#17         |->  A#23[A#25[(app A#26[(var X#9)] T#27)]],
           T#24         |->  A#25[(app A#26[(var X#9)] T#27)],
           A#14         |->  A#25[(app A#26 T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#21=A#23[A#25[(app A#26[(var X#9)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#21=A#23[A#25[(app A#26[(var X#9)] T#27[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#21=A#23[A#25[(app A#26[(var X#9)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#21=A#23[A#25[(app A#26[(\ X#10.S#13)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#23[(app A#24[A#14[(var X#9)]] T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#22[X#11,(var X#21)]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#21= A#23[(app A#24[A#14[(\ X#10.S#13)]] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#22[X#11,(var X#21)]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {A#20,T#17,T#7,A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#21=A#23[(app A#24[A#14[(var X#9)]] T#25)];X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]} in A#15[(var X#11)]),
           EE#16[.1,.2] |-> {X#21=A#23[(app A#24[[.2]] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];EE#22[[.1],(var X#21)]},
           X#18         |->  X#21,
           E#19         |->  {X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]},
           T#17         |->  A#23[(app A#24[A#14[(var X#9)]] T#25)],
           A#20         |->  A#23[(app A#24 T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#21=A#23[(app A#24[A#14[(var X#9)]] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#21=A#23[(app A#24[A#14[(var X#9)]] T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#21=A#23[(app A#24[A#14[(var X#9)]] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#21=A#23[(app A#24[A#14[(\ X#10.S#13)]] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#23[(app A#24[(var X#9)] T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#22[X#11,(var X#21)]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#21= A#23[(app A#24[(\ X#10.S#13)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#22[X#11,(var X#21)]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {T#17,T#7,A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#23[(app A#24[[.]] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#21=A#23[(app A#24[(var X#9)] T#25)];X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]} in A#15[(var X#11)]),
           EE#16[.1,.2] |-> {X#21=[.2];EE#22[[.1],(var X#21)]},
           X#18         |->  X#21,
           E#19         |->  {X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]},
           A#20         |->  [.],
           T#17         |->  A#23[(app A#24[(var X#9)] T#25)],
           A#14         |->  A#23[(app A#24 T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#21=A#23[(app A#24[(var X#9)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#21=A#23[(app A#24[(var X#9)] T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#21=A#23[(app A#24[(var X#9)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#21=A#23[(app A#24[(\ X#10.S#13)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#13);E#12;EE#22[X#11,(var X#21)]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#8[(var X#9)]
       ;X#9= (\ X#10.S#13)
       ;E#17
       ;EE#16[X#11,A#14[(var X#9)]]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#1= C#8[(\ X#10.S#13)]
       ;X#9= (\ X#10.S#13)
       ;E#17
       ;EE#16[X#11,A#14[(\ X#10.S#13)]]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),C#8),
             ((var X#9),C#8),
             (S#13,C#8),
             ((var X#9),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#15[(var X#11)],
           X#2   |->  X#9,
           X#3   |->  X#10,
           S#5   |->  S#13,
           E#12  |->  {X#1=C#8[(\ X#10.S#13)];E#17},
           E#4   |->  {E#17;EE#16[X#11,A#14[(var X#9)]]}}

and instantiated rules:

                                  (letrec {X#1=C#8[(\ X#10.S#13)];X#9=(\ X#10.S#13);E#17;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#1=C#8[(var X#9)];X#9=(\ X#10.S#13);E#17;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#1=C#8[(\ X#10.S#13)];X#9=(\ X#10.S#13);E#17;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#1=C#8[(\ X#10.S#13)];X#9=(\ X#10.S#13);E#17;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#18[A#20[(app A#21[(var X#9)] C#22[(var X#9)])]]
       ;X#9= (\ X#10.S#13)
       ;E#12
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#11= A#18[A#20[(app A#21[(\ X#10.S#13)] C#22[(\ X#10.S#13)])]]
       ;X#9= (\ X#10.S#13)
       ;E#12
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {C#19,A#17,C#8,A#14,A#18}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),A#18[A#20[(app A#21[(var X#9)] C#22)]]),
             ((var X#9),A#18[A#20[(app A#21[(var X#9)] C#22)]]),
             (S#13,A#18[A#20[(app A#21[(var X#9)] C#22)]]),
             ((var X#9),A#18[A#20[(app A#21[(var X#9)] C#22[[.]])]]),
             ((var X#9),A#20[(app A#21[[.]] C#22[(\ X#10.S#13)])]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#13,
           EE#16[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#1          |->  X#11,
           E#4          |->  {E#12},
           A#17         |->  A#18,
           C#8          |->  A#18[A#20[(app A#21[(var X#9)] C#22)]],
           C#19         |->  A#20[(app A#21[(var X#9)] C#22)],
           A#14         |->  A#20[(app A#21 C#22[(\ X#10.S#13)])]}

and instantiated rules:

                                  (letrec {X#11=A#18[A#20[(app A#21[(var X#9)] C#22[(\ X#10.S#13)])]];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#18[A#20[(app A#21[(var X#9)] C#22[(var X#9)])]];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#18[A#20[(app A#21[(var X#9)] C#22[(\ X#10.S#13)])]];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#11=A#18[A#20[(app A#21[(\ X#10.S#13)] C#22[(\ X#10.S#13)])]];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#18[(app A#19[A#14[(var X#9)]] C#20[(var X#9)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#11= A#18[(app A#19[A#14[(\ X#10.S#13)]] C#20[(\ X#10.S#13)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {A#17,C#8,A#14}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),A#18[(app A#19[A#14[(var X#9)]] C#20)]),
             ((var X#9),A#18[(app A#19[A#14[(var X#9)]] C#20)]),
             (S#13,A#18[(app A#19[A#14[(var X#9)]] C#20)]),
             ((var X#9),A#18[(app A#19[A#14[(var X#9)]] C#20[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#13,
           EE#16[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] C#20[(\ X#10.S#13)])]},
           X#1          |->  X#11,
           E#4          |->  {E#12},
           C#8          |->  A#18[(app A#19[A#14[(var X#9)]] C#20)],
           A#17         |->  A#18[(app A#19 C#20[(\ X#10.S#13)])]}

and instantiated rules:

                                  (letrec {X#11=A#18[(app A#19[A#14[(var X#9)]] C#20[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#18[(app A#19[A#14[(var X#9)]] C#20[(var X#9)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#18[(app A#19[A#14[(var X#9)]] C#20[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#11=A#18[(app A#19[A#14[(\ X#10.S#13)]] C#20[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#18[(app A#19[(var X#9)] C#20[(var X#9)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#11= A#18[(app A#19[(\ X#10.S#13)] C#20[(\ X#10.S#13)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {C#8,A#14}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),A#18[(app A#19[(var X#9)] C#20)]),
             ((var X#9),A#18[(app A#19[(var X#9)] C#20)]),
             (S#13,A#18[(app A#19[(var X#9)] C#20)]),
             ((var X#9),A#18[(app A#19[(var X#9)] C#20[[.]])]),
             ((var X#9),A#18[(app A#19[[.]] C#20[(\ X#10.S#13)])]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#13,
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#11,
           E#4          |->  {E#12},
           A#17         |->  [.],
           C#8          |->  A#18[(app A#19[(var X#9)] C#20)],
           A#14         |->  A#18[(app A#19 C#20[(\ X#10.S#13)])]}

and instantiated rules:

                                  (letrec {X#11=A#18[(app A#19[(var X#9)] C#20[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#18[(app A#19[(var X#9)] C#20[(var X#9)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#18[(app A#19[(var X#9)] C#20[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#11=A#18[(app A#19[(\ X#10.S#13)] C#20[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#20[(app A#21[(var X#18)] C#22[(var X#9)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#19[X#18,A#14[(var X#9)]]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#11= A#20[(app A#21[(var X#18)] C#22[(\ X#10.S#13)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#19[X#18,A#14[(\ X#10.S#13)]]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {A#17,C#8,A#14}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),A#20[(app A#21[(var X#18)] C#22)]),
             ((var X#9),A#20[(app A#21[(var X#18)] C#22)]),
             (S#13,A#20[(app A#21[(var X#18)] C#22)]),
             ((var X#9),A#20[(app A#21[(var X#18)] C#22[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#13,
           EE#16[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] C#22[(\ X#10.S#13)])];EE#19[X#18,[.2]]},
           X#1          |->  X#11,
           E#4          |->  {E#12;EE#19[X#18,A#14[(var X#9)]]},
           C#8          |->  A#20[(app A#21[(var X#18)] C#22)],
           A#17         |->  A#20[(app A#21 C#22[(\ X#10.S#13)])]}

and instantiated rules:

                                  (letrec {X#11=A#20[(app A#21[(var X#18)] C#22[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12;EE#19[X#18,A#14[(var X#9)]]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#20[(app A#21[(var X#18)] C#22[(var X#9)])];X#9=(\ X#10.S#13);E#12;EE#19[X#18,A#14[(var X#9)]]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#20[(app A#21[(var X#18)] C#22[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12;EE#19[X#18,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#11=A#20[(app A#21[(var X#18)] C#22[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12;EE#19[X#18,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] C#24[(var X#9)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#20[X#11,(var X#18)]
       ;EE#21[X#19,A#14[(var X#9)]]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] C#24[(\ X#10.S#13)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#20[X#11,(var X#18)]
       ;EE#21[X#19,A#14[(\ X#10.S#13)]]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {A#17,C#8,A#14}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),A#22[(app A#23[(var X#19)] C#24)]),
             ((var X#9),A#22[(app A#23[(var X#19)] C#24)]),
             (S#13,A#22[(app A#23[(var X#19)] C#24)]),
             ((var X#9),A#22[(app A#23[(var X#19)] C#24[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#13,
           EE#16[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#10.S#13)])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#1          |->  X#18,
           E#4          |->  {E#12;EE#20[X#11,(var X#18)];EE#21[X#19,A#14[(var X#9)]]},
           C#8          |->  A#22[(app A#23[(var X#19)] C#24)],
           A#17         |->  A#22[(app A#23 C#24[(\ X#10.S#13)])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12;EE#20[X#11,(var X#18)];EE#21[X#19,A#14[(var X#9)]]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(var X#9)])];X#9=(\ X#10.S#13);E#12;EE#20[X#11,(var X#18)];EE#21[X#19,A#14[(var X#9)]]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12;EE#20[X#11,(var X#18)];EE#21[X#19,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12;EE#20[X#11,(var X#18)];EE#21[X#19,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[A#22[(app A#23[(var X#9)] C#24[(var X#9)])]]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#19[X#11,(var X#18)]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#18= A#20[A#22[(app A#23[(\ X#10.S#13)] C#24[(\ X#10.S#13)])]]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#19[X#11,(var X#18)]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {C#21,A#17,C#8,A#14,A#20}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),A#20[A#22[(app A#23[(var X#9)] C#24)]]),
             ((var X#9),A#20[A#22[(app A#23[(var X#9)] C#24)]]),
             (S#13,A#20[A#22[(app A#23[(var X#9)] C#24)]]),
             ((var X#9),A#20[A#22[(app A#23[(var X#9)] C#24[[.]])]]),
             ((var X#9),A#22[(app A#23[[.]] C#24[(\ X#10.S#13)])]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#13,
           EE#16[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#12;EE#19[X#11,(var X#18)]},
           A#17         |->  A#20,
           C#8          |->  A#20[A#22[(app A#23[(var X#9)] C#24)]],
           C#21         |->  A#22[(app A#23[(var X#9)] C#24)],
           A#14         |->  A#22[(app A#23 C#24[(\ X#10.S#13)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[A#22[(app A#23[(var X#9)] C#24[(\ X#10.S#13)])]];X#9=(\ X#10.S#13);E#12;EE#19[X#11,(var X#18)]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#18=A#20[A#22[(app A#23[(var X#9)] C#24[(var X#9)])]];X#9=(\ X#10.S#13);E#12;EE#19[X#11,(var X#18)]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#18=A#20[A#22[(app A#23[(var X#9)] C#24[(\ X#10.S#13)])]];X#9=(\ X#10.S#13);E#12;EE#19[X#11,(var X#18)]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#18=A#20[A#22[(app A#23[(\ X#10.S#13)] C#24[(\ X#10.S#13)])]];X#9=(\ X#10.S#13);E#12;EE#19[X#11,(var X#18)]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[A#14[(var X#9)]] C#22[(var X#9)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#19[X#11,(var X#18)]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[A#14[(\ X#10.S#13)]] C#22[(\ X#10.S#13)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#19[X#11,(var X#18)]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {A#17,C#8,A#14}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),A#20[(app A#21[A#14[(var X#9)]] C#22)]),
             ((var X#9),A#20[(app A#21[A#14[(var X#9)]] C#22)]),
             (S#13,A#20[(app A#21[A#14[(var X#9)]] C#22)]),
             ((var X#9),A#20[(app A#21[A#14[(var X#9)]] C#22[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#13,
           EE#16[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] C#22[(\ X#10.S#13)])];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#12;EE#19[X#11,(var X#18)]},
           C#8          |->  A#20[(app A#21[A#14[(var X#9)]] C#22)],
           A#17         |->  A#20[(app A#21 C#22[(\ X#10.S#13)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[A#14[(var X#9)]] C#22[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12;EE#19[X#11,(var X#18)]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#18=A#20[(app A#21[A#14[(var X#9)]] C#22[(var X#9)])];X#9=(\ X#10.S#13);E#12;EE#19[X#11,(var X#18)]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[A#14[(var X#9)]] C#22[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12;EE#19[X#11,(var X#18)]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#18=A#20[(app A#21[A#14[(\ X#10.S#13)]] C#22[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12;EE#19[X#11,(var X#18)]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(var X#9)] C#22[(var X#9)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#19[X#11,(var X#18)]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(\ X#10.S#13)] C#22[(\ X#10.S#13)])]
       ;X#9= (\ X#10.S#13)
       ;E#12
       ;EE#19[X#11,(var X#18)]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {C#8,A#14}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),A#20[(app A#21[(var X#9)] C#22)]),
             ((var X#9),A#20[(app A#21[(var X#9)] C#22)]),
             (S#13,A#20[(app A#21[(var X#9)] C#22)]),
             ((var X#9),A#20[(app A#21[(var X#9)] C#22[[.]])]),
             ((var X#9),A#20[(app A#21[[.]] C#22[(\ X#10.S#13)])]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#13,
           EE#16[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#12;EE#19[X#11,(var X#18)]},
           A#17         |->  [.],
           C#8          |->  A#20[(app A#21[(var X#9)] C#22)],
           A#14         |->  A#20[(app A#21 C#22[(\ X#10.S#13)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(var X#9)] C#22[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12;EE#19[X#11,(var X#18)]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#18=A#20[(app A#21[(var X#9)] C#22[(var X#9)])];X#9=(\ X#10.S#13);E#12;EE#19[X#11,(var X#18)]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(var X#9)] C#22[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12;EE#19[X#11,(var X#18)]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#18=A#20[(app A#21[(\ X#10.S#13)] C#22[(\ X#10.S#13)])];X#9=(\ X#10.S#13);E#12;EE#19[X#11,(var X#18)]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.C#18[(var X#2)])
       ;E#17
       ;EE#16[X#11,A#14[(var X#9)]]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.C#18[(\ X#3.S#5)])
       ;E#17
       ;EE#16[X#11,A#14[(\ X#10.C#18[(\ X#3.S#5)])]]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {C#8,A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),(\ X#10.C#18)),
             ((var X#2),(\ X#10.C#18)),
             (S#5,(\ X#10.C#18)),
             ((var X#2),(\ X#10.C#18[[.]])),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#15[(var X#11)],
           E#12  |->  {X#2=(\ X#3.S#5);E#17},
           X#1   |->  X#9,
           E#4   |->  {E#17;EE#16[X#11,A#14[(var X#9)]]},
           C#8   |->  (\ X#10.C#18),
           S#13  |->  C#18[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#18[(\ X#3.S#5)]);E#17;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#18[(var X#2)]);E#17;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#18[(\ X#3.S#5)]);E#17;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#18[(\ X#3.S#5)]);E#17;EE#16[X#11,A#14[(\ X#10.C#18[(\ X#3.S#5)])]]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#10.S#13)
       ;X#9= (var X#2)
       ;E#17
       ;EE#16[X#11,A#14[(var X#9)]]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#2= (\ X#10.S#13)
       ;X#9= (\ X#10.S#13)
       ;E#17
       ;EE#16[X#11,A#14[(\ X#10.S#13)]]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((\ X#10.S#13),[.]),
             ((var X#2),[.]),
             (S#13,[.]),
             ((var X#2),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#15[(var X#11)],
           E#12  |->  {X#2=(\ X#10.S#13);E#17},
           X#1   |->  X#9,
           E#4   |->  {E#17;EE#16[X#11,A#14[(var X#9)]]},
           C#8   |->  [.],
           X#3   |->  X#10,
           S#5   |->  S#13}

and instantiated rules:

                                  (letrec {X#2=(\ X#10.S#13);X#9=(\ X#10.S#13);E#17;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#2=(\ X#10.S#13);X#9=(var X#2);E#17;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#2=(\ X#10.S#13);X#9=(\ X#10.S#13);E#17;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#2=(\ X#10.S#13);X#9=(\ X#10.S#13);E#17;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#8[(var X#2)]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#18
       ;EE#16[X#11,A#14[(var X#9)]]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#1= C#8[(\ X#3.S#5)]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#18
       ;EE#16[X#11,A#14[(\ X#10.S#13)]]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#15[(var X#11)],
           E#12  |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#18},
           E#17  |->  {X#1=C#8[(\ X#3.S#5)];E#18},
           E#4   |->  {X#9=(\ X#10.S#13);E#18;EE#16[X#11,A#14[(var X#9)]]}}

and instantiated rules:

                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#18;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#18;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#18;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#18;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#19[A#21[(app A#22[(var X#9)] C#23[(var X#2)])]]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#11= A#19[A#21[(app A#22[(\ X#10.S#13)] C#23[(\ X#3.S#5)])]]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {C#20,A#18,C#8,A#14,A#19}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#19[A#21[(app A#22[(var X#9)] C#23)]]),
             ((var X#2),A#19[A#21[(app A#22[(var X#9)] C#23)]]),
             (S#5,A#19[A#21[(app A#22[(var X#9)] C#23)]]),
             ((var X#2),A#19[A#21[(app A#22[(var X#9)] C#23[[.]])]]),
             ((var X#9),A#21[(app A#22[[.]] C#23[(\ X#3.S#5)])]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           E#12         |->  {X#2=(\ X#3.S#5);E#17},
           EE#16[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#1          |->  X#11,
           E#4          |->  {X#9=(\ X#10.S#13);E#17},
           A#18         |->  A#19,
           C#8          |->  A#19[A#21[(app A#22[(var X#9)] C#23)]],
           C#20         |->  A#21[(app A#22[(var X#9)] C#23)],
           A#14         |->  A#21[(app A#22 C#23[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#11=A#19[A#21[(app A#22[(var X#9)] C#23[(\ X#3.S#5)])]];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#19[A#21[(app A#22[(var X#9)] C#23[(var X#2)])]];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#19[A#21[(app A#22[(var X#9)] C#23[(\ X#3.S#5)])]];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#11=A#19[A#21[(app A#22[(\ X#10.S#13)] C#23[(\ X#3.S#5)])]];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#19[(app A#20[A#14[(var X#9)]] C#21[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#11= A#19[(app A#20[A#14[(\ X#10.S#13)]] C#21[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {A#18,C#8,A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#19[(app A#20[A#14[(var X#9)]] C#21)]),
             ((var X#2),A#19[(app A#20[A#14[(var X#9)]] C#21)]),
             (S#5,A#19[(app A#20[A#14[(var X#9)]] C#21)]),
             ((var X#2),A#19[(app A#20[A#14[(var X#9)]] C#21[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           E#12         |->  {X#2=(\ X#3.S#5);E#17},
           EE#16[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] C#21[(\ X#3.S#5)])]},
           X#1          |->  X#11,
           E#4          |->  {X#9=(\ X#10.S#13);E#17},
           C#8          |->  A#19[(app A#20[A#14[(var X#9)]] C#21)],
           A#18         |->  A#19[(app A#20 C#21[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#11=A#19[(app A#20[A#14[(var X#9)]] C#21[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#19[(app A#20[A#14[(var X#9)]] C#21[(var X#2)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#19[(app A#20[A#14[(var X#9)]] C#21[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#11=A#19[(app A#20[A#14[(\ X#10.S#13)]] C#21[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#19[(app A#20[(var X#9)] C#21[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#11= A#19[(app A#20[(\ X#10.S#13)] C#21[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {C#8,A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#19[(app A#20[(var X#9)] C#21)]),
             ((var X#2),A#19[(app A#20[(var X#9)] C#21)]),
             (S#5,A#19[(app A#20[(var X#9)] C#21)]),
             ((var X#2),A#19[(app A#20[(var X#9)] C#21[[.]])]),
             ((var X#9),A#19[(app A#20[[.]] C#21[(\ X#3.S#5)])]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           E#12         |->  {X#2=(\ X#3.S#5);E#17},
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#11,
           E#4          |->  {X#9=(\ X#10.S#13);E#17},
           A#18         |->  [.],
           C#8          |->  A#19[(app A#20[(var X#9)] C#21)],
           A#14         |->  A#19[(app A#20 C#21[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#11=A#19[(app A#20[(var X#9)] C#21[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#19[(app A#20[(var X#9)] C#21[(var X#2)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#19[(app A#20[(var X#9)] C#21[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#11=A#19[(app A#20[(\ X#10.S#13)] C#21[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#21[(app A#22[(var X#19)] C#23[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
       ;EE#20[X#19,A#14[(var X#9)]]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#11= A#21[(app A#22[(var X#19)] C#23[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
       ;EE#20[X#19,A#14[(\ X#10.S#13)]]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {A#18,C#8,A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#21[(app A#22[(var X#19)] C#23)]),
             ((var X#2),A#21[(app A#22[(var X#19)] C#23)]),
             (S#5,A#21[(app A#22[(var X#19)] C#23)]),
             ((var X#2),A#21[(app A#22[(var X#19)] C#23[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           E#12         |->  {X#2=(\ X#3.S#5);E#17},
           EE#16[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] C#23[(\ X#3.S#5)])];EE#20[X#19,[.2]]},
           X#1          |->  X#11,
           E#4          |->  {X#9=(\ X#10.S#13);E#17;EE#20[X#19,A#14[(var X#9)]]},
           C#8          |->  A#21[(app A#22[(var X#19)] C#23)],
           A#18         |->  A#21[(app A#22 C#23[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#11=A#21[(app A#22[(var X#19)] C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#19,A#14[(var X#9)]]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#21[(app A#22[(var X#19)] C#23[(var X#2)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#19,A#14[(var X#9)]]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#21[(app A#22[(var X#19)] C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#19,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#11=A#21[(app A#22[(var X#19)] C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#19,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] C#25[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
       ;EE#21[X#11,(var X#19)]
       ;EE#22[X#20,A#14[(var X#9)]]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] C#25[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
       ;EE#21[X#11,(var X#19)]
       ;EE#22[X#20,A#14[(\ X#10.S#13)]]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {A#18,C#8,A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#23[(app A#24[(var X#20)] C#25)]),
             ((var X#2),A#23[(app A#24[(var X#20)] C#25)]),
             (S#5,A#23[(app A#24[(var X#20)] C#25)]),
             ((var X#2),A#23[(app A#24[(var X#20)] C#25[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           E#12         |->  {X#2=(\ X#3.S#5);E#17},
           EE#16[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] C#25[(\ X#3.S#5)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#1          |->  X#19,
           E#4          |->  {X#9=(\ X#10.S#13);E#17;EE#21[X#11,(var X#19)];EE#22[X#20,A#14[(var X#9)]]},
           C#8          |->  A#23[(app A#24[(var X#20)] C#25)],
           A#18         |->  A#23[(app A#24 C#25[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#21[X#11,(var X#19)];EE#22[X#20,A#14[(var X#9)]]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#2)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#21[X#11,(var X#19)];EE#22[X#20,A#14[(var X#9)]]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#21[X#11,(var X#19)];EE#22[X#20,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#21[X#11,(var X#19)];EE#22[X#20,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(app A#24[(var X#9)] C#25[(var X#2)])]]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
       ;EE#20[X#11,(var X#19)]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[(\ X#10.S#13)] C#25[(\ X#3.S#5)])]]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
       ;EE#20[X#11,(var X#19)]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {C#22,A#18,C#8,A#14,A#21}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#21[A#23[(app A#24[(var X#9)] C#25)]]),
             ((var X#2),A#21[A#23[(app A#24[(var X#9)] C#25)]]),
             (S#5,A#21[A#23[(app A#24[(var X#9)] C#25)]]),
             ((var X#2),A#21[A#23[(app A#24[(var X#9)] C#25[[.]])]]),
             ((var X#9),A#23[(app A#24[[.]] C#25[(\ X#3.S#5)])]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           E#12         |->  {X#2=(\ X#3.S#5);E#17},
           EE#16[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {X#9=(\ X#10.S#13);E#17;EE#20[X#11,(var X#19)]},
           A#18         |->  A#21,
           C#8          |->  A#21[A#23[(app A#24[(var X#9)] C#25)]],
           C#22         |->  A#23[(app A#24[(var X#9)] C#25)],
           A#14         |->  A#23[(app A#24 C#25[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#9)] C#25[(\ X#3.S#5)])]];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#11,(var X#19)]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#19=A#21[A#23[(app A#24[(var X#9)] C#25[(var X#2)])]];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#11,(var X#19)]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#9)] C#25[(\ X#3.S#5)])]];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#11,(var X#19)]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#19=A#21[A#23[(app A#24[(\ X#10.S#13)] C#25[(\ X#3.S#5)])]];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#11,(var X#19)]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[A#14[(var X#9)]] C#23[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
       ;EE#20[X#11,(var X#19)]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[A#14[(\ X#10.S#13)]] C#23[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
       ;EE#20[X#11,(var X#19)]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {A#18,C#8,A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#21[(app A#22[A#14[(var X#9)]] C#23)]),
             ((var X#2),A#21[(app A#22[A#14[(var X#9)]] C#23)]),
             (S#5,A#21[(app A#22[A#14[(var X#9)]] C#23)]),
             ((var X#2),A#21[(app A#22[A#14[(var X#9)]] C#23[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           E#12         |->  {X#2=(\ X#3.S#5);E#17},
           EE#16[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] C#23[(\ X#3.S#5)])];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {X#9=(\ X#10.S#13);E#17;EE#20[X#11,(var X#19)]},
           C#8          |->  A#21[(app A#22[A#14[(var X#9)]] C#23)],
           A#18         |->  A#21[(app A#22 C#23[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[A#14[(var X#9)]] C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#11,(var X#19)]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#19=A#21[(app A#22[A#14[(var X#9)]] C#23[(var X#2)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#11,(var X#19)]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[A#14[(var X#9)]] C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#11,(var X#19)]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#19=A#21[(app A#22[A#14[(\ X#10.S#13)]] C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#11,(var X#19)]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(var X#9)] C#23[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
       ;EE#20[X#11,(var X#19)]
     in
        A#15[(var X#11)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(\ X#10.S#13)] C#23[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#13)
       ;E#17
       ;EE#20[X#11,(var X#19)]
     in
        A#15[(var X#11)]
     )
  )

where

   Delta1 = {C#8,A#14}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#21[(app A#22[(var X#9)] C#23)]),
             ((var X#2),A#21[(app A#22[(var X#9)] C#23)]),
             (S#5,A#21[(app A#22[(var X#9)] C#23)]),
             ((var X#2),A#21[(app A#22[(var X#9)] C#23[[.]])]),
             ((var X#9),A#21[(app A#22[[.]] C#23[(\ X#3.S#5)])]),
             ((var X#11),A#15[[.]]),
             ((var X#11),A#15[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(\ X#10.S#13)]]} in A#15[(var X#11)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#13);E#12;EE#16[X#11,A#14[(var X#9)]]} in A#15[(var X#11)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#11),A#15[[.]]),((var X#11),A#15[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#15[(var X#11)],
           E#12         |->  {X#2=(\ X#3.S#5);E#17},
           EE#16[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {X#9=(\ X#10.S#13);E#17;EE#20[X#11,(var X#19)]},
           A#18         |->  [.],
           C#8          |->  A#21[(app A#22[(var X#9)] C#23)],
           A#14         |->  A#21[(app A#22 C#23[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(var X#9)] C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#11,(var X#19)]} in A#15[(var X#11)])
    -cp-e1->                      (letrec {X#19=A#21[(app A#22[(var X#9)] C#23[(var X#2)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#11,(var X#19)]} in A#15[(var X#11)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(var X#9)] C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#11,(var X#19)]} in A#15[(var X#11)])
    -SR,cp-e1->                   (letrec {X#19=A#21[(app A#22[(\ X#10.S#13)] C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#13);E#17;EE#20[X#11,(var X#19)]} in A#15[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (\ X#10.S#14)
       ;E#13
       ;EE#17[X#11,A#15[(var X#12)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#20[(app A#21[(var X#11)] T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
    ,
     (letrec
        X#9= (\ X#10.S#14)
       ;E#13
       ;EE#17[X#11,A#15[(\ X#10.S#14)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#20[(app A#21[(var X#11)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
  )

where

   Delta1 = {A#16,T#19,T#7,A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#20[(app A#21[[.]] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#20[(app A#21[[.]] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#20[(app A#21[(var X#11)] T#22)]),
           T#19  |->  A#20[(app A#21[(var X#11)] T#22)],
           A#16  |->  A#20[(app A#21 T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#20[(app A#21[(var X#11)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -cp-e1->                      (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#20[(app A#21[(var X#11)] T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#20[(app A#21[(var X#11)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#20[(app A#21[(var X#11)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= T#19[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;X#9= (\ X#10.S#14)
       ;E#22
       ;EE#17[X#11,A#15[(var X#12)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#20= T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;X#9= (\ X#10.S#14)
       ;E#22
       ;EE#17[X#11,A#15[(\ X#10.S#14)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {T#7,A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#20=T#19;X#9=(\ X#10.S#14);E#22;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)]),
           E#13  |->  {X#20=T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#22},
           E#21  |->  {X#9=(\ X#10.S#14);E#22;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|}}

and instantiated rules:

                                  (letrec {X#20=T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#14);E#22;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#20=T#19[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#14);E#22;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#20=T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#14);E#22;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#20=T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(\ X#10.S#14);E#22;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#23[A#25[(app A#26[(var X#12)] T#27[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#11= A#23[A#25[(app A#26[(\ X#10.S#14)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {T#24,A#22,T#19,T#7,A#15,A#23}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#25[(app A#26[[.]] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#11=A#23[A#25[(app A#26[(var X#12)] T#27)]];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)]),
           EE#17[.1,.2] |-> {[.1]=A#23[[.2]]},
           X#20         |->  X#11,
           E#21         |->  {X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|},
           A#22         |->  A#23,
           T#19         |->  A#23[A#25[(app A#26[(var X#12)] T#27)]],
           T#24         |->  A#25[(app A#26[(var X#12)] T#27)],
           A#15         |->  A#25[(app A#26 T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#11=A#23[A#25[(app A#26[(var X#12)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#23[A#25[(app A#26[(var X#12)] T#27[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#23[A#25[(app A#26[(var X#12)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#11=A#23[A#25[(app A#26[(\ X#10.S#14)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#23[(app A#24[A#15[(var X#12)]] T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#11= A#23[(app A#24[A#15[(\ X#10.S#14)]] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {A#22,T#19,T#7,A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#11=A#23[(app A#24[A#15[(var X#12)]] T#25)];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)]),
           EE#17[.1,.2] |-> {[.1]=A#23[(app A#24[[.2]] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]},
           X#20         |->  X#11,
           E#21         |->  {X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|},
           T#19         |->  A#23[(app A#24[A#15[(var X#12)]] T#25)],
           A#22         |->  A#23[(app A#24 T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#11=A#23[(app A#24[A#15[(var X#12)]] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#23[(app A#24[A#15[(var X#12)]] T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#23[(app A#24[A#15[(var X#12)]] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#11=A#23[(app A#24[A#15[(\ X#10.S#14)]] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#23[(app A#24[(var X#12)] T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#11= A#23[(app A#24[(\ X#10.S#14)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {T#19,T#7,A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#23[(app A#24[[.]] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#11=A#23[(app A#24[(var X#12)] T#25)];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)]),
           EE#17[.1,.2] |-> {[.1]=[.2]},
           X#20         |->  X#11,
           E#21         |->  {X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|},
           A#22         |->  [.],
           T#19         |->  A#23[(app A#24[(var X#12)] T#25)],
           A#15         |->  A#23[(app A#24 T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#11=A#23[(app A#24[(var X#12)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#23[(app A#24[(var X#12)] T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#23[(app A#24[(var X#12)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#11=A#23[(app A#24[(\ X#10.S#14)] T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#25[(app A#26[(var X#23)] T#27[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#24[X#23,A#15[(var X#12)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#11= A#25[(app A#26[(var X#23)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#24[X#23,A#15[(\ X#10.S#14)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {A#22,T#19,T#7,A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#11=A#25[(app A#26[(var X#23)] T#27)];X#9=(\ X#10.S#14);E#13;EE#24[X#23,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)]),
           EE#17[.1,.2] |-> {[.1]=A#25[(app A#26[(var X#23)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];EE#24[X#23,[.2]]},
           X#20         |->  X#11,
           E#21         |->  {X#9=(\ X#10.S#14);E#13;EE#24[X#23,A#15[(var X#12)]];VV#18|X#12,(var X#9)|},
           T#19         |->  A#25[(app A#26[(var X#23)] T#27)],
           A#22         |->  A#25[(app A#26 T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#11=A#25[(app A#26[(var X#23)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#24[X#23,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#25[(app A#26[(var X#23)] T#27[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#24[X#23,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#25[(app A#26[(var X#23)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#24[X#23,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#11=A#25[(app A#26[(var X#23)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#24[X#23,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#23= A#27[(app A#28[(var X#24)] T#29[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#25[X#11,(var X#23)]
       ;EE#26[X#24,A#15[(var X#12)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#23= A#27[(app A#28[(var X#24)] T#29[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#25[X#11,(var X#23)]
       ;EE#26[X#24,A#15[(\ X#10.S#14)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {A#22,T#19,T#7,A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#23=A#27[(app A#28[(var X#24)] T#29)];X#9=(\ X#10.S#14);E#13;EE#25[X#11,(var X#23)];EE#26[X#24,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)]),
           EE#17[.1,.2] |-> {X#23=A#27[(app A#28[(var X#24)] T#29[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];EE#25[[.1],(var X#23)];EE#26[X#24,[.2]]},
           X#20         |->  X#23,
           E#21         |->  {X#9=(\ X#10.S#14);E#13;EE#25[X#11,(var X#23)];EE#26[X#24,A#15[(var X#12)]];VV#18|X#12,(var X#9)|},
           T#19         |->  A#27[(app A#28[(var X#24)] T#29)],
           A#22         |->  A#27[(app A#28 T#29[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#23=A#27[(app A#28[(var X#24)] T#29[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#25[X#11,(var X#23)];EE#26[X#24,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#23=A#27[(app A#28[(var X#24)] T#29[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#25[X#11,(var X#23)];EE#26[X#24,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#23=A#27[(app A#28[(var X#24)] T#29[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#25[X#11,(var X#23)];EE#26[X#24,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#23=A#27[(app A#28[(var X#24)] T#29[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#25[X#11,(var X#23)];EE#26[X#24,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#23= A#25[A#27[(app A#28[(var X#12)] T#29[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#24[X#11,(var X#23)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#23= A#25[A#27[(app A#28[(\ X#10.S#14)] T#29[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#24[X#11,(var X#23)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {T#26,A#22,T#19,T#7,A#15,A#25}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#27[(app A#28[[.]] T#29[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#23=A#25[A#27[(app A#28[(var X#12)] T#29)]];X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)]),
           EE#17[.1,.2] |-> {X#23=A#25[[.2]];EE#24[[.1],(var X#23)]},
           X#20         |->  X#23,
           E#21         |->  {X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|},
           A#22         |->  A#25,
           T#19         |->  A#25[A#27[(app A#28[(var X#12)] T#29)]],
           T#26         |->  A#27[(app A#28[(var X#12)] T#29)],
           A#15         |->  A#27[(app A#28 T#29[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#23=A#25[A#27[(app A#28[(var X#12)] T#29[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#23=A#25[A#27[(app A#28[(var X#12)] T#29[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#23=A#25[A#27[(app A#28[(var X#12)] T#29[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#23=A#25[A#27[(app A#28[(\ X#10.S#14)] T#29[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]];X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#23= A#25[(app A#26[A#15[(var X#12)]] T#27[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#24[X#11,(var X#23)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#23= A#25[(app A#26[A#15[(\ X#10.S#14)]] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#24[X#11,(var X#23)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {A#22,T#19,T#7,A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#23=A#25[(app A#26[A#15[(var X#12)]] T#27)];X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)]),
           EE#17[.1,.2] |-> {X#23=A#25[(app A#26[[.2]] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];EE#24[[.1],(var X#23)]},
           X#20         |->  X#23,
           E#21         |->  {X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|},
           T#19         |->  A#25[(app A#26[A#15[(var X#12)]] T#27)],
           A#22         |->  A#25[(app A#26 T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#23=A#25[(app A#26[A#15[(var X#12)]] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#23=A#25[(app A#26[A#15[(var X#12)]] T#27[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#23=A#25[(app A#26[A#15[(var X#12)]] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#23=A#25[(app A#26[A#15[(\ X#10.S#14)]] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#23= A#25[(app A#26[(var X#12)] T#27[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#24[X#11,(var X#23)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#23= A#25[(app A#26[(\ X#10.S#14)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#24[X#11,(var X#23)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {T#19,T#7,A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#25[(app A#26[[.]] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#23=A#25[(app A#26[(var X#12)] T#27)];X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)]),
           EE#17[.1,.2] |-> {X#23=[.2];EE#24[[.1],(var X#23)]},
           X#20         |->  X#23,
           E#21         |->  {X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|},
           A#22         |->  [.],
           T#19         |->  A#25[(app A#26[(var X#12)] T#27)],
           A#15         |->  A#25[(app A#26 T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#23=A#25[(app A#26[(var X#12)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#23=A#25[(app A#26[(var X#12)] T#27[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#23=A#25[(app A#26[(var X#12)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#23=A#25[(app A#26[(\ X#10.S#14)] T#27[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(\ X#10.S#14);E#13;EE#24[X#11,(var X#23)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#8[(var X#9)]
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;EE#17[X#11,A#15[(var X#12)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#1= C#8[(\ X#10.S#14)]
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;EE#17[X#11,A#15[(\ X#10.S#14)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {A#15}
   Delta2 = {}
   Delta3 = {((\ X#10.S#14),C#8),
             ((var X#9),C#8),
             (S#14,C#8),
             ((var X#9),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#16[(var X#11)],
           X#2   |->  X#9,
           X#3   |->  X#10,
           S#5   |->  S#14,
           E#13  |->  {X#1=C#8[(\ X#10.S#14)];E#19},
           E#4   |->  {E#19;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|}}

and instantiated rules:

                                  (letrec {X#1=C#8[(\ X#10.S#14)];X#9=(\ X#10.S#14);E#19;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#1=C#8[(var X#9)];X#9=(\ X#10.S#14);E#19;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#1=C#8[(\ X#10.S#14)];X#9=(\ X#10.S#14);E#19;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#1=C#8[(\ X#10.S#14)];X#9=(\ X#10.S#14);E#19;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#20[A#22[(app A#23[(var X#12)] C#24[(var X#9)])]]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#11= A#20[A#22[(app A#23[(\ X#10.S#14)] C#24[(\ X#10.S#14)])]]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {C#21,A#19,C#8,A#15,A#20}
   Delta2 = {}
   Delta3 = {((\ X#10.S#14),A#20[A#22[(app A#23[(var X#12)] C#24)]]),
             ((var X#9),A#20[A#22[(app A#23[(var X#12)] C#24)]]),
             (S#14,A#20[A#22[(app A#23[(var X#12)] C#24)]]),
             ((var X#9),A#20[A#22[(app A#23[(var X#12)] C#24[[.]])]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#22[(app A#23[[.]] C#24[(\ X#10.S#14)])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#14,
           EE#17[.1,.2] |-> {[.1]=A#20[[.2]]},
           X#1          |->  X#11,
           E#4          |->  {E#13;VV#18|X#12,(var X#9)|},
           A#19         |->  A#20,
           C#8          |->  A#20[A#22[(app A#23[(var X#12)] C#24)]],
           C#21         |->  A#22[(app A#23[(var X#12)] C#24)],
           A#15         |->  A#22[(app A#23 C#24[(\ X#10.S#14)])]}

and instantiated rules:

                                  (letrec {X#11=A#20[A#22[(app A#23[(var X#12)] C#24[(\ X#10.S#14)])]];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#20[A#22[(app A#23[(var X#12)] C#24[(var X#9)])]];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#20[A#22[(app A#23[(var X#12)] C#24[(\ X#10.S#14)])]];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#11=A#20[A#22[(app A#23[(\ X#10.S#14)] C#24[(\ X#10.S#14)])]];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#20[(app A#21[A#15[(var X#12)]] C#22[(var X#9)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#11= A#20[(app A#21[A#15[(\ X#10.S#14)]] C#22[(\ X#10.S#14)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {A#19,C#8,A#15}
   Delta2 = {}
   Delta3 = {((\ X#10.S#14),A#20[(app A#21[A#15[(var X#12)]] C#22)]),
             ((var X#9),A#20[(app A#21[A#15[(var X#12)]] C#22)]),
             (S#14,A#20[(app A#21[A#15[(var X#12)]] C#22)]),
             ((var X#9),A#20[(app A#21[A#15[(var X#12)]] C#22[[.]])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#14,
           EE#17[.1,.2] |-> {[.1]=A#20[(app A#21[[.2]] C#22[(\ X#10.S#14)])]},
           X#1          |->  X#11,
           E#4          |->  {E#13;VV#18|X#12,(var X#9)|},
           C#8          |->  A#20[(app A#21[A#15[(var X#12)]] C#22)],
           A#19         |->  A#20[(app A#21 C#22[(\ X#10.S#14)])]}

and instantiated rules:

                                  (letrec {X#11=A#20[(app A#21[A#15[(var X#12)]] C#22[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#20[(app A#21[A#15[(var X#12)]] C#22[(var X#9)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#20[(app A#21[A#15[(var X#12)]] C#22[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#11=A#20[(app A#21[A#15[(\ X#10.S#14)]] C#22[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#20[(app A#21[(var X#12)] C#22[(var X#9)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#11= A#20[(app A#21[(\ X#10.S#14)] C#22[(\ X#10.S#14)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {C#8,A#15}
   Delta2 = {}
   Delta3 = {((\ X#10.S#14),A#20[(app A#21[(var X#12)] C#22)]),
             ((var X#9),A#20[(app A#21[(var X#12)] C#22)]),
             (S#14,A#20[(app A#21[(var X#12)] C#22)]),
             ((var X#9),A#20[(app A#21[(var X#12)] C#22[[.]])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#20[(app A#21[[.]] C#22[(\ X#10.S#14)])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#14,
           EE#17[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#11,
           E#4          |->  {E#13;VV#18|X#12,(var X#9)|},
           A#19         |->  [.],
           C#8          |->  A#20[(app A#21[(var X#12)] C#22)],
           A#15         |->  A#20[(app A#21 C#22[(\ X#10.S#14)])]}

and instantiated rules:

                                  (letrec {X#11=A#20[(app A#21[(var X#12)] C#22[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#20[(app A#21[(var X#12)] C#22[(var X#9)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#20[(app A#21[(var X#12)] C#22[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#11=A#20[(app A#21[(\ X#10.S#14)] C#22[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#22[(app A#23[(var X#20)] C#24[(var X#9)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#21[X#20,A#15[(var X#12)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#11= A#22[(app A#23[(var X#20)] C#24[(\ X#10.S#14)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#21[X#20,A#15[(\ X#10.S#14)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {A#19,C#8,A#15}
   Delta2 = {}
   Delta3 = {((\ X#10.S#14),A#22[(app A#23[(var X#20)] C#24)]),
             ((var X#9),A#22[(app A#23[(var X#20)] C#24)]),
             (S#14,A#22[(app A#23[(var X#20)] C#24)]),
             ((var X#9),A#22[(app A#23[(var X#20)] C#24[[.]])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#14,
           EE#17[.1,.2] |-> {[.1]=A#22[(app A#23[(var X#20)] C#24[(\ X#10.S#14)])];EE#21[X#20,[.2]]},
           X#1          |->  X#11,
           E#4          |->  {E#13;EE#21[X#20,A#15[(var X#12)]];VV#18|X#12,(var X#9)|},
           C#8          |->  A#22[(app A#23[(var X#20)] C#24)],
           A#19         |->  A#22[(app A#23 C#24[(\ X#10.S#14)])]}

and instantiated rules:

                                  (letrec {X#11=A#22[(app A#23[(var X#20)] C#24[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;EE#21[X#20,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#22[(app A#23[(var X#20)] C#24[(var X#9)])];X#9=(\ X#10.S#14);E#13;EE#21[X#20,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#22[(app A#23[(var X#20)] C#24[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;EE#21[X#20,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#11=A#22[(app A#23[(var X#20)] C#24[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;EE#21[X#20,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#24[(app A#25[(var X#21)] C#26[(var X#9)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#22[X#11,(var X#20)]
       ;EE#23[X#21,A#15[(var X#12)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#20= A#24[(app A#25[(var X#21)] C#26[(\ X#10.S#14)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#22[X#11,(var X#20)]
       ;EE#23[X#21,A#15[(\ X#10.S#14)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {A#19,C#8,A#15}
   Delta2 = {}
   Delta3 = {((\ X#10.S#14),A#24[(app A#25[(var X#21)] C#26)]),
             ((var X#9),A#24[(app A#25[(var X#21)] C#26)]),
             (S#14,A#24[(app A#25[(var X#21)] C#26)]),
             ((var X#9),A#24[(app A#25[(var X#21)] C#26[[.]])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#14,
           EE#17[.1,.2] |-> {X#20=A#24[(app A#25[(var X#21)] C#26[(\ X#10.S#14)])];EE#22[[.1],(var X#20)];EE#23[X#21,[.2]]},
           X#1          |->  X#20,
           E#4          |->  {E#13;EE#22[X#11,(var X#20)];EE#23[X#21,A#15[(var X#12)]];VV#18|X#12,(var X#9)|},
           C#8          |->  A#24[(app A#25[(var X#21)] C#26)],
           A#19         |->  A#24[(app A#25 C#26[(\ X#10.S#14)])]}

and instantiated rules:

                                  (letrec {X#20=A#24[(app A#25[(var X#21)] C#26[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;EE#22[X#11,(var X#20)];EE#23[X#21,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#20=A#24[(app A#25[(var X#21)] C#26[(var X#9)])];X#9=(\ X#10.S#14);E#13;EE#22[X#11,(var X#20)];EE#23[X#21,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#20=A#24[(app A#25[(var X#21)] C#26[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;EE#22[X#11,(var X#20)];EE#23[X#21,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#20=A#24[(app A#25[(var X#21)] C#26[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;EE#22[X#11,(var X#20)];EE#23[X#21,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[A#24[(app A#25[(var X#12)] C#26[(var X#9)])]]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#21[X#11,(var X#20)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#20= A#22[A#24[(app A#25[(\ X#10.S#14)] C#26[(\ X#10.S#14)])]]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#21[X#11,(var X#20)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {C#23,A#19,C#8,A#15,A#22}
   Delta2 = {}
   Delta3 = {((\ X#10.S#14),A#22[A#24[(app A#25[(var X#12)] C#26)]]),
             ((var X#9),A#22[A#24[(app A#25[(var X#12)] C#26)]]),
             (S#14,A#22[A#24[(app A#25[(var X#12)] C#26)]]),
             ((var X#9),A#22[A#24[(app A#25[(var X#12)] C#26[[.]])]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#24[(app A#25[[.]] C#26[(\ X#10.S#14)])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#14,
           EE#17[.1,.2] |-> {X#20=A#22[[.2]];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {E#13;EE#21[X#11,(var X#20)];VV#18|X#12,(var X#9)|},
           A#19         |->  A#22,
           C#8          |->  A#22[A#24[(app A#25[(var X#12)] C#26)]],
           C#23         |->  A#24[(app A#25[(var X#12)] C#26)],
           A#15         |->  A#24[(app A#25 C#26[(\ X#10.S#14)])]}

and instantiated rules:

                                  (letrec {X#20=A#22[A#24[(app A#25[(var X#12)] C#26[(\ X#10.S#14)])]];X#9=(\ X#10.S#14);E#13;EE#21[X#11,(var X#20)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#20=A#22[A#24[(app A#25[(var X#12)] C#26[(var X#9)])]];X#9=(\ X#10.S#14);E#13;EE#21[X#11,(var X#20)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#20=A#22[A#24[(app A#25[(var X#12)] C#26[(\ X#10.S#14)])]];X#9=(\ X#10.S#14);E#13;EE#21[X#11,(var X#20)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#20=A#22[A#24[(app A#25[(\ X#10.S#14)] C#26[(\ X#10.S#14)])]];X#9=(\ X#10.S#14);E#13;EE#21[X#11,(var X#20)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app A#23[A#15[(var X#12)]] C#24[(var X#9)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#21[X#11,(var X#20)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#20= A#22[(app A#23[A#15[(\ X#10.S#14)]] C#24[(\ X#10.S#14)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#21[X#11,(var X#20)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {A#19,C#8,A#15}
   Delta2 = {}
   Delta3 = {((\ X#10.S#14),A#22[(app A#23[A#15[(var X#12)]] C#24)]),
             ((var X#9),A#22[(app A#23[A#15[(var X#12)]] C#24)]),
             (S#14,A#22[(app A#23[A#15[(var X#12)]] C#24)]),
             ((var X#9),A#22[(app A#23[A#15[(var X#12)]] C#24[[.]])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#14,
           EE#17[.1,.2] |-> {X#20=A#22[(app A#23[[.2]] C#24[(\ X#10.S#14)])];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {E#13;EE#21[X#11,(var X#20)];VV#18|X#12,(var X#9)|},
           C#8          |->  A#22[(app A#23[A#15[(var X#12)]] C#24)],
           A#19         |->  A#22[(app A#23 C#24[(\ X#10.S#14)])]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app A#23[A#15[(var X#12)]] C#24[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;EE#21[X#11,(var X#20)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#20=A#22[(app A#23[A#15[(var X#12)]] C#24[(var X#9)])];X#9=(\ X#10.S#14);E#13;EE#21[X#11,(var X#20)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#20=A#22[(app A#23[A#15[(var X#12)]] C#24[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;EE#21[X#11,(var X#20)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#20=A#22[(app A#23[A#15[(\ X#10.S#14)]] C#24[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;EE#21[X#11,(var X#20)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app A#23[(var X#12)] C#24[(var X#9)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#21[X#11,(var X#20)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#20= A#22[(app A#23[(\ X#10.S#14)] C#24[(\ X#10.S#14)])]
       ;X#9= (\ X#10.S#14)
       ;E#13
       ;EE#21[X#11,(var X#20)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {C#8,A#15}
   Delta2 = {}
   Delta3 = {((\ X#10.S#14),A#22[(app A#23[(var X#12)] C#24)]),
             ((var X#9),A#22[(app A#23[(var X#12)] C#24)]),
             (S#14,A#22[(app A#23[(var X#12)] C#24)]),
             ((var X#9),A#22[(app A#23[(var X#12)] C#24[[.]])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#22[(app A#23[[.]] C#24[(\ X#10.S#14)])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           X#2          |->  X#9,
           X#3          |->  X#10,
           S#5          |->  S#14,
           EE#17[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {E#13;EE#21[X#11,(var X#20)];VV#18|X#12,(var X#9)|},
           A#19         |->  [.],
           C#8          |->  A#22[(app A#23[(var X#12)] C#24)],
           A#15         |->  A#22[(app A#23 C#24[(\ X#10.S#14)])]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app A#23[(var X#12)] C#24[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;EE#21[X#11,(var X#20)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#20=A#22[(app A#23[(var X#12)] C#24[(var X#9)])];X#9=(\ X#10.S#14);E#13;EE#21[X#11,(var X#20)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#20=A#22[(app A#23[(var X#12)] C#24[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;EE#21[X#11,(var X#20)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#20=A#22[(app A#23[(\ X#10.S#14)] C#24[(\ X#10.S#14)])];X#9=(\ X#10.S#14);E#13;EE#21[X#11,(var X#20)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.C#20[(var X#2)])
       ;E#19
       ;EE#17[X#11,A#15[(var X#12)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.C#20[(\ X#3.S#5)])
       ;E#19
       ;EE#17[X#11,A#15[(\ X#10.C#20[(\ X#3.S#5)])]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {C#8,A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),(\ X#10.C#20)),
             ((var X#2),(\ X#10.C#20)),
             (S#5,(\ X#10.C#20)),
             ((var X#2),(\ X#10.C#20[[.]])),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#16[(var X#11)],
           E#13  |->  {X#2=(\ X#3.S#5);E#19},
           X#1   |->  X#9,
           E#4   |->  {E#19;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|},
           C#8   |->  (\ X#10.C#20),
           S#14  |->  C#20[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#20[(\ X#3.S#5)]);E#19;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#20[(var X#2)]);E#19;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#20[(\ X#3.S#5)]);E#19;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#2=(\ X#3.S#5);X#9=(\ X#10.C#20[(\ X#3.S#5)]);E#19;EE#17[X#11,A#15[(\ X#10.C#20[(\ X#3.S#5)])]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#10.S#14)
       ;X#9= (var X#2)
       ;E#19
       ;EE#17[X#11,A#15[(var X#12)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#2= (\ X#10.S#14)
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;EE#17[X#11,A#15[(\ X#10.S#14)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {A#15}
   Delta2 = {}
   Delta3 = {((\ X#10.S#14),[.]),
             ((var X#2),[.]),
             (S#14,[.]),
             ((var X#2),[.]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#16[(var X#11)],
           E#13  |->  {X#2=(\ X#10.S#14);E#19},
           X#1   |->  X#9,
           E#4   |->  {E#19;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|},
           C#8   |->  [.],
           X#3   |->  X#10,
           S#5   |->  S#14}

and instantiated rules:

                                  (letrec {X#2=(\ X#10.S#14);X#9=(\ X#10.S#14);E#19;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#2=(\ X#10.S#14);X#9=(var X#2);E#19;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#2=(\ X#10.S#14);X#9=(\ X#10.S#14);E#19;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#2=(\ X#10.S#14);X#9=(\ X#10.S#14);E#19;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#8[(var X#2)]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#14)
       ;E#20
       ;EE#17[X#11,A#15[(var X#12)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#1= C#8[(\ X#3.S#5)]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#14)
       ;E#20
       ;EE#17[X#11,A#15[(\ X#10.S#14)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#16[(var X#11)],
           E#13  |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#20},
           E#19  |->  {X#1=C#8[(\ X#3.S#5)];E#20},
           E#4   |->  {X#9=(\ X#10.S#14);E#20;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|}}

and instantiated rules:

                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#20;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#20;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#20;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#20;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#21[A#23[(app A#24[(var X#12)] C#25[(var X#2)])]]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#11= A#21[A#23[(app A#24[(\ X#10.S#14)] C#25[(\ X#3.S#5)])]]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {C#22,A#20,C#8,A#15,A#21}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#21[A#23[(app A#24[(var X#12)] C#25)]]),
             ((var X#2),A#21[A#23[(app A#24[(var X#12)] C#25)]]),
             (S#5,A#21[A#23[(app A#24[(var X#12)] C#25)]]),
             ((var X#2),A#21[A#23[(app A#24[(var X#12)] C#25[[.]])]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#23[(app A#24[[.]] C#25[(\ X#3.S#5)])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           E#13         |->  {X#2=(\ X#3.S#5);E#19},
           EE#17[.1,.2] |-> {[.1]=A#21[[.2]]},
           X#1          |->  X#11,
           E#4          |->  {X#9=(\ X#10.S#14);E#19;VV#18|X#12,(var X#9)|},
           A#20         |->  A#21,
           C#8          |->  A#21[A#23[(app A#24[(var X#12)] C#25)]],
           C#22         |->  A#23[(app A#24[(var X#12)] C#25)],
           A#15         |->  A#23[(app A#24 C#25[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#11=A#21[A#23[(app A#24[(var X#12)] C#25[(\ X#3.S#5)])]];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#21[A#23[(app A#24[(var X#12)] C#25[(var X#2)])]];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#21[A#23[(app A#24[(var X#12)] C#25[(\ X#3.S#5)])]];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#11=A#21[A#23[(app A#24[(\ X#10.S#14)] C#25[(\ X#3.S#5)])]];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#21[(app A#22[A#15[(var X#12)]] C#23[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#11= A#21[(app A#22[A#15[(\ X#10.S#14)]] C#23[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {A#20,C#8,A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#21[(app A#22[A#15[(var X#12)]] C#23)]),
             ((var X#2),A#21[(app A#22[A#15[(var X#12)]] C#23)]),
             (S#5,A#21[(app A#22[A#15[(var X#12)]] C#23)]),
             ((var X#2),A#21[(app A#22[A#15[(var X#12)]] C#23[[.]])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           E#13         |->  {X#2=(\ X#3.S#5);E#19},
           EE#17[.1,.2] |-> {[.1]=A#21[(app A#22[[.2]] C#23[(\ X#3.S#5)])]},
           X#1          |->  X#11,
           E#4          |->  {X#9=(\ X#10.S#14);E#19;VV#18|X#12,(var X#9)|},
           C#8          |->  A#21[(app A#22[A#15[(var X#12)]] C#23)],
           A#20         |->  A#21[(app A#22 C#23[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#11=A#21[(app A#22[A#15[(var X#12)]] C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#21[(app A#22[A#15[(var X#12)]] C#23[(var X#2)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#21[(app A#22[A#15[(var X#12)]] C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#11=A#21[(app A#22[A#15[(\ X#10.S#14)]] C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#21[(app A#22[(var X#12)] C#23[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#11= A#21[(app A#22[(\ X#10.S#14)] C#23[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {C#8,A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#21[(app A#22[(var X#12)] C#23)]),
             ((var X#2),A#21[(app A#22[(var X#12)] C#23)]),
             (S#5,A#21[(app A#22[(var X#12)] C#23)]),
             ((var X#2),A#21[(app A#22[(var X#12)] C#23[[.]])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#21[(app A#22[[.]] C#23[(\ X#3.S#5)])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           E#13         |->  {X#2=(\ X#3.S#5);E#19},
           EE#17[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#11,
           E#4          |->  {X#9=(\ X#10.S#14);E#19;VV#18|X#12,(var X#9)|},
           A#20         |->  [.],
           C#8          |->  A#21[(app A#22[(var X#12)] C#23)],
           A#15         |->  A#21[(app A#22 C#23[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#11=A#21[(app A#22[(var X#12)] C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#21[(app A#22[(var X#12)] C#23[(var X#2)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#21[(app A#22[(var X#12)] C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#11=A#21[(app A#22[(\ X#10.S#14)] C#23[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= A#23[(app A#24[(var X#21)] C#25[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;EE#22[X#21,A#15[(var X#12)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#11= A#23[(app A#24[(var X#21)] C#25[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;EE#22[X#21,A#15[(\ X#10.S#14)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {A#20,C#8,A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#23[(app A#24[(var X#21)] C#25)]),
             ((var X#2),A#23[(app A#24[(var X#21)] C#25)]),
             (S#5,A#23[(app A#24[(var X#21)] C#25)]),
             ((var X#2),A#23[(app A#24[(var X#21)] C#25[[.]])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           E#13         |->  {X#2=(\ X#3.S#5);E#19},
           EE#17[.1,.2] |-> {[.1]=A#23[(app A#24[(var X#21)] C#25[(\ X#3.S#5)])];EE#22[X#21,[.2]]},
           X#1          |->  X#11,
           E#4          |->  {X#9=(\ X#10.S#14);E#19;EE#22[X#21,A#15[(var X#12)]];VV#18|X#12,(var X#9)|},
           C#8          |->  A#23[(app A#24[(var X#21)] C#25)],
           A#20         |->  A#23[(app A#24 C#25[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#11=A#23[(app A#24[(var X#21)] C#25[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;EE#22[X#21,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#11=A#23[(app A#24[(var X#21)] C#25[(var X#2)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;EE#22[X#21,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#11=A#23[(app A#24[(var X#21)] C#25[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;EE#22[X#21,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#11=A#23[(app A#24[(var X#21)] C#25[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(\ X#10.S#14);E#19;EE#22[X#21,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#21= A#25[(app A#26[(var X#22)] C#27[(var X#2)])]
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;EE#23[X#11,(var X#21)]
       ;EE#24[X#22,A#15[(var X#12)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#21= A#25[(app A#26[(var X#22)] C#27[(\ X#3.S#5)])]
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;EE#23[X#11,(var X#21)]
       ;EE#24[X#22,A#15[(\ X#10.S#14)]]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {A#20,C#8,A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#25[(app A#26[(var X#22)] C#27)]),
             ((var X#2),A#25[(app A#26[(var X#22)] C#27)]),
             (S#5,A#25[(app A#26[(var X#22)] C#27)]),
             ((var X#2),A#25[(app A#26[(var X#22)] C#27[[.]])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           E#13         |->  {X#2=(\ X#3.S#5);E#19},
           EE#17[.1,.2] |-> {X#21=A#25[(app A#26[(var X#22)] C#27[(\ X#3.S#5)])];EE#23[[.1],(var X#21)];EE#24[X#22,[.2]]},
           X#1          |->  X#21,
           E#4          |->  {X#9=(\ X#10.S#14);E#19;EE#23[X#11,(var X#21)];EE#24[X#22,A#15[(var X#12)]];VV#18|X#12,(var X#9)|},
           C#8          |->  A#25[(app A#26[(var X#22)] C#27)],
           A#20         |->  A#25[(app A#26 C#27[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#21=A#25[(app A#26[(var X#22)] C#27[(\ X#3.S#5)])];X#9=(\ X#10.S#14);E#19;EE#23[X#11,(var X#21)];EE#24[X#22,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#2)])];X#9=(\ X#10.S#14);E#19;EE#23[X#11,(var X#21)];EE#24[X#22,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#21=A#25[(app A#26[(var X#22)] C#27[(\ X#3.S#5)])];X#9=(\ X#10.S#14);E#19;EE#23[X#11,(var X#21)];EE#24[X#22,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#2=(\ X#3.S#5);X#21=A#25[(app A#26[(var X#22)] C#27[(\ X#3.S#5)])];X#9=(\ X#10.S#14);E#19;EE#23[X#11,(var X#21)];EE#24[X#22,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#21= A#23[A#25[(app A#26[(var X#12)] C#27[(var X#2)])]]
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;EE#22[X#11,(var X#21)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#21= A#23[A#25[(app A#26[(\ X#10.S#14)] C#27[(\ X#3.S#5)])]]
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;EE#22[X#11,(var X#21)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {C#24,A#20,C#8,A#15,A#23}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#23[A#25[(app A#26[(var X#12)] C#27)]]),
             ((var X#2),A#23[A#25[(app A#26[(var X#12)] C#27)]]),
             (S#5,A#23[A#25[(app A#26[(var X#12)] C#27)]]),
             ((var X#2),A#23[A#25[(app A#26[(var X#12)] C#27[[.]])]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#25[(app A#26[[.]] C#27[(\ X#3.S#5)])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           E#13         |->  {X#2=(\ X#3.S#5);E#19},
           EE#17[.1,.2] |-> {X#21=A#23[[.2]];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {X#9=(\ X#10.S#14);E#19;EE#22[X#11,(var X#21)];VV#18|X#12,(var X#9)|},
           A#20         |->  A#23,
           C#8          |->  A#23[A#25[(app A#26[(var X#12)] C#27)]],
           C#24         |->  A#25[(app A#26[(var X#12)] C#27)],
           A#15         |->  A#25[(app A#26 C#27[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#21=A#23[A#25[(app A#26[(var X#12)] C#27[(\ X#3.S#5)])]];X#9=(\ X#10.S#14);E#19;EE#22[X#11,(var X#21)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#21=A#23[A#25[(app A#26[(var X#12)] C#27[(var X#2)])]];X#9=(\ X#10.S#14);E#19;EE#22[X#11,(var X#21)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#21=A#23[A#25[(app A#26[(var X#12)] C#27[(\ X#3.S#5)])]];X#9=(\ X#10.S#14);E#19;EE#22[X#11,(var X#21)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#2=(\ X#3.S#5);X#21=A#23[A#25[(app A#26[(\ X#10.S#14)] C#27[(\ X#3.S#5)])]];X#9=(\ X#10.S#14);E#19;EE#22[X#11,(var X#21)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#21= A#23[(app A#24[A#15[(var X#12)]] C#25[(var X#2)])]
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;EE#22[X#11,(var X#21)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#21= A#23[(app A#24[A#15[(\ X#10.S#14)]] C#25[(\ X#3.S#5)])]
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;EE#22[X#11,(var X#21)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {A#20,C#8,A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#23[(app A#24[A#15[(var X#12)]] C#25)]),
             ((var X#2),A#23[(app A#24[A#15[(var X#12)]] C#25)]),
             (S#5,A#23[(app A#24[A#15[(var X#12)]] C#25)]),
             ((var X#2),A#23[(app A#24[A#15[(var X#12)]] C#25[[.]])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#15[[.]]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           E#13         |->  {X#2=(\ X#3.S#5);E#19},
           EE#17[.1,.2] |-> {X#21=A#23[(app A#24[[.2]] C#25[(\ X#3.S#5)])];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {X#9=(\ X#10.S#14);E#19;EE#22[X#11,(var X#21)];VV#18|X#12,(var X#9)|},
           C#8          |->  A#23[(app A#24[A#15[(var X#12)]] C#25)],
           A#20         |->  A#23[(app A#24 C#25[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#21=A#23[(app A#24[A#15[(var X#12)]] C#25[(\ X#3.S#5)])];X#9=(\ X#10.S#14);E#19;EE#22[X#11,(var X#21)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#21=A#23[(app A#24[A#15[(var X#12)]] C#25[(var X#2)])];X#9=(\ X#10.S#14);E#19;EE#22[X#11,(var X#21)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#21=A#23[(app A#24[A#15[(var X#12)]] C#25[(\ X#3.S#5)])];X#9=(\ X#10.S#14);E#19;EE#22[X#11,(var X#21)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#2=(\ X#3.S#5);X#21=A#23[(app A#24[A#15[(\ X#10.S#14)]] C#25[(\ X#3.S#5)])];X#9=(\ X#10.S#14);E#19;EE#22[X#11,(var X#21)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#21= A#23[(app A#24[(var X#12)] C#25[(var X#2)])]
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;EE#22[X#11,(var X#21)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#21= A#23[(app A#24[(\ X#10.S#14)] C#25[(\ X#3.S#5)])]
       ;X#9= (\ X#10.S#14)
       ;E#19
       ;EE#22[X#11,(var X#21)]
       ;VV#18|X#12,(var X#9)|
     in
        A#16[(var X#11)]
     )
  )

where

   Delta1 = {C#8,A#15}
   Delta2 = {}
   Delta3 = {((\ X#3.S#5),A#23[(app A#24[(var X#12)] C#25)]),
             ((var X#2),A#23[(app A#24[(var X#12)] C#25)]),
             (S#5,A#23[(app A#24[(var X#12)] C#25)]),
             ((var X#2),A#23[(app A#24[(var X#12)] C#25[[.]])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]]),
             ((var X#12),A#23[(app A#24[[.]] C#25[(\ X#3.S#5)])]),
             ((var X#9),[.]),
             ((var X#11),A#16[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,cp-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(\ X#10.S#14)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    and constraints: A#15/= [.]

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(\ X#10.S#14);E#13;EE#17[X#11,A#15[(var X#12)]];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])}
      Delta1=  {A#15}
      Delta2=  {}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#2),C#8[[.]]),((var X#9),[.]),((var X#11),A#16[[.]]),((var X#12),A#15[[.]]),((var X#9),[.]),((var X#11),A#16[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#16[(var X#11)],
           E#13         |->  {X#2=(\ X#3.S#5);E#19},
           EE#17[.1,.2] |-> {X#21=[.2];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {X#9=(\ X#10.S#14);E#19;EE#22[X#11,(var X#21)];VV#18|X#12,(var X#9)|},
           A#20         |->  [.],
           C#8          |->  A#23[(app A#24[(var X#12)] C#25)],
           A#15         |->  A#23[(app A#24 C#25[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#21=A#23[(app A#24[(var X#12)] C#25[(\ X#3.S#5)])];X#9=(\ X#10.S#14);E#19;EE#22[X#11,(var X#21)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#21=A#23[(app A#24[(var X#12)] C#25[(var X#2)])];X#9=(\ X#10.S#14);E#19;EE#22[X#11,(var X#21)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#21=A#23[(app A#24[(var X#12)] C#25[(\ X#3.S#5)])];X#9=(\ X#10.S#14);E#19;EE#22[X#11,(var X#21)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    -SR,cp-e2->                   (letrec {X#2=(\ X#3.S#5);X#21=A#23[(app A#24[(\ X#10.S#14)] C#25[(\ X#3.S#5)])];X#9=(\ X#10.S#14);E#19;EE#22[X#11,(var X#21)];VV#18|X#12,(var X#9)|} in A#16[(var X#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        (letrec
           E#10
        in
           T#13[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
        )
     )
    ,
     (letrec
        E#10
       ;E#9
     in
        T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
     )
  )

where

   Delta1 = {T#12,T#7}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             [{E#9},(letrec {E#10} in [.])],
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-in1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in (letrec {E#10} in S#11))
    -SR,llet-in1->                (letrec {E#10;E#9} in S#11)
    and constraints: E#9/= {}, E#10/= {}, ({E#9},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in (letrec {E#10} in S#11))}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),[{E#9},(letrec {E#10} in [.])],((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#9} in (letrec {E#10} in T#13)),
           T#12  |->  (letrec {E#10} in T#13),
           S#11  |->  T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {E#9} in (letrec {E#10} in T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]))
    -cp-e1->                      (letrec {E#9} in (letrec {E#10} in T#13[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]))
    ................................................................................
                                  (letrec {E#9} in (letrec {E#10} in T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]))
    -SR,llet-in1->                (letrec {E#10;E#9} in T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        (letrec
           X#14= T#13[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
          ;E#16
        in
           S#11
        )
     )
    ,
     (letrec
        X#14= T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;E#16
       ;E#9
     in
        S#11
     )
  )

where

   Delta1 = {T#12,T#7}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             [{E#9},(letrec {X#14=T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#16} in [.])],
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-in1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in (letrec {E#10} in S#11))
    -SR,llet-in1->                (letrec {E#10;E#9} in S#11)
    and constraints: E#9/= {}, E#10/= {}, ({E#9},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in (letrec {E#10} in S#11))}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),[{E#9},(letrec {E#10} in [.])],((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#9} in (letrec {X#14=T#13;E#16} in S#11)),
           T#12  |->  (letrec {X#14=T#13;E#16} in S#11),
           E#10  |->  {X#14=T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {E#9} in (letrec {X#14=T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#16} in S#11))
    -cp-e1->                      (letrec {E#9} in (letrec {X#14=T#13[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#16} in S#11))
    ................................................................................
                                  (letrec {E#9} in (letrec {X#14=T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#16} in S#11))
    -SR,llet-in1->                (letrec {X#14=T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#16;E#9} in S#11)
    

================================================================================
Critical Pair:

  (
     (letrec {E#9} in (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#14} in S#11))
    ,
     (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#14;E#9} in S#11)
  )

where

   Delta1 = {T#7}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             [{E#9},(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#14} in [.])],
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-in1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in (letrec {E#10} in S#11))
    -SR,llet-in1->                (letrec {E#10;E#9} in S#11)
    and constraints: E#9/= {}, E#10/= {}, ({E#9},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in (letrec {E#10} in S#11))}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),[{E#9},(letrec {E#10} in [.])],((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#9} in [.]),
           T#12  |->  [.],
           S#6   |->  S#11,
           E#10  |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#14},
           E#13  |->  {X#1=C#8[(\ X#3.S#5)];E#14},
           E#4   |->  {E#14}}

and instantiated rules:

                                  (letrec {E#9} in (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#14} in S#11))
    -cp-e1->                      (letrec {E#9} in (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#14} in S#11))
    ................................................................................
                                  (letrec {E#9} in (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#14} in S#11))
    -SR,llet-in1->                (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#14;E#9} in S#11)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;E#15
     in
        (letrec {E#10} in S#11)
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;E#10
       ;E#15
     in
        S#11
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             [{X#13=T#12[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#15},(letrec {E#10} in [.])],
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-in1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in (letrec {E#10} in S#11))
    -SR,llet-in1->                (letrec {E#10;E#9} in S#11)
    and constraints: E#9/= {}, E#10/= {}, ({E#9},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in (letrec {E#10} in S#11))}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),[{E#9},(letrec {E#10} in [.])],((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#13=T#12;E#15} in (letrec {E#10} in S#11)),
           E#9   |->  {X#13=T#12[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#15} in (letrec {E#10} in S#11))
    -cp-e1->                      (letrec {X#13=T#12[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#15} in (letrec {E#10} in S#11))
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#15} in (letrec {E#10} in S#11))
    -SR,llet-in1->                (letrec {X#13=T#12[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#10;E#15} in S#11)
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#13} in (letrec {E#10} in S#11))
    ,
     (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#10;E#13} in S#11)
  )

where

   Delta1 = {}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             [{X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#13},(letrec {E#10} in [.])],
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-in1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in (letrec {E#10} in S#11))
    -SR,llet-in1->                (letrec {E#10;E#9} in S#11)
    and constraints: E#9/= {}, E#10/= {}, ({E#9},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in (letrec {E#10} in S#11))}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),[{E#9},(letrec {E#10} in [.])],((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  (letrec {E#10} in S#11),
           E#9   |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#13},
           E#12  |->  {X#1=C#8[(\ X#3.S#5)];E#13},
           E#4   |->  {E#13}}

and instantiated rules:

                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#13} in (letrec {E#10} in S#11))
    -cp-e1->                      (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#13} in (letrec {E#10} in S#11))
    ................................................................................
                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#13} in (letrec {E#10} in S#11))
    -SR,llet-in1->                (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#10;E#13} in S#11)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (letrec {E#10} in S#12)
       ;E#11
     in
        A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
    ,
     (letrec
        X#9= S#12
       ;E#10
       ;E#11
     in
        A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
  )

where

   Delta1 = {A#13,T#14,T#7}
   Delta2 = {E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])],(letrec {E#10} in [.])),
             [{E#11},(letrec {E#10} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),A#15[(app A#16[[.]] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]),
             ((var X#9),A#15[(app A#16[[.]] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])
    -SR,llet-e1->                 (letrec {X#9=S#12;E#10;E#11} in A#13[(var X#9)])
    and constraints: E#10/= {}, (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11},(letrec {E#10} in [.])],((var X#2),C#8[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#15[(app A#16[(var X#9)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#9)] T#17)],
           A#13  |->  A#15[(app A#16 T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -cp-e1->                      (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    ................................................................................
                                  (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -SR,llet-e1->                 (letrec {X#9=S#12;E#10;E#11} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (letrec
                E#10
             in
                T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
             )
       ;E#11
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#9= T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;E#10
       ;E#11
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#14,T#7}
   Delta2 = {E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{E#11},(letrec {E#10} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])
    -SR,llet-e1->                 (letrec {X#9=S#12;E#10;E#11} in A#13[(var X#9)])
    and constraints: E#10/= {}, (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11},(letrec {E#10} in [.])],((var X#2),C#8[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#9=(letrec {E#10} in T#17);E#11} in A#13[(var X#9)]),
           X#15  |->  X#9,
           E#16  |->  {E#11},
           T#14  |->  (letrec {E#10} in T#17),
           S#12  |->  T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {X#9=(letrec {E#10} in T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#11} in A#13[(var X#9)])
    -cp-e1->                      (letrec {X#9=(letrec {E#10} in T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#11} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#9=(letrec {E#10} in T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#11} in A#13[(var X#9)])
    -SR,llet-e1->                 (letrec {X#9=T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#10;E#11} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (letrec
                X#18= T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
               ;E#20
             in
                S#12
             )
       ;E#11
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#18= T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;X#9= S#12
       ;E#11
       ;E#20
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#14,T#7}
   Delta2 = {E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (A#13[(var X#9)],(letrec {X#18=T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#20} in [.])),
             [{E#11},(letrec {X#18=T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#20} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])
    -SR,llet-e1->                 (letrec {X#9=S#12;E#10;E#11} in A#13[(var X#9)])
    and constraints: E#10/= {}, (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11},(letrec {E#10} in [.])],((var X#2),C#8[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#9=(letrec {X#18=T#17;E#20} in S#12);E#11} in A#13[(var X#9)]),
           X#15  |->  X#9,
           E#16  |->  {E#11},
           T#14  |->  (letrec {X#18=T#17;E#20} in S#12),
           E#10  |->  {X#18=T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#20},
           E#19  |->  {E#20}}

and instantiated rules:

                                  (letrec {X#9=(letrec {X#18=T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#20} in S#12);E#11} in A#13[(var X#9)])
    -cp-e1->                      (letrec {X#9=(letrec {X#18=T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#20} in S#12);E#11} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#9=(letrec {X#18=T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#20} in S#12);E#11} in A#13[(var X#9)])
    -SR,llet-e1->                 (letrec {X#18=T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=S#12;E#11;E#20} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#18} in S#12)
       ;E#11
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= C#8[(\ X#3.S#5)]
       ;X#2= (\ X#3.S#5)
       ;X#9= S#12
       ;E#11
       ;E#18
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (A#13[(var X#9)],(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#18} in [.])),
             [{E#11},(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#18} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])
    -SR,llet-e1->                 (letrec {X#9=S#12;E#10;E#11} in A#13[(var X#9)])
    and constraints: E#10/= {}, (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11},(letrec {E#10} in [.])],((var X#2),C#8[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#9=[.];E#11} in A#13[(var X#9)]),
           X#15  |->  X#9,
           E#16  |->  {E#11},
           T#14  |->  [.],
           S#6   |->  S#12,
           E#10  |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#18},
           E#17  |->  {X#1=C#8[(\ X#3.S#5)];E#18},
           E#4   |->  {E#18}}

and instantiated rules:

                                  (letrec {X#9=(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#18} in S#12);E#11} in A#13[(var X#9)])
    -cp-e1->                      (letrec {X#9=(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#18} in S#12);E#11} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#9=(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#18} in S#12);E#11} in A#13[(var X#9)])
    -SR,llet-e1->                 (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=S#12;E#11;E#18} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;X#9= (letrec {E#10} in S#12)
       ;E#17
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;X#9= S#12
       ;E#10
       ;E#17
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17},(letrec {E#10} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])
    -SR,llet-e1->                 (letrec {X#9=S#12;E#10;E#11} in A#13[(var X#9)])
    and constraints: E#10/= {}, (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11},(letrec {E#10} in [.])],((var X#2),C#8[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#15=T#14;X#9=(letrec {E#10} in S#12);E#17} in A#13[(var X#9)]),
           E#11  |->  {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17},
           E#16  |->  {X#9=(letrec {E#10} in S#12);E#17}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(letrec {E#10} in S#12);E#17} in A#13[(var X#9)])
    -cp-e1->                      (letrec {X#15=T#14[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(letrec {E#10} in S#12);E#17} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(letrec {E#10} in S#12);E#17} in A#13[(var X#9)])
    -SR,llet-e1->                 (letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=S#12;E#10;E#17} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (letrec {E#10} in C#15[(var X#2)])
       ;E#14
     in
        A#13[(var X#9)]
     )
    ,
     (letrec {X#2=(\ X#3.S#5);X#9=C#15[(\ X#3.S#5)];E#10;E#14} in A#13[(var X#9)])
  )

where

   Delta1 = {C#8}
   Delta2 = {E#10}
   Delta3 = {((\ X#3.S#5),(letrec {E#10} in C#15)),
             ((var X#2),(letrec {E#10} in C#15)),
             (S#5,(letrec {E#10} in C#15)),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#2=(\ X#3.S#5);E#14},(letrec {E#10} in [.])],
             ((var X#2),(letrec {E#10} in C#15[[.]])),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])
    -SR,llet-e1->                 (letrec {X#9=S#12;E#10;E#11} in A#13[(var X#9)])
    and constraints: E#10/= {}, (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11},(letrec {E#10} in [.])],((var X#2),C#8[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#13[(var X#9)],
           E#11  |->  {X#2=(\ X#3.S#5);E#14},
           X#1   |->  X#9,
           E#4   |->  {E#14},
           C#8   |->  (letrec {E#10} in C#15),
           S#12  |->  C#15[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=(letrec {E#10} in C#15[(\ X#3.S#5)]);E#14} in A#13[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=(letrec {E#10} in C#15[(var X#2)]);E#14} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=(letrec {E#10} in C#15[(\ X#3.S#5)]);E#14} in A#13[(var X#9)])
    -SR,llet-e1->                 (letrec {X#2=(\ X#3.S#5);X#9=C#15[(\ X#3.S#5)];E#10;E#14} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (letrec {X#16=C#15[(var X#2)];E#18} in S#12)
       ;E#14
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= C#15[(\ X#3.S#5)]
       ;X#2= (\ X#3.S#5)
       ;X#9= S#12
       ;E#14
       ;E#18
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {C#8}
   Delta2 = {E#10}
   Delta3 = {((\ X#3.S#5),(letrec {X#16=C#15;E#18} in S#12)),
             ((var X#2),(letrec {X#16=C#15;E#18} in S#12)),
             (S#5,(letrec {X#16=C#15;E#18} in S#12)),
             (A#13[(var X#9)],(letrec {X#16=C#15[(\ X#3.S#5)];E#18} in [.])),
             [{X#2=(\ X#3.S#5);E#14},(letrec {X#16=C#15[(\ X#3.S#5)];E#18} in [.])],
             ((var X#2),(letrec {X#16=C#15[[.]];E#18} in S#12)),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])
    -SR,llet-e1->                 (letrec {X#9=S#12;E#10;E#11} in A#13[(var X#9)])
    and constraints: E#10/= {}, (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11},(letrec {E#10} in [.])],((var X#2),C#8[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#13[(var X#9)],
           E#11  |->  {X#2=(\ X#3.S#5);E#14},
           X#1   |->  X#9,
           E#4   |->  {E#14},
           C#8   |->  (letrec {X#16=C#15;E#18} in S#12),
           E#10  |->  {X#16=C#15[(\ X#3.S#5)];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=(letrec {X#16=C#15[(\ X#3.S#5)];E#18} in S#12);E#14} in A#13[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=(letrec {X#16=C#15[(var X#2)];E#18} in S#12);E#14} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=(letrec {X#16=C#15[(\ X#3.S#5)];E#18} in S#12);E#14} in A#13[(var X#9)])
    -SR,llet-e1->                 (letrec {X#16=C#15[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=S#12;E#14;E#18} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#8[(var X#2)]
       ;X#2= (\ X#3.S#5)
       ;X#9= (letrec {E#10} in S#12)
       ;E#15
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= C#8[(\ X#3.S#5)]
       ;X#2= (\ X#3.S#5)
       ;X#9= S#12
       ;E#10
       ;E#15
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15},(letrec {E#10} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])
    -SR,llet-e1->                 (letrec {X#9=S#12;E#10;E#11} in A#13[(var X#9)])
    and constraints: E#10/= {}, (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#10} in S#12);E#11} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11},(letrec {E#10} in [.])],((var X#2),C#8[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#13[(var X#9)],
           E#11  |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15},
           E#14  |->  {X#1=C#8[(\ X#3.S#5)];E#15},
           E#4   |->  {X#9=(letrec {E#10} in S#12);E#15}}

and instantiated rules:

                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(letrec {E#10} in S#12);E#15} in A#13[(var X#9)])
    -cp-e1->                      (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);X#9=(letrec {E#10} in S#12);E#15} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(letrec {E#10} in S#12);E#15} in A#13[(var X#9)])
    -SR,llet-e1->                 (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=S#12;E#10;E#15} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (letrec {E#11} in S#13)
       ;E#12
       ;EE#15[X#10,(var X#9)]
     in
        A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
    ,
     (letrec
        X#9= S#13
       ;E#11
       ;E#12
       ;EE#15[X#10,(var X#9)]
     in
        A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
  )

where

   Delta1 = {A#14,T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),
             (A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])],(letrec {E#11} in [.])),
             [{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#17[(app A#18[[.]] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]),
             ((var X#9),[.]),
             ((var X#10),A#17[(app A#18[[.]] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#17[(app A#18[(var X#10)] T#19)]),
           T#16  |->  A#17[(app A#18[(var X#10)] T#19)],
           A#14  |->  A#17[(app A#18 T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -cp-e1->                      (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (letrec
                E#11
             in
                T#19[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
             )
       ;E#12
       ;EE#15[X#10,(var X#9)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#9= T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;E#11
       ;E#12
       ;EE#15[X#10,(var X#9)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),
             (A#14[(var X#10)],(letrec {E#11} in [.])),
             [{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#9=(letrec {E#11} in T#19);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)]),
           X#17  |->  X#9,
           E#18  |->  {E#12;EE#15[X#10,(var X#9)]},
           T#16  |->  (letrec {E#11} in T#19),
           S#13  |->  T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {X#9=(letrec {E#11} in T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -cp-e1->                      (letrec {X#9=(letrec {E#11} in T#19[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (letrec
                X#20= T#19[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
               ;E#22
             in
                S#13
             )
       ;E#12
       ;EE#15[X#10,(var X#9)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#20= T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;X#9= S#13
       ;E#12
       ;E#22
       ;EE#15[X#10,(var X#9)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#9),(letrec {X#20=T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#12;E#22;EE#15[X#10,(var X#9)]} in [.])),
             (A#14[(var X#10)],(letrec {X#20=T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#22} in [.])),
             [{E#12;EE#15[X#10,(var X#9)]},(letrec {X#20=T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#22} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#9=(letrec {X#20=T#19;E#22} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)]),
           X#17  |->  X#9,
           E#18  |->  {E#12;EE#15[X#10,(var X#9)]},
           T#16  |->  (letrec {X#20=T#19;E#22} in S#13),
           E#11  |->  {X#20=T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#22},
           E#21  |->  {E#22}}

and instantiated rules:

                                  (letrec {X#9=(letrec {X#20=T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#22} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -cp-e1->                      (letrec {X#9=(letrec {X#20=T#19[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#22} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#9=(letrec {X#20=T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#22} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#20=T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=S#13;E#12;E#22;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#20} in S#13)
       ;E#12
       ;EE#15[X#10,(var X#9)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#1= C#8[(\ X#3.S#5)]
       ;X#2= (\ X#3.S#5)
       ;X#9= S#13
       ;E#12
       ;E#20
       ;EE#15[X#10,(var X#9)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#9),(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#12;E#20;EE#15[X#10,(var X#9)]} in [.])),
             (A#14[(var X#10)],(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#20} in [.])),
             [{E#12;EE#15[X#10,(var X#9)]},(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#20} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#9=[.];E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)]),
           X#17  |->  X#9,
           E#18  |->  {E#12;EE#15[X#10,(var X#9)]},
           T#16  |->  [.],
           S#6   |->  S#13,
           E#11  |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#20},
           E#19  |->  {X#1=C#8[(\ X#3.S#5)];E#20},
           E#4   |->  {E#20}}

and instantiated rules:

                                  (letrec {X#9=(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#20} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -cp-e1->                      (letrec {X#9=(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#20} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#9=(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#20} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=S#13;E#12;E#20;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;X#9= (letrec {E#11} in S#13)
       ;E#19
       ;EE#15[X#10,(var X#9)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;X#9= S#13
       ;E#11
       ;E#19
       ;EE#15[X#10,(var X#9)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#9),(letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#11;E#19;EE#15[X#10,(var X#9)]} in [.])),
             (A#14[(var X#10)],(letrec {E#11} in [.])),
             [{X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#17=T#16;X#9=(letrec {E#11} in S#13);E#19;EE#15[X#10,(var X#9)]} in A#14[(var X#10)]),
           E#12  |->  {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19},
           E#18  |->  {X#9=(letrec {E#11} in S#13);E#19;EE#15[X#10,(var X#9)]}}

and instantiated rules:

                                  (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(letrec {E#11} in S#13);E#19;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -cp-e1->                      (letrec {X#17=T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(letrec {E#11} in S#13);E#19;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=(letrec {E#11} in S#13);E#19;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];X#9=S#13;E#11;E#19;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[(app A#21[(var X#9)] T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (letrec {E#11} in S#13)
       ;E#12
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[(app A#21[(var X#9)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= S#13
       ;E#11
       ;E#12
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#9),(letrec {X#10=A#20[(app A#21[(var X#9)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;E#12} in [.])),
             (A#14[(var X#10)],(letrec {E#11} in [.])),
             [{X#10=A#20[(app A#21[(var X#9)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#12},(letrec {E#11} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#10=A#20[(app A#21[(var X#9)] T#22)];X#9=(letrec {E#11} in S#13);E#12} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {[.1]=A#20[(app A#21[[.2]] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]},
           X#17         |->  X#10,
           E#18         |->  {X#9=(letrec {E#11} in S#13);E#12},
           T#16         |->  A#20[(app A#21[(var X#9)] T#22)],
           A#19         |->  A#20[(app A#21 T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#10=A#20[(app A#21[(var X#9)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(letrec {E#11} in S#13);E#12} in A#14[(var X#10)])
    -cp-e1->                      (letrec {X#10=A#20[(app A#21[(var X#9)] T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(letrec {E#11} in S#13);E#12} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[(app A#21[(var X#9)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(letrec {E#11} in S#13);E#12} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#10=A#20[(app A#21[(var X#9)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=S#13;E#11;E#12} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (letrec {E#11} in S#13)
       ;E#12
       ;EE#21[X#20,(var X#9)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= S#13
       ;E#11
       ;E#12
       ;EE#21[X#20,(var X#9)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#9),(letrec {X#10=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;E#12;EE#21[X#20,(var X#9)]} in [.])),
             (A#14[(var X#10)],(letrec {E#11} in [.])),
             [{X#10=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#12;EE#21[X#20,(var X#9)]},(letrec {E#11} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#10=A#22[(app A#23[(var X#20)] T#24)];X#9=(letrec {E#11} in S#13);E#12;EE#21[X#20,(var X#9)]} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {[.1]=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];EE#21[X#20,[.2]]},
           X#17         |->  X#10,
           E#18         |->  {X#9=(letrec {E#11} in S#13);E#12;EE#21[X#20,(var X#9)]},
           T#16         |->  A#22[(app A#23[(var X#20)] T#24)],
           A#19         |->  A#22[(app A#23 T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(letrec {E#11} in S#13);E#12;EE#21[X#20,(var X#9)]} in A#14[(var X#10)])
    -cp-e1->                      (letrec {X#10=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(letrec {E#11} in S#13);E#12;EE#21[X#20,(var X#9)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(letrec {E#11} in S#13);E#12;EE#21[X#20,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#10=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=S#13;E#11;E#12;EE#21[X#20,(var X#9)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (letrec {E#11} in S#13)
       ;E#12
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#21,(var X#9)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#20= A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= S#13
       ;E#11
       ;E#12
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#21,(var X#9)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#9),(letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;E#12;EE#22[X#10,(var X#20)];EE#23[X#21,(var X#9)]} in [.])),
             (A#14[(var X#10)],(letrec {E#11} in [.])),
             [{X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#12;EE#22[X#10,(var X#20)];EE#23[X#21,(var X#9)]},(letrec {E#11} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26)];X#9=(letrec {E#11} in S#13);E#12;EE#22[X#10,(var X#20)];EE#23[X#21,(var X#9)]} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];EE#22[[.1],(var X#20)];EE#23[X#21,[.2]]},
           X#17         |->  X#20,
           E#18         |->  {X#9=(letrec {E#11} in S#13);E#12;EE#22[X#10,(var X#20)];EE#23[X#21,(var X#9)]},
           T#16         |->  A#24[(app A#25[(var X#21)] T#26)],
           A#19         |->  A#24[(app A#25 T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(letrec {E#11} in S#13);E#12;EE#22[X#10,(var X#20)];EE#23[X#21,(var X#9)]} in A#14[(var X#10)])
    -cp-e1->                      (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(letrec {E#11} in S#13);E#12;EE#22[X#10,(var X#20)];EE#23[X#21,(var X#9)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(letrec {E#11} in S#13);E#12;EE#22[X#10,(var X#20)];EE#23[X#21,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=S#13;E#11;E#12;EE#22[X#10,(var X#20)];EE#23[X#21,(var X#9)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= (letrec {E#11} in S#13)
       ;E#12
       ;EE#21[X#10,(var X#20)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#20= A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;X#9= S#13
       ;E#11
       ;E#12
       ;EE#21[X#10,(var X#20)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#9),(letrec {X#20=A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#11;E#12;EE#21[X#10,(var X#20)]} in [.])),
             (A#14[(var X#10)],(letrec {E#11} in [.])),
             [{X#20=A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#12;EE#21[X#10,(var X#20)]},(letrec {E#11} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=A#22[(app A#23[(var X#9)] T#24)];X#9=(letrec {E#11} in S#13);E#12;EE#21[X#10,(var X#20)]} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {X#20=A#22[(app A#23[[.2]] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {X#9=(letrec {E#11} in S#13);E#12;EE#21[X#10,(var X#20)]},
           T#16         |->  A#22[(app A#23[(var X#9)] T#24)],
           A#19         |->  A#22[(app A#23 T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(letrec {E#11} in S#13);E#12;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    -cp-e1->                      (letrec {X#20=A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(letrec {E#11} in S#13);E#12;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#20=A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=(letrec {E#11} in S#13);E#12;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#20=A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];X#9=S#13;E#11;E#12;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (letrec {E#11} in C#17[(var X#2)])
       ;E#16
       ;EE#15[X#10,(var X#9)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= C#17[(\ X#3.S#5)]
       ;E#11
       ;E#16
       ;EE#15[X#10,(var X#9)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),(letrec {E#11} in C#17)),
             ((var X#2),(letrec {E#11} in C#17)),
             (S#5,(letrec {E#11} in C#17)),
             ((var X#9),(letrec {X#2=(\ X#3.S#5);E#11;E#16;EE#15[X#10,(var X#9)]} in [.])),
             (A#14[(var X#10)],(letrec {E#11} in [.])),
             [{X#2=(\ X#3.S#5);E#16;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],
             ((var X#2),(letrec {E#11} in C#17[[.]])),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#14[(var X#10)],
           E#12  |->  {X#2=(\ X#3.S#5);E#16},
           X#1   |->  X#9,
           E#4   |->  {E#16;EE#15[X#10,(var X#9)]},
           C#8   |->  (letrec {E#11} in C#17),
           S#13  |->  C#17[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=(letrec {E#11} in C#17[(\ X#3.S#5)]);E#16;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=(letrec {E#11} in C#17[(var X#2)]);E#16;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=(letrec {E#11} in C#17[(\ X#3.S#5)]);E#16;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#2=(\ X#3.S#5);X#9=C#17[(\ X#3.S#5)];E#11;E#16;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (letrec {X#18=C#17[(var X#2)];E#20} in S#13)
       ;E#16
       ;EE#15[X#10,(var X#9)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#18= C#17[(\ X#3.S#5)]
       ;X#2= (\ X#3.S#5)
       ;X#9= S#13
       ;E#16
       ;E#20
       ;EE#15[X#10,(var X#9)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),(letrec {X#18=C#17;E#20} in S#13)),
             ((var X#2),(letrec {X#18=C#17;E#20} in S#13)),
             (S#5,(letrec {X#18=C#17;E#20} in S#13)),
             ((var X#9),(letrec {X#18=C#17[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#16;E#20;EE#15[X#10,(var X#9)]} in [.])),
             (A#14[(var X#10)],(letrec {X#18=C#17[(\ X#3.S#5)];E#20} in [.])),
             [{X#2=(\ X#3.S#5);E#16;EE#15[X#10,(var X#9)]},(letrec {X#18=C#17[(\ X#3.S#5)];E#20} in [.])],
             ((var X#2),(letrec {X#18=C#17[[.]];E#20} in S#13)),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#14[(var X#10)],
           E#12  |->  {X#2=(\ X#3.S#5);E#16},
           X#1   |->  X#9,
           E#4   |->  {E#16;EE#15[X#10,(var X#9)]},
           C#8   |->  (letrec {X#18=C#17;E#20} in S#13),
           E#11  |->  {X#18=C#17[(\ X#3.S#5)];E#20},
           E#19  |->  {E#20}}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=(letrec {X#18=C#17[(\ X#3.S#5)];E#20} in S#13);E#16;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=(letrec {X#18=C#17[(var X#2)];E#20} in S#13);E#16;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=(letrec {X#18=C#17[(\ X#3.S#5)];E#20} in S#13);E#16;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#18=C#17[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=S#13;E#16;E#20;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#8[(var X#2)]
       ;X#2= (\ X#3.S#5)
       ;X#9= (letrec {E#11} in S#13)
       ;E#17
       ;EE#15[X#10,(var X#9)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#1= C#8[(\ X#3.S#5)]
       ;X#2= (\ X#3.S#5)
       ;X#9= S#13
       ;E#11
       ;E#17
       ;EE#15[X#10,(var X#9)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             ((var X#9),(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#11;E#17;EE#15[X#10,(var X#9)]} in [.])),
             (A#14[(var X#10)],(letrec {E#11} in [.])),
             [{X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],
             ((var X#2),C#8[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#14[(var X#10)],
           E#12  |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17},
           E#16  |->  {X#1=C#8[(\ X#3.S#5)];E#17},
           E#4   |->  {X#9=(letrec {E#11} in S#13);E#17;EE#15[X#10,(var X#9)]}}

and instantiated rules:

                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(letrec {E#11} in S#13);E#17;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -cp-e1->                      (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);X#9=(letrec {E#11} in S#13);E#17;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=(letrec {E#11} in S#13);E#17;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);X#9=S#13;E#11;E#17;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#18[(app A#19[(var X#9)] C#20[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (letrec {E#11} in S#13)
       ;E#16
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#18[(app A#19[(var X#9)] C#20[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= S#13
       ;E#11
       ;E#16
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#17,C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),A#18[(app A#19[(var X#9)] C#20)]),
             ((var X#2),A#18[(app A#19[(var X#9)] C#20)]),
             (S#5,A#18[(app A#19[(var X#9)] C#20)]),
             ((var X#9),(letrec {X#10=A#18[(app A#19[(var X#9)] C#20[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#11;E#16} in [.])),
             (A#14[(var X#10)],(letrec {E#11} in [.])),
             [{X#10=A#18[(app A#19[(var X#9)] C#20[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16},(letrec {E#11} in [.])],
             ((var X#2),A#18[(app A#19[(var X#9)] C#20[[.]])]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#10)],
           E#12         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] C#20[(\ X#3.S#5)])]},
           X#1          |->  X#10,
           E#4          |->  {X#9=(letrec {E#11} in S#13);E#16},
           C#8          |->  A#18[(app A#19[(var X#9)] C#20)],
           A#17         |->  A#18[(app A#19 C#20[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#18[(app A#19[(var X#9)] C#20[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(letrec {E#11} in S#13);E#16} in A#14[(var X#10)])
    -cp-e1->                      (letrec {X#10=A#18[(app A#19[(var X#9)] C#20[(var X#2)])];X#2=(\ X#3.S#5);X#9=(letrec {E#11} in S#13);E#16} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#18[(app A#19[(var X#9)] C#20[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(letrec {E#11} in S#13);E#16} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#10=A#18[(app A#19[(var X#9)] C#20[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=S#13;E#11;E#16} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[(app A#21[(var X#18)] C#22[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (letrec {E#11} in S#13)
       ;E#16
       ;EE#19[X#18,(var X#9)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= S#13
       ;E#11
       ;E#16
       ;EE#19[X#18,(var X#9)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#17,C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),A#20[(app A#21[(var X#18)] C#22)]),
             ((var X#2),A#20[(app A#21[(var X#18)] C#22)]),
             (S#5,A#20[(app A#21[(var X#18)] C#22)]),
             ((var X#9),(letrec {X#10=A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#11;E#16;EE#19[X#18,(var X#9)]} in [.])),
             (A#14[(var X#10)],(letrec {E#11} in [.])),
             [{X#10=A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#19[X#18,(var X#9)]},(letrec {E#11} in [.])],
             ((var X#2),A#20[(app A#21[(var X#18)] C#22[[.]])]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#10)],
           E#12         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])];EE#19[X#18,[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#9=(letrec {E#11} in S#13);E#16;EE#19[X#18,(var X#9)]},
           C#8          |->  A#20[(app A#21[(var X#18)] C#22)],
           A#17         |->  A#20[(app A#21 C#22[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(letrec {E#11} in S#13);E#16;EE#19[X#18,(var X#9)]} in A#14[(var X#10)])
    -cp-e1->                      (letrec {X#10=A#20[(app A#21[(var X#18)] C#22[(var X#2)])];X#2=(\ X#3.S#5);X#9=(letrec {E#11} in S#13);E#16;EE#19[X#18,(var X#9)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(letrec {E#11} in S#13);E#16;EE#19[X#18,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#10=A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=S#13;E#11;E#16;EE#19[X#18,(var X#9)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] C#24[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (letrec {E#11} in S#13)
       ;E#16
       ;EE#20[X#10,(var X#18)]
       ;EE#21[X#19,(var X#9)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= S#13
       ;E#11
       ;E#16
       ;EE#20[X#10,(var X#18)]
       ;EE#21[X#19,(var X#9)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#17,C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),A#22[(app A#23[(var X#19)] C#24)]),
             ((var X#2),A#22[(app A#23[(var X#19)] C#24)]),
             (S#5,A#22[(app A#23[(var X#19)] C#24)]),
             ((var X#9),(letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#11;E#16;EE#20[X#10,(var X#18)];EE#21[X#19,(var X#9)]} in [.])),
             (A#14[(var X#10)],(letrec {E#11} in [.])),
             [{X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#20[X#10,(var X#18)];EE#21[X#19,(var X#9)]},(letrec {E#11} in [.])],
             ((var X#2),A#22[(app A#23[(var X#19)] C#24[[.]])]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#10)],
           E#12         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#1          |->  X#18,
           E#4          |->  {X#9=(letrec {E#11} in S#13);E#16;EE#20[X#10,(var X#18)];EE#21[X#19,(var X#9)]},
           C#8          |->  A#22[(app A#23[(var X#19)] C#24)],
           A#17         |->  A#22[(app A#23 C#24[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(letrec {E#11} in S#13);E#16;EE#20[X#10,(var X#18)];EE#21[X#19,(var X#9)]} in A#14[(var X#10)])
    -cp-e1->                      (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(var X#2)])];X#2=(\ X#3.S#5);X#9=(letrec {E#11} in S#13);E#16;EE#20[X#10,(var X#18)];EE#21[X#19,(var X#9)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(letrec {E#11} in S#13);E#16;EE#20[X#10,(var X#18)];EE#21[X#19,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=S#13;E#11;E#16;EE#20[X#10,(var X#18)];EE#21[X#19,(var X#9)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(var X#9)] C#22[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= (letrec {E#11} in S#13)
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(var X#9)] C#22[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;X#9= S#13
       ;E#11
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#17,C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),A#20[(app A#21[(var X#9)] C#22)]),
             ((var X#2),A#20[(app A#21[(var X#9)] C#22)]),
             (S#5,A#20[(app A#21[(var X#9)] C#22)]),
             ((var X#9),(letrec {X#18=A#20[(app A#21[(var X#9)] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#11;E#16;EE#19[X#10,(var X#18)]} in [.])),
             (A#14[(var X#10)],(letrec {E#11} in [.])),
             [{X#18=A#20[(app A#21[(var X#9)] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#19[X#10,(var X#18)]},(letrec {E#11} in [.])],
             ((var X#2),A#20[(app A#21[(var X#9)] C#22[[.]])]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]]),
             ((var X#9),[.]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,llet-e2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#9=S#13;E#11;E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])
    and constraints: E#11/= {}, ((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])), (A#14[(var X#10)],(letrec {E#11} in [.])), ({E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {X#9=(letrec {E#11} in S#13);E#12;EE#15[X#10,(var X#9)]} in A#14[(var X#10)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),((var X#9),(letrec {E#11;E#12;EE#15[X#10,(var X#9)]} in [.])),(A#14[(var X#10)],(letrec {E#11} in [.])),[{E#12;EE#15[X#10,(var X#9)]},(letrec {E#11} in [.])],((var X#2),C#8[[.]]),((var X#9),[.]),((var X#10),A#14[[.]]),((var X#9),[.]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#10)],
           E#12         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] C#22[(\ X#3.S#5)])];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {X#9=(letrec {E#11} in S#13);E#16;EE#19[X#10,(var X#18)]},
           C#8          |->  A#20[(app A#21[(var X#9)] C#22)],
           A#17         |->  A#20[(app A#21 C#22[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(var X#9)] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(letrec {E#11} in S#13);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -cp-e1->                      (letrec {X#18=A#20[(app A#21[(var X#9)] C#22[(var X#2)])];X#2=(\ X#3.S#5);X#9=(letrec {E#11} in S#13);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(var X#9)] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=(letrec {E#11} in S#13);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -SR,llet-e2->                 (letrec {X#18=A#20[(app A#21[(var X#9)] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);X#9=S#13;E#11;E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     A#13[(app (letrec {E#9} in T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#10)]
    ,
     A#13[(letrec
              E#9
           in
              (app T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#10)
           )]
  )

where

   Delta1 = {T#15,T#14,A#12,T#7,A#13}
   Delta2 = {E#9}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#10,(letrec {E#9} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  A#12[(app (letrec {E#9} in S#11) S#10)]
    -SR,lapp1->                   A#12[(letrec {E#9} in (app S#11 S#10))]
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        A#12[(app (letrec {E#9} in S#11) S#10)]}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#10,(letrec {E#9} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {A#12  |->  A#13,
           T#7   |->  A#13[(app (letrec {E#9} in T#16) S#10)],
           T#14  |->  (app (letrec {E#9} in T#16) S#10),
           T#15  |->  (letrec {E#9} in T#16),
           S#11  |->  T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  A#13[(app (letrec {E#9} in T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#10)]
    -cp-e1->                      A#13[(app (letrec {E#9} in T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#10)]
    ................................................................................
                                  A#13[(app (letrec {E#9} in T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#10)]
    -SR,lapp1->                   A#13[(letrec {E#9} in (app T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#10))]
    

================================================================================
Critical Pair:

  (
     A#13[(app (letrec
                   X#17= T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
                  ;E#19
                in
                   S#11
                ) S#10)]
    ,
     A#13[(letrec
              X#17= T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
             ;E#19
           in
              (app S#11 S#10)
           )]
  )

where

   Delta1 = {T#15,T#14,A#12,T#7,A#13}
   Delta2 = {E#9}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#10,(letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  A#12[(app (letrec {E#9} in S#11) S#10)]
    -SR,lapp1->                   A#12[(letrec {E#9} in (app S#11 S#10))]
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        A#12[(app (letrec {E#9} in S#11) S#10)]}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#10,(letrec {E#9} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {A#12  |->  A#13,
           T#7   |->  A#13[(app (letrec {X#17=T#16;E#19} in S#11) S#10)],
           T#14  |->  (app (letrec {X#17=T#16;E#19} in S#11) S#10),
           T#15  |->  (letrec {X#17=T#16;E#19} in S#11),
           E#9   |->  {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19},
           E#18  |->  {E#19}}

and instantiated rules:

                                  A#13[(app (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19} in S#11) S#10)]
    -cp-e1->                      A#13[(app (letrec {X#17=T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19} in S#11) S#10)]
    ................................................................................
                                  A#13[(app (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19} in S#11) S#10)]
    -SR,lapp1->                   A#13[(letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19} in (app S#11 S#10))]
    

================================================================================
Critical Pair:

  (
     A#13[(app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#17} in S#11) S#10)]
    ,
     A#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17} in (app S#11 S#10))]
  )

where

   Delta1 = {T#14,A#12,T#7,A#13}
   Delta2 = {E#9}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#10,(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  A#12[(app (letrec {E#9} in S#11) S#10)]
    -SR,lapp1->                   A#12[(letrec {E#9} in (app S#11 S#10))]
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        A#12[(app (letrec {E#9} in S#11) S#10)]}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#10,(letrec {E#9} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {A#12  |->  A#13,
           T#7   |->  A#13[(app [.] S#10)],
           T#14  |->  (app [.] S#10),
           T#15  |->  [.],
           S#6   |->  S#11,
           E#9   |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17},
           E#16  |->  {X#1=C#8[(\ X#3.S#5)];E#17},
           E#4   |->  {E#17}}

and instantiated rules:

                                  A#13[(app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17} in S#11) S#10)]
    -cp-e1->                      A#13[(app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#17} in S#11) S#10)]
    ................................................................................
                                  A#13[(app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17} in S#11) S#10)]
    -SR,lapp1->                   A#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17} in (app S#11 S#10))]
    

================================================================================
Critical Pair:

  (
     A#13[(app (letrec {E#9} in S#11) T#15[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    ,
     A#13[(letrec
              E#9
           in
              (app S#11 T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])
           )]
  )

where

   Delta1 = {T#14,A#12,T#7,A#13}
   Delta2 = {E#9}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {E#9} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  A#12[(app (letrec {E#9} in S#11) S#10)]
    -SR,lapp1->                   A#12[(letrec {E#9} in (app S#11 S#10))]
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        A#12[(app (letrec {E#9} in S#11) S#10)]}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#10,(letrec {E#9} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {A#12  |->  A#13,
           T#7   |->  A#13[(app (letrec {E#9} in S#11) T#15)],
           T#14  |->  (app (letrec {E#9} in S#11) T#15),
           S#10  |->  T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  A#13[(app (letrec {E#9} in S#11) T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    -cp-e1->                      A#13[(app (letrec {E#9} in S#11) T#15[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    ................................................................................
                                  A#13[(app (letrec {E#9} in S#11) T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    -SR,lapp1->                   A#13[(letrec {E#9} in (app S#11 T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]))]
    

================================================================================
Critical Pair:

  (
     A#13[(app A#14[(app (letrec {E#9} in S#11) S#10)] T#15[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    ,
     A#13[(app A#14[(letrec {E#9} in (app S#11 S#10))] T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
  )

where

   Delta1 = {A#12,T#7}
   Delta2 = {E#9}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#10,(letrec {E#9} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  A#12[(app (letrec {E#9} in S#11) S#10)]
    -SR,lapp1->                   A#12[(letrec {E#9} in (app S#11 S#10))]
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        A#12[(app (letrec {E#9} in S#11) S#10)]}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#10,(letrec {E#9} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  A#13[(app A#14[(app (letrec {E#9} in S#11) S#10)] T#15)],
           A#12  |->  A#13[(app A#14 T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  A#13[(app A#14[(app (letrec {E#9} in S#11) S#10)] T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    -cp-e1->                      A#13[(app A#14[(app (letrec {E#9} in S#11) S#10)] T#15[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    ................................................................................
                                  A#13[(app A#14[(app (letrec {E#9} in S#11) S#10)] T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    -SR,lapp1->                   A#13[(app A#14[(letrec {E#9} in (app S#11 S#10))] T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#9} in T#14[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#10)
    ,
     (letrec
        E#9
     in
        (app T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#10)
     )
  )

where

   Delta1 = {T#13,T#7}
   Delta2 = {E#9}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#10,(letrec {E#9} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  A#12[(app (letrec {E#9} in S#11) S#10)]
    -SR,lapp1->                   A#12[(letrec {E#9} in (app S#11 S#10))]
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        A#12[(app (letrec {E#9} in S#11) S#10)]}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#10,(letrec {E#9} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {A#12  |->  [.],
           T#7   |->  (app (letrec {E#9} in T#14) S#10),
           T#13  |->  (letrec {E#9} in T#14),
           S#11  |->  T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (app (letrec {E#9} in T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#10)
    -cp-e1->                      (app (letrec {E#9} in T#14[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#10)
    ................................................................................
                                  (app (letrec {E#9} in T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#10)
    -SR,lapp1->                   (letrec {E#9} in (app T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#10))
    

================================================================================
Critical Pair:

  (
     (app (letrec
             X#15= T#14[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
            ;E#17
          in
             S#11
          ) S#10)
    ,
     (letrec
        X#15= T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;E#17
     in
        (app S#11 S#10)
     )
  )

where

   Delta1 = {T#13,T#7}
   Delta2 = {E#9}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#10,(letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  A#12[(app (letrec {E#9} in S#11) S#10)]
    -SR,lapp1->                   A#12[(letrec {E#9} in (app S#11 S#10))]
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        A#12[(app (letrec {E#9} in S#11) S#10)]}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#10,(letrec {E#9} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {A#12  |->  [.],
           T#7   |->  (app (letrec {X#15=T#14;E#17} in S#11) S#10),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#11),
           E#9   |->  {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (app (letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17} in S#11) S#10)
    -cp-e1->                      (app (letrec {X#15=T#14[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17} in S#11) S#10)
    ................................................................................
                                  (app (letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17} in S#11) S#10)
    -SR,lapp1->                   (letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17} in (app S#11 S#10))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#15} in S#11) S#10)
    ,
     (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15} in (app S#11 S#10))
  )

where

   Delta1 = {T#7}
   Delta2 = {E#9}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#10,(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  A#12[(app (letrec {E#9} in S#11) S#10)]
    -SR,lapp1->                   A#12[(letrec {E#9} in (app S#11 S#10))]
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        A#12[(app (letrec {E#9} in S#11) S#10)]}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#10,(letrec {E#9} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {A#12  |->  [.],
           T#7   |->  (app [.] S#10),
           T#13  |->  [.],
           S#6   |->  S#11,
           E#9   |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15},
           E#14  |->  {X#1=C#8[(\ X#3.S#5)];E#15},
           E#4   |->  {E#15}}

and instantiated rules:

                                  (app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15} in S#11) S#10)
    -cp-e1->                      (app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#15} in S#11) S#10)
    ................................................................................
                                  (app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15} in S#11) S#10)
    -SR,lapp1->                   (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15} in (app S#11 S#10))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#9} in S#11) T#13[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])
    ,
     (letrec
        E#9
     in
        (app S#11 T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {E#9}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {E#9} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp1-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  A#12[(app (letrec {E#9} in S#11) S#10)]
    -SR,lapp1->                   A#12[(letrec {E#9} in (app S#11 S#10))]
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        A#12[(app (letrec {E#9} in S#11) S#10)]}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#10,(letrec {E#9} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {A#12  |->  [.],
           T#7   |->  (app (letrec {E#9} in S#11) T#13),
           S#10  |->  T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (app (letrec {E#9} in S#11) T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])
    -cp-e1->                      (app (letrec {E#9} in S#11) T#13[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])
    ................................................................................
                                  (app (letrec {E#9} in S#11) T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])
    -SR,lapp1->                   (letrec {E#9} in (app S#11 T#13[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        A#15[(app (letrec
                      E#10
                   in
                      T#18[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
                   ) S#11)]
     )
    ,
     (letrec
        E#9
     in
        A#15[(letrec
                 E#10
              in
                 (app T#18[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#11)
              )]
     )
  )

where

   Delta1 = {T#17,T#16,A#13,T#14,T#7,A#15}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])
    -SR,lapp2->                   (letrec {E#9} in A#13[(letrec {E#10} in (app S#12 S#11))])
    and constraints: E#9/= {}, E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(letrec {E#10} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#9} in A#15[(app (letrec {E#10} in T#18) S#11)]),
           A#13  |->  A#15,
           T#14  |->  A#15[(app (letrec {E#10} in T#18) S#11)],
           T#16  |->  (app (letrec {E#10} in T#18) S#11),
           T#17  |->  (letrec {E#10} in T#18),
           S#12  |->  T#18[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {E#9} in A#15[(app (letrec {E#10} in T#18[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#11)])
    -cp-e1->                      (letrec {E#9} in A#15[(app (letrec {E#10} in T#18[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#11)])
    ................................................................................
                                  (letrec {E#9} in A#15[(app (letrec {E#10} in T#18[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#11)])
    -SR,lapp2->                   (letrec {E#9} in A#15[(letrec {E#10} in (app T#18[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#11))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        A#15[(app (letrec
                      X#19= T#18[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
                     ;E#21
                   in
                      S#12
                   ) S#11)]
     )
    ,
     (letrec
        E#9
     in
        A#15[(letrec
                 X#19= T#18[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
                ;E#21
              in
                 (app S#12 S#11)
              )]
     )
  )

where

   Delta1 = {T#17,T#16,A#13,T#14,T#7,A#15}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#11,(letrec {X#19=T#18[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#21} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])
    -SR,lapp2->                   (letrec {E#9} in A#13[(letrec {E#10} in (app S#12 S#11))])
    and constraints: E#9/= {}, E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(letrec {E#10} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#9} in A#15[(app (letrec {X#19=T#18;E#21} in S#12) S#11)]),
           A#13  |->  A#15,
           T#14  |->  A#15[(app (letrec {X#19=T#18;E#21} in S#12) S#11)],
           T#16  |->  (app (letrec {X#19=T#18;E#21} in S#12) S#11),
           T#17  |->  (letrec {X#19=T#18;E#21} in S#12),
           E#10  |->  {X#19=T#18[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#21},
           E#20  |->  {E#21}}

and instantiated rules:

                                  (letrec {E#9} in A#15[(app (letrec {X#19=T#18[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#21} in S#12) S#11)])
    -cp-e1->                      (letrec {E#9} in A#15[(app (letrec {X#19=T#18[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#21} in S#12) S#11)])
    ................................................................................
                                  (letrec {E#9} in A#15[(app (letrec {X#19=T#18[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#21} in S#12) S#11)])
    -SR,lapp2->                   (letrec {E#9} in A#15[(letrec {X#19=T#18[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#21} in (app S#12 S#11))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        A#15[(app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#19} in S#12) S#11)]
     )
    ,
     (letrec
        E#9
     in
        A#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#19} in (app S#12 S#11))]
     )
  )

where

   Delta1 = {T#16,A#13,T#14,T#7,A#15}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#11,(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#19} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])
    -SR,lapp2->                   (letrec {E#9} in A#13[(letrec {E#10} in (app S#12 S#11))])
    and constraints: E#9/= {}, E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(letrec {E#10} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#9} in A#15[(app [.] S#11)]),
           A#13  |->  A#15,
           T#14  |->  A#15[(app [.] S#11)],
           T#16  |->  (app [.] S#11),
           T#17  |->  [.],
           S#6   |->  S#12,
           E#10  |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#19},
           E#18  |->  {X#1=C#8[(\ X#3.S#5)];E#19},
           E#4   |->  {E#19}}

and instantiated rules:

                                  (letrec {E#9} in A#15[(app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#19} in S#12) S#11)])
    -cp-e1->                      (letrec {E#9} in A#15[(app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#19} in S#12) S#11)])
    ................................................................................
                                  (letrec {E#9} in A#15[(app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#19} in S#12) S#11)])
    -SR,lapp2->                   (letrec {E#9} in A#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#19} in (app S#12 S#11))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        A#15[(app (letrec {E#10} in S#12) T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
    ,
     (letrec
        E#9
     in
        A#15[(letrec
                 E#10
              in
                 (app S#12 T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])
              )]
     )
  )

where

   Delta1 = {T#16,A#13,T#14,T#7,A#15}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {E#10} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])
    -SR,lapp2->                   (letrec {E#9} in A#13[(letrec {E#10} in (app S#12 S#11))])
    and constraints: E#9/= {}, E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(letrec {E#10} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#9} in A#15[(app (letrec {E#10} in S#12) T#17)]),
           A#13  |->  A#15,
           T#14  |->  A#15[(app (letrec {E#10} in S#12) T#17)],
           T#16  |->  (app (letrec {E#10} in S#12) T#17),
           S#11  |->  T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {E#9} in A#15[(app (letrec {E#10} in S#12) T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -cp-e1->                      (letrec {E#9} in A#15[(app (letrec {E#10} in S#12) T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    ................................................................................
                                  (letrec {E#9} in A#15[(app (letrec {E#10} in S#12) T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -SR,lapp2->                   (letrec {E#9} in A#15[(letrec {E#10} in (app S#12 T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        A#15[(app A#16[(app (letrec {E#10} in S#12) S#11)] T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
    ,
     (letrec
        E#9
     in
        A#15[(app A#16[(letrec {E#10} in (app S#12 S#11))] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
  )

where

   Delta1 = {A#13,T#14,T#7}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])
    -SR,lapp2->                   (letrec {E#9} in A#13[(letrec {E#10} in (app S#12 S#11))])
    and constraints: E#9/= {}, E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(letrec {E#10} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#9} in A#15[(app A#16[(app (letrec {E#10} in S#12) S#11)] T#17)]),
           T#14  |->  A#15[(app A#16[(app (letrec {E#10} in S#12) S#11)] T#17)],
           A#13  |->  A#15[(app A#16 T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {E#9} in A#15[(app A#16[(app (letrec {E#10} in S#12) S#11)] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -cp-e1->                      (letrec {E#9} in A#15[(app A#16[(app (letrec {E#10} in S#12) S#11)] T#17[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    ................................................................................
                                  (letrec {E#9} in A#15[(app A#16[(app (letrec {E#10} in S#12) S#11)] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -SR,lapp2->                   (letrec {E#9} in A#15[(app A#16[(letrec {E#10} in (app S#12 S#11))] T#17[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        (app (letrec
                E#10
             in
                T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
             ) S#11)
     )
    ,
     (letrec
        E#9
     in
        (letrec
           E#10
        in
           (app T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#11)
        )
     )
  )

where

   Delta1 = {T#15,T#14,T#7}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])
    -SR,lapp2->                   (letrec {E#9} in A#13[(letrec {E#10} in (app S#12 S#11))])
    and constraints: E#9/= {}, E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(letrec {E#10} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#9} in (app (letrec {E#10} in T#16) S#11)),
           A#13  |->  [.],
           T#14  |->  (app (letrec {E#10} in T#16) S#11),
           T#15  |->  (letrec {E#10} in T#16),
           S#12  |->  T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {E#9} in (app (letrec {E#10} in T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#11))
    -cp-e1->                      (letrec {E#9} in (app (letrec {E#10} in T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#11))
    ................................................................................
                                  (letrec {E#9} in (app (letrec {E#10} in T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#11))
    -SR,lapp2->                   (letrec {E#9} in (letrec {E#10} in (app T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#11)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        (app (letrec
                X#17= T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
               ;E#19
             in
                S#12
             ) S#11)
     )
    ,
     (letrec
        E#9
     in
        (letrec
           X#17= T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
          ;E#19
        in
           (app S#12 S#11)
        )
     )
  )

where

   Delta1 = {T#15,T#14,T#7}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#11,(letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])
    -SR,lapp2->                   (letrec {E#9} in A#13[(letrec {E#10} in (app S#12 S#11))])
    and constraints: E#9/= {}, E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(letrec {E#10} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#9} in (app (letrec {X#17=T#16;E#19} in S#12) S#11)),
           A#13  |->  [.],
           T#14  |->  (app (letrec {X#17=T#16;E#19} in S#12) S#11),
           T#15  |->  (letrec {X#17=T#16;E#19} in S#12),
           E#10  |->  {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19},
           E#18  |->  {E#19}}

and instantiated rules:

                                  (letrec {E#9} in (app (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19} in S#12) S#11))
    -cp-e1->                      (letrec {E#9} in (app (letrec {X#17=T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19} in S#12) S#11))
    ................................................................................
                                  (letrec {E#9} in (app (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19} in S#12) S#11))
    -SR,lapp2->                   (letrec {E#9} in (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19} in (app S#12 S#11)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        (app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#17} in S#12) S#11)
     )
    ,
     (letrec
        E#9
     in
        (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17} in (app S#12 S#11))
     )
  )

where

   Delta1 = {T#14,T#7}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#11,(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])
    -SR,lapp2->                   (letrec {E#9} in A#13[(letrec {E#10} in (app S#12 S#11))])
    and constraints: E#9/= {}, E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(letrec {E#10} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#9} in (app [.] S#11)),
           A#13  |->  [.],
           T#14  |->  (app [.] S#11),
           T#15  |->  [.],
           S#6   |->  S#12,
           E#10  |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17},
           E#16  |->  {X#1=C#8[(\ X#3.S#5)];E#17},
           E#4   |->  {E#17}}

and instantiated rules:

                                  (letrec {E#9} in (app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17} in S#12) S#11))
    -cp-e1->                      (letrec {E#9} in (app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#17} in S#12) S#11))
    ................................................................................
                                  (letrec {E#9} in (app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17} in S#12) S#11))
    -SR,lapp2->                   (letrec {E#9} in (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17} in (app S#12 S#11)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        (app (letrec {E#10} in S#12) T#15[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])
     )
    ,
     (letrec
        E#9
     in
        (letrec
           E#10
        in
           (app S#12 T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])
        )
     )
  )

where

   Delta1 = {T#14,T#7}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {E#10} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])
    -SR,lapp2->                   (letrec {E#9} in A#13[(letrec {E#10} in (app S#12 S#11))])
    and constraints: E#9/= {}, E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(letrec {E#10} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#9} in (app (letrec {E#10} in S#12) T#15)),
           A#13  |->  [.],
           T#14  |->  (app (letrec {E#10} in S#12) T#15),
           S#11  |->  T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {E#9} in (app (letrec {E#10} in S#12) T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]))
    -cp-e1->                      (letrec {E#9} in (app (letrec {E#10} in S#12) T#15[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]))
    ................................................................................
                                  (letrec {E#9} in (app (letrec {E#10} in S#12) T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]))
    -SR,lapp2->                   (letrec {E#9} in (letrec {E#10} in (app S#12 T#15[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;E#17
     in
        A#13[(app (letrec {E#10} in S#12) S#11)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;E#17
     in
        A#13[(letrec {E#10} in (app S#12 S#11))]
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])
    -SR,lapp2->                   (letrec {E#9} in A#13[(letrec {E#10} in (app S#12 S#11))])
    and constraints: E#9/= {}, E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(letrec {E#10} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#15=T#14;E#17} in A#13[(app (letrec {E#10} in S#12) S#11)]),
           E#9   |->  {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17} in A#13[(app (letrec {E#10} in S#12) S#11)])
    -cp-e1->                      (letrec {X#15=T#14[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17} in A#13[(app (letrec {E#10} in S#12) S#11)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17} in A#13[(app (letrec {E#10} in S#12) S#11)])
    -SR,lapp2->                   (letrec {X#15=T#14[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#17} in A#13[(letrec {E#10} in (app S#12 S#11))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#8[(var X#2)]
       ;X#2= (\ X#3.S#5)
       ;E#15
     in
        A#13[(app (letrec {E#10} in S#12) S#11)]
     )
    ,
     (letrec
        X#1= C#8[(\ X#3.S#5)]
       ;X#2= (\ X#3.S#5)
       ;E#15
     in
        A#13[(letrec {E#10} in (app S#12 S#11))]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9,E#10}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#8[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp2-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])
    -SR,lapp2->                   (letrec {E#9} in A#13[(letrec {E#10} in (app S#12 S#11))])
    and constraints: E#9/= {}, E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#9} in A#13[(app (letrec {E#10} in S#12) S#11)])}
      Delta1=  {}
      Delta2=  {E#9,E#10}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#11,(letrec {E#10} in [.])),((var X#2),C#8[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#13[(app (letrec {E#10} in S#12) S#11)],
           E#9   |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15},
           E#14  |->  {X#1=C#8[(\ X#3.S#5)];E#15},
           E#4   |->  {E#15}}

and instantiated rules:

                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15} in A#13[(app (letrec {E#10} in S#12) S#11)])
    -cp-e1->                      (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#15} in A#13[(app (letrec {E#10} in S#12) S#11)])
    ................................................................................
                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15} in A#13[(app (letrec {E#10} in S#12) S#11)])
    -SR,lapp2->                   (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#15} in A#13[(letrec {E#10} in (app S#12 S#11))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#10
       ;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]
     in
        A#17[(app A#18[(var X#9)] T#19[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
    ,
     (letrec
        E#10
       ;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]
     in
        A#17[(app A#18[(var X#9)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
     )
  )

where

   Delta1 = {A#14,T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#17[(app A#18[[.]] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]),
             ((var X#9),A#17[(app A#18[[.]] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#17[(app A#18[(var X#9)] T#19)]),
           T#16  |->  A#17[(app A#18[(var X#9)] T#19)],
           A#14  |->  A#17[(app A#18 T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#17[(app A#18[(var X#9)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -cp-e1->                      (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#17[(app A#18[(var X#9)] T#19[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#17[(app A#18[(var X#9)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#17[(app A#18[(var X#9)] T#19[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;E#19
       ;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#17= T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
       ;E#19
       ;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7   |->  (letrec {X#17=T#16;E#19;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)]),
           E#10  |->  {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19},
           E#18  |->  {E#19;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]}}

and instantiated rules:

                                  (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#17=T#16[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#17=T#16[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#19;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= A#20[(app (letrec
                           E#11
                        in
                           T#23[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
                        ) S#12)]
       ;E#10
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#9= A#20[(letrec
                      E#11
                   in
                      (app T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#12)
                   )]
       ;E#10
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#22,T#21,A#19,T#16,T#7,A#20}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#9=A#20[(app (letrec {E#11} in T#23) S#12)];E#10} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#20[[.2]]},
           X#17         |->  X#9,
           E#18         |->  {E#10},
           A#19         |->  A#20,
           T#16         |->  A#20[(app (letrec {E#11} in T#23) S#12)],
           T#21         |->  (app (letrec {E#11} in T#23) S#12),
           T#22         |->  (letrec {E#11} in T#23),
           S#13         |->  T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {X#9=A#20[(app (letrec {E#11} in T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#12)];E#10} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#9=A#20[(app (letrec {E#11} in T#23[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#12)];E#10} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#9=A#20[(app (letrec {E#11} in T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#12)];E#10} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#9=A#20[(letrec {E#11} in (app T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#12))];E#10} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= A#20[(app (letrec
                           X#24= T#23[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
                          ;E#26
                        in
                           S#13
                        ) S#12)]
       ;E#10
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#9= A#20[(letrec
                      X#24= T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
                     ;E#26
                   in
                      (app S#13 S#12)
                   )]
       ;E#10
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#22,T#21,A#19,T#16,T#7,A#20}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {X#24=T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#26} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#9=A#20[(app (letrec {X#24=T#23;E#26} in S#13) S#12)];E#10} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#20[[.2]]},
           X#17         |->  X#9,
           E#18         |->  {E#10},
           A#19         |->  A#20,
           T#16         |->  A#20[(app (letrec {X#24=T#23;E#26} in S#13) S#12)],
           T#21         |->  (app (letrec {X#24=T#23;E#26} in S#13) S#12),
           T#22         |->  (letrec {X#24=T#23;E#26} in S#13),
           E#11         |->  {X#24=T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#26},
           E#25         |->  {E#26}}

and instantiated rules:

                                  (letrec {X#9=A#20[(app (letrec {X#24=T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#26} in S#13) S#12)];E#10} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#9=A#20[(app (letrec {X#24=T#23[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#26} in S#13) S#12)];E#10} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#9=A#20[(app (letrec {X#24=T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#26} in S#13) S#12)];E#10} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#9=A#20[(letrec {X#24=T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#26} in (app S#13 S#12))];E#10} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= A#20[(app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#24} in S#13) S#12)]
       ;E#10
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#9= A#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#24} in (app S#13 S#12))]
       ;E#10
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#21,A#19,T#16,T#7,A#20}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#24} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#9=A#20[(app [.] S#12)];E#10} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#20[[.2]]},
           X#17         |->  X#9,
           E#18         |->  {E#10},
           A#19         |->  A#20,
           T#16         |->  A#20[(app [.] S#12)],
           T#21         |->  (app [.] S#12),
           T#22         |->  [.],
           S#6          |->  S#13,
           E#11         |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#24},
           E#23         |->  {X#1=C#8[(\ X#3.S#5)];E#24},
           E#4          |->  {E#24}}

and instantiated rules:

                                  (letrec {X#9=A#20[(app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#24} in S#13) S#12)];E#10} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#9=A#20[(app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#24} in S#13) S#12)];E#10} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#9=A#20[(app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#24} in S#13) S#12)];E#10} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#9=A#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#24} in (app S#13 S#12))];E#10} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= A#20[(app (letrec {E#11} in S#13) T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#10
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#9= A#20[(letrec
                      E#11
                   in
                      (app S#13 T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])
                   )]
       ;E#10
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#21,A#19,T#16,T#7,A#20}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {E#11} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#9=A#20[(app (letrec {E#11} in S#13) T#22)];E#10} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#20[[.2]]},
           X#17         |->  X#9,
           E#18         |->  {E#10},
           A#19         |->  A#20,
           T#16         |->  A#20[(app (letrec {E#11} in S#13) T#22)],
           T#21         |->  (app (letrec {E#11} in S#13) T#22),
           S#12         |->  T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {X#9=A#20[(app (letrec {E#11} in S#13) T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#9=A#20[(app (letrec {E#11} in S#13) T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#9=A#20[(app (letrec {E#11} in S#13) T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#9=A#20[(letrec {E#11} in (app S#13 T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]))];E#10} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= A#20[(app A#21[(app (letrec {E#11} in S#13) S#12)] T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#10
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#9= A#20[(app A#21[(letrec {E#11} in (app S#13 S#12))] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#10
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#19,T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#9=A#20[(app A#21[(app (letrec {E#11} in S#13) S#12)] T#22)];E#10} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#20[(app A#21[[.2]] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]},
           X#17         |->  X#9,
           E#18         |->  {E#10},
           T#16         |->  A#20[(app A#21[(app (letrec {E#11} in S#13) S#12)] T#22)],
           A#19         |->  A#20[(app A#21 T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#9=A#20[(app A#21[(app (letrec {E#11} in S#13) S#12)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#9=A#20[(app A#21[(app (letrec {E#11} in S#13) S#12)] T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#9=A#20[(app A#21[(app (letrec {E#11} in S#13) S#12)] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#9=A#20[(app A#21[(letrec {E#11} in (app S#13 S#12))] T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (app (letrec
                     E#11
                  in
                     T#21[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
                  ) S#12)
       ;E#10
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#9= (letrec
                E#11
             in
                (app T#21[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#12)
             )
       ;E#10
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#20,T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#9=(app (letrec {E#11} in T#21) S#12);E#10} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#17         |->  X#9,
           E#18         |->  {E#10},
           A#19         |->  [.],
           T#16         |->  (app (letrec {E#11} in T#21) S#12),
           T#20         |->  (letrec {E#11} in T#21),
           S#13         |->  T#21[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {X#9=(app (letrec {E#11} in T#21[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#12);E#10} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#9=(app (letrec {E#11} in T#21[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#12);E#10} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#9=(app (letrec {E#11} in T#21[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#12);E#10} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#9=(letrec {E#11} in (app T#21[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#12));E#10} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (app (letrec
                     X#22= T#21[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
                    ;E#24
                  in
                     S#13
                  ) S#12)
       ;E#10
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#9= (letrec
                X#22= T#21[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
               ;E#24
             in
                (app S#13 S#12)
             )
       ;E#10
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#20,T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {X#22=T#21[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#24} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#9=(app (letrec {X#22=T#21;E#24} in S#13) S#12);E#10} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#17         |->  X#9,
           E#18         |->  {E#10},
           A#19         |->  [.],
           T#16         |->  (app (letrec {X#22=T#21;E#24} in S#13) S#12),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#13),
           E#11         |->  {X#22=T#21[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#9=(app (letrec {X#22=T#21[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#24} in S#13) S#12);E#10} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#9=(app (letrec {X#22=T#21[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#24} in S#13) S#12);E#10} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#9=(app (letrec {X#22=T#21[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#24} in S#13) S#12);E#10} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#9=(letrec {X#22=T#21[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#24} in (app S#13 S#12));E#10} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#22} in S#13) S#12)
       ;E#10
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#9= (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#22} in (app S#13 S#12))
       ;E#10
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#22} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#9=(app [.] S#12);E#10} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#17         |->  X#9,
           E#18         |->  {E#10},
           A#19         |->  [.],
           T#16         |->  (app [.] S#12),
           T#20         |->  [.],
           S#6          |->  S#13,
           E#11         |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#22},
           E#21         |->  {X#1=C#8[(\ X#3.S#5)];E#22},
           E#4          |->  {E#22}}

and instantiated rules:

                                  (letrec {X#9=(app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#22} in S#13) S#12);E#10} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#9=(app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#22} in S#13) S#12);E#10} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#9=(app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#22} in S#13) S#12);E#10} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#9=(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#22} in (app S#13 S#12));E#10} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= (app (letrec {E#11} in S#13) T#20[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])
       ;E#10
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#9= (letrec
                E#11
             in
                (app S#13 T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])
             )
       ;E#10
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {E#11} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#9=(app (letrec {E#11} in S#13) T#20);E#10} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#17         |->  X#9,
           E#18         |->  {E#10},
           A#19         |->  [.],
           T#16         |->  (app (letrec {E#11} in S#13) T#20),
           S#12         |->  T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {X#9=(app (letrec {E#11} in S#13) T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#10} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#9=(app (letrec {E#11} in S#13) T#20[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#10} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#9=(app (letrec {E#11} in S#13) T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#10} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#9=(letrec {E#11} in (app S#13 T#20[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]));E#10} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#10
       ;EE#21[X#20,(app (letrec {E#11} in S#13) S#12)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#9= A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#10
       ;EE#21[X#20,(letrec {E#11} in (app S#13 S#12))]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#19,T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#9=A#22[(app A#23[(var X#20)] T#24)];E#10;EE#21[X#20,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];EE#21[X#20,[.2]]},
           X#17         |->  X#9,
           E#18         |->  {E#10;EE#21[X#20,(app (letrec {E#11} in S#13) S#12)]},
           T#16         |->  A#22[(app A#23[(var X#20)] T#24)],
           A#19         |->  A#22[(app A#23 T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#9=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10;EE#21[X#20,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#9=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10;EE#21[X#20,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#9=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10;EE#21[X#20,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#9=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10;EE#21[X#20,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#10
       ;EE#22[X#9,(var X#20)]
       ;EE#23[X#21,(app (letrec {E#11} in S#13) S#12)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#20= A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#10
       ;EE#22[X#9,(var X#20)]
       ;EE#23[X#21,(letrec {E#11} in (app S#13 S#12))]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#19,T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26)];E#10;EE#22[X#9,(var X#20)];EE#23[X#21,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];EE#22[[.1],(var X#20)];EE#23[X#21,[.2]]},
           X#17         |->  X#20,
           E#18         |->  {E#10;EE#22[X#9,(var X#20)];EE#23[X#21,(app (letrec {E#11} in S#13) S#12)]},
           T#16         |->  A#24[(app A#25[(var X#21)] T#26)],
           A#19         |->  A#24[(app A#25 T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10;EE#22[X#9,(var X#20)];EE#23[X#21,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10;EE#22[X#9,(var X#20)];EE#23[X#21,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10;EE#22[X#9,(var X#20)];EE#23[X#21,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10;EE#22[X#9,(var X#20)];EE#23[X#21,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app (letrec
                            E#11
                         in
                            T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
                         ) S#12)]
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#20= A#22[(letrec
                       E#11
                    in
                       (app T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#12)
                    )]
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#24,T#23,A#19,T#16,T#7,A#22}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=A#22[(app (letrec {E#11} in T#25) S#12)];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#20=A#22[[.2]];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {E#10;EE#21[X#9,(var X#20)]},
           A#19         |->  A#22,
           T#16         |->  A#22[(app (letrec {E#11} in T#25) S#12)],
           T#23         |->  (app (letrec {E#11} in T#25) S#12),
           T#24         |->  (letrec {E#11} in T#25),
           S#13         |->  T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app (letrec {E#11} in T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#12)];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#20=A#22[(app (letrec {E#11} in T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#12)];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#20=A#22[(app (letrec {E#11} in T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#12)];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#20=A#22[(letrec {E#11} in (app T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#12))];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app (letrec
                            X#26= T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
                           ;E#28
                         in
                            S#13
                         ) S#12)]
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#20= A#22[(letrec
                       X#26= T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
                      ;E#28
                    in
                       (app S#13 S#12)
                    )]
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#24,T#23,A#19,T#16,T#7,A#22}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {X#26=T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#28} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=A#22[(app (letrec {X#26=T#25;E#28} in S#13) S#12)];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#20=A#22[[.2]];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {E#10;EE#21[X#9,(var X#20)]},
           A#19         |->  A#22,
           T#16         |->  A#22[(app (letrec {X#26=T#25;E#28} in S#13) S#12)],
           T#23         |->  (app (letrec {X#26=T#25;E#28} in S#13) S#12),
           T#24         |->  (letrec {X#26=T#25;E#28} in S#13),
           E#11         |->  {X#26=T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#28},
           E#27         |->  {E#28}}

and instantiated rules:

                                  (letrec {X#20=A#22[(app (letrec {X#26=T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#28} in S#13) S#12)];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#20=A#22[(app (letrec {X#26=T#25[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#28} in S#13) S#12)];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#20=A#22[(app (letrec {X#26=T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#28} in S#13) S#12)];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#20=A#22[(letrec {X#26=T#25[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#28} in (app S#13 S#12))];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#26} in S#13) S#12)]
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#20= A#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#26} in (app S#13 S#12))]
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#23,A#19,T#16,T#7,A#22}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#26} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=A#22[(app [.] S#12)];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#20=A#22[[.2]];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {E#10;EE#21[X#9,(var X#20)]},
           A#19         |->  A#22,
           T#16         |->  A#22[(app [.] S#12)],
           T#23         |->  (app [.] S#12),
           T#24         |->  [.],
           S#6          |->  S#13,
           E#11         |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#26},
           E#25         |->  {X#1=C#8[(\ X#3.S#5)];E#26},
           E#4          |->  {E#26}}

and instantiated rules:

                                  (letrec {X#20=A#22[(app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#26} in S#13) S#12)];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#20=A#22[(app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#26} in S#13) S#12)];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#20=A#22[(app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#26} in S#13) S#12)];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#20=A#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#26} in (app S#13 S#12))];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app (letrec {E#11} in S#13) T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#20= A#22[(letrec
                       E#11
                    in
                       (app S#13 T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])
                    )]
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#23,A#19,T#16,T#7,A#22}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {E#11} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=A#22[(app (letrec {E#11} in S#13) T#24)];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#20=A#22[[.2]];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {E#10;EE#21[X#9,(var X#20)]},
           A#19         |->  A#22,
           T#16         |->  A#22[(app (letrec {E#11} in S#13) T#24)],
           T#23         |->  (app (letrec {E#11} in S#13) T#24),
           S#12         |->  T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app (letrec {E#11} in S#13) T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#20=A#22[(app (letrec {E#11} in S#13) T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#20=A#22[(app (letrec {E#11} in S#13) T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#20=A#22[(letrec {E#11} in (app S#13 T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]))];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app A#23[(app (letrec {E#11} in S#13) S#12)] T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#20= A#22[(app A#23[(letrec {E#11} in (app S#13 S#12))] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#19,T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=A#22[(app A#23[(app (letrec {E#11} in S#13) S#12)] T#24)];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#20=A#22[(app A#23[[.2]] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {E#10;EE#21[X#9,(var X#20)]},
           T#16         |->  A#22[(app A#23[(app (letrec {E#11} in S#13) S#12)] T#24)],
           A#19         |->  A#22[(app A#23 T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app A#23[(app (letrec {E#11} in S#13) S#12)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#20=A#22[(app A#23[(app (letrec {E#11} in S#13) S#12)] T#24[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#20=A#22[(app A#23[(app (letrec {E#11} in S#13) S#12)] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#20=A#22[(app A#23[(letrec {E#11} in (app S#13 S#12))] T#24[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])];E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= (app (letrec
                      E#11
                   in
                      T#23[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
                   ) S#12)
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#20= (letrec
                 E#11
              in
                 (app T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#12)
              )
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#22,T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=(app (letrec {E#11} in T#23) S#12);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {E#10;EE#21[X#9,(var X#20)]},
           A#19         |->  [.],
           T#16         |->  (app (letrec {E#11} in T#23) S#12),
           T#22         |->  (letrec {E#11} in T#23),
           S#13         |->  T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {X#20=(app (letrec {E#11} in T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#12);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#20=(app (letrec {E#11} in T#23[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#12);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#20=(app (letrec {E#11} in T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]) S#12);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#20=(letrec {E#11} in (app T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)] S#12));E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= (app (letrec
                      X#24= T#23[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
                     ;E#26
                   in
                      S#13
                   ) S#12)
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#20= (letrec
                 X#24= T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
                ;E#26
              in
                 (app S#13 S#12)
              )
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#22,T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {X#24=T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#26} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=(app (letrec {X#24=T#23;E#26} in S#13) S#12);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {E#10;EE#21[X#9,(var X#20)]},
           A#19         |->  [.],
           T#16         |->  (app (letrec {X#24=T#23;E#26} in S#13) S#12),
           T#22         |->  (letrec {X#24=T#23;E#26} in S#13),
           E#11         |->  {X#24=T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#26},
           E#25         |->  {E#26}}

and instantiated rules:

                                  (letrec {X#20=(app (letrec {X#24=T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#26} in S#13) S#12);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#20=(app (letrec {X#24=T#23[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)];E#26} in S#13) S#12);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#20=(app (letrec {X#24=T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#26} in S#13) S#12);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#20=(letrec {X#24=T#23[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)];E#26} in (app S#13 S#12));E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= (app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#24} in S#13) S#12)
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#20= (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#24} in (app S#13 S#12))
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#24} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=(app [.] S#12);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {E#10;EE#21[X#9,(var X#20)]},
           A#19         |->  [.],
           T#16         |->  (app [.] S#12),
           T#22         |->  [.],
           S#6          |->  S#13,
           E#11         |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#24},
           E#23         |->  {X#1=C#8[(\ X#3.S#5)];E#24},
           E#4          |->  {E#24}}

and instantiated rules:

                                  (letrec {X#20=(app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#24} in S#13) S#12);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#20=(app (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#24} in S#13) S#12);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#20=(app (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#24} in S#13) S#12);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#20=(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#24} in (app S#13 S#12));E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= (app (letrec {E#11} in S#13) T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)])
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#20= (letrec
                 E#11
              in
                 (app S#13 T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)])
              )
       ;E#10
       ;EE#21[X#9,(var X#20)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#16,T#7}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)],(letrec {E#11} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  (letrec {X#20=(app (letrec {E#11} in S#13) T#22);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {E#10;EE#21[X#9,(var X#20)]},
           A#19         |->  [.],
           T#16         |->  (app (letrec {E#11} in S#13) T#22),
           S#12         |->  T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]}

and instantiated rules:

                                  (letrec {X#20=(app (letrec {E#11} in S#13) T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#20=(app (letrec {E#11} in S#13) T#22[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#20=(app (letrec {E#11} in S#13) T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]);E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#20=(letrec {E#11} in (app S#13 T#22[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]));E#10;EE#21[X#9,(var X#20)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#8[(var X#2)]
       ;X#2= (\ X#3.S#5)
       ;E#17
       ;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#1= C#8[(\ X#3.S#5)]
       ;X#2= (\ X#3.S#5)
       ;E#17
       ;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),C#8),
             ((var X#2),C#8),
             (S#5,C#8),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),C#8[[.]]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7   |->  [.],
           S#6   |->  A#14[(var X#9)],
           E#10  |->  {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17},
           E#16  |->  {X#1=C#8[(\ X#3.S#5)];E#17},
           E#4   |->  {E#17;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]}}

and instantiated rules:

                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#17;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#17;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#18[(app (letrec {E#11} in C#21[(var X#2)]) S#12)]
       ;E#16
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#18[(letrec {E#11} in (app C#21[(\ X#3.S#5)] S#12))]
       ;E#16
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#20,C#19,A#17,C#8,A#18}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),A#18[(app (letrec {E#11} in C#21) S#12)]),
             ((var X#2),A#18[(app (letrec {E#11} in C#21) S#12)]),
             (S#5,A#18[(app (letrec {E#11} in C#21) S#12)]),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),A#18[(app (letrec {E#11} in C#21[[.]]) S#12)]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#1          |->  X#9,
           E#4          |->  {E#16},
           A#17         |->  A#18,
           C#8          |->  A#18[(app (letrec {E#11} in C#21) S#12)],
           C#19         |->  (app (letrec {E#11} in C#21) S#12),
           C#20         |->  (letrec {E#11} in C#21),
           S#13         |->  C#21[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app (letrec {E#11} in C#21[(\ X#3.S#5)]) S#12)];E#16} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app (letrec {E#11} in C#21[(var X#2)]) S#12)];E#16} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app (letrec {E#11} in C#21[(\ X#3.S#5)]) S#12)];E#16} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#2=(\ X#3.S#5);X#9=A#18[(letrec {E#11} in (app C#21[(\ X#3.S#5)] S#12))];E#16} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#18[(app (letrec {X#22=C#21[(var X#2)];E#24} in S#13) S#12)]
       ;E#16
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#18[(letrec {X#22=C#21[(\ X#3.S#5)];E#24} in (app S#13 S#12))]
       ;E#16
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#20,C#19,A#17,C#8,A#18}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),A#18[(app (letrec {X#22=C#21;E#24} in S#13) S#12)]),
             ((var X#2),A#18[(app (letrec {X#22=C#21;E#24} in S#13) S#12)]),
             (S#5,A#18[(app (letrec {X#22=C#21;E#24} in S#13) S#12)]),
             (S#12,(letrec {X#22=C#21[(\ X#3.S#5)];E#24} in [.])),
             ((var X#2),A#18[(app (letrec {X#22=C#21[[.]];E#24} in S#13) S#12)]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#1          |->  X#9,
           E#4          |->  {E#16},
           A#17         |->  A#18,
           C#8          |->  A#18[(app (letrec {X#22=C#21;E#24} in S#13) S#12)],
           C#19         |->  (app (letrec {X#22=C#21;E#24} in S#13) S#12),
           C#20         |->  (letrec {X#22=C#21;E#24} in S#13),
           E#11         |->  {X#22=C#21[(\ X#3.S#5)];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app (letrec {X#22=C#21[(\ X#3.S#5)];E#24} in S#13) S#12)];E#16} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app (letrec {X#22=C#21[(var X#2)];E#24} in S#13) S#12)];E#16} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app (letrec {X#22=C#21[(\ X#3.S#5)];E#24} in S#13) S#12)];E#16} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#2=(\ X#3.S#5);X#9=A#18[(letrec {X#22=C#21[(\ X#3.S#5)];E#24} in (app S#13 S#12))];E#16} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#18[(app (letrec {E#11} in S#13) C#20[(var X#2)])]
       ;E#16
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#18[(letrec {E#11} in (app S#13 C#20[(\ X#3.S#5)]))]
       ;E#16
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#19,A#17,C#8,A#18}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),A#18[(app (letrec {E#11} in S#13) C#20)]),
             ((var X#2),A#18[(app (letrec {E#11} in S#13) C#20)]),
             (S#5,A#18[(app (letrec {E#11} in S#13) C#20)]),
             (C#20[(\ X#3.S#5)],(letrec {E#11} in [.])),
             ((var X#2),A#18[(app (letrec {E#11} in S#13) C#20[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#1          |->  X#9,
           E#4          |->  {E#16},
           A#17         |->  A#18,
           C#8          |->  A#18[(app (letrec {E#11} in S#13) C#20)],
           C#19         |->  (app (letrec {E#11} in S#13) C#20),
           S#12         |->  C#20[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app (letrec {E#11} in S#13) C#20[(\ X#3.S#5)])];E#16} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app (letrec {E#11} in S#13) C#20[(var X#2)])];E#16} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app (letrec {E#11} in S#13) C#20[(\ X#3.S#5)])];E#16} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#2=(\ X#3.S#5);X#9=A#18[(letrec {E#11} in (app S#13 C#20[(\ X#3.S#5)]))];E#16} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#18[(app A#19[(app (letrec {E#11} in S#13) S#12)] C#20[(var X#2)])]
       ;E#16
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#18[(app A#19[(letrec {E#11} in (app S#13 S#12))] C#20[(\ X#3.S#5)])]
       ;E#16
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#17,C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),A#18[(app A#19[(app (letrec {E#11} in S#13) S#12)] C#20)]),
             ((var X#2),A#18[(app A#19[(app (letrec {E#11} in S#13) S#12)] C#20)]),
             (S#5,A#18[(app A#19[(app (letrec {E#11} in S#13) S#12)] C#20)]),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),A#18[(app A#19[(app (letrec {E#11} in S#13) S#12)] C#20[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] C#20[(\ X#3.S#5)])]},
           X#1          |->  X#9,
           E#4          |->  {E#16},
           C#8          |->  A#18[(app A#19[(app (letrec {E#11} in S#13) S#12)] C#20)],
           A#17         |->  A#18[(app A#19 C#20[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app A#19[(app (letrec {E#11} in S#13) S#12)] C#20[(\ X#3.S#5)])];E#16} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app A#19[(app (letrec {E#11} in S#13) S#12)] C#20[(var X#2)])];E#16} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app A#19[(app (letrec {E#11} in S#13) S#12)] C#20[(\ X#3.S#5)])];E#16} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#2=(\ X#3.S#5);X#9=A#18[(app A#19[(letrec {E#11} in (app S#13 S#12))] C#20[(\ X#3.S#5)])];E#16} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (app (letrec {E#11} in C#19[(var X#2)]) S#12)
       ;E#16
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (letrec {E#11} in (app C#19[(\ X#3.S#5)] S#12))
       ;E#16
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#18,C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),(app (letrec {E#11} in C#19) S#12)),
             ((var X#2),(app (letrec {E#11} in C#19) S#12)),
             (S#5,(app (letrec {E#11} in C#19) S#12)),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),(app (letrec {E#11} in C#19[[.]]) S#12)),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#9,
           E#4          |->  {E#16},
           A#17         |->  [.],
           C#8          |->  (app (letrec {E#11} in C#19) S#12),
           C#18         |->  (letrec {E#11} in C#19),
           S#13         |->  C#19[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=(app (letrec {E#11} in C#19[(\ X#3.S#5)]) S#12);E#16} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=(app (letrec {E#11} in C#19[(var X#2)]) S#12);E#16} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=(app (letrec {E#11} in C#19[(\ X#3.S#5)]) S#12);E#16} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#2=(\ X#3.S#5);X#9=(letrec {E#11} in (app C#19[(\ X#3.S#5)] S#12));E#16} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (app (letrec {X#20=C#19[(var X#2)];E#22} in S#13) S#12)
       ;E#16
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (letrec {X#20=C#19[(\ X#3.S#5)];E#22} in (app S#13 S#12))
       ;E#16
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#18,C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),(app (letrec {X#20=C#19;E#22} in S#13) S#12)),
             ((var X#2),(app (letrec {X#20=C#19;E#22} in S#13) S#12)),
             (S#5,(app (letrec {X#20=C#19;E#22} in S#13) S#12)),
             (S#12,(letrec {X#20=C#19[(\ X#3.S#5)];E#22} in [.])),
             ((var X#2),(app (letrec {X#20=C#19[[.]];E#22} in S#13) S#12)),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#9,
           E#4          |->  {E#16},
           A#17         |->  [.],
           C#8          |->  (app (letrec {X#20=C#19;E#22} in S#13) S#12),
           C#18         |->  (letrec {X#20=C#19;E#22} in S#13),
           E#11         |->  {X#20=C#19[(\ X#3.S#5)];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=(app (letrec {X#20=C#19[(\ X#3.S#5)];E#22} in S#13) S#12);E#16} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=(app (letrec {X#20=C#19[(var X#2)];E#22} in S#13) S#12);E#16} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=(app (letrec {X#20=C#19[(\ X#3.S#5)];E#22} in S#13) S#12);E#16} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#2=(\ X#3.S#5);X#9=(letrec {X#20=C#19[(\ X#3.S#5)];E#22} in (app S#13 S#12));E#16} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (app (letrec {E#11} in S#13) C#18[(var X#2)])
       ;E#16
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= (letrec {E#11} in (app S#13 C#18[(\ X#3.S#5)]))
       ;E#16
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),(app (letrec {E#11} in S#13) C#18)),
             ((var X#2),(app (letrec {E#11} in S#13) C#18)),
             (S#5,(app (letrec {E#11} in S#13) C#18)),
             (C#18[(\ X#3.S#5)],(letrec {E#11} in [.])),
             ((var X#2),(app (letrec {E#11} in S#13) C#18[[.]])),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#9,
           E#4          |->  {E#16},
           A#17         |->  [.],
           C#8          |->  (app (letrec {E#11} in S#13) C#18),
           S#12         |->  C#18[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=(app (letrec {E#11} in S#13) C#18[(\ X#3.S#5)]);E#16} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=(app (letrec {E#11} in S#13) C#18[(var X#2)]);E#16} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=(app (letrec {E#11} in S#13) C#18[(\ X#3.S#5)]);E#16} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#2=(\ X#3.S#5);X#9=(letrec {E#11} in (app S#13 C#18[(\ X#3.S#5)]));E#16} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#20[(app A#21[(var X#18)] C#22[(var X#2)])]
       ;E#16
       ;EE#19[X#18,(app (letrec {E#11} in S#13) S#12)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#2= (\ X#3.S#5)
       ;X#9= A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])]
       ;E#16
       ;EE#19[X#18,(letrec {E#11} in (app S#13 S#12))]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#17,C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),A#20[(app A#21[(var X#18)] C#22)]),
             ((var X#2),A#20[(app A#21[(var X#18)] C#22)]),
             (S#5,A#20[(app A#21[(var X#18)] C#22)]),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),A#20[(app A#21[(var X#18)] C#22[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])];EE#19[X#18,[.2]]},
           X#1          |->  X#9,
           E#4          |->  {E#16;EE#19[X#18,(app (letrec {E#11} in S#13) S#12)]},
           C#8          |->  A#20[(app A#21[(var X#18)] C#22)],
           A#17         |->  A#20[(app A#21 C#22[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#2=(\ X#3.S#5);X#9=A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])];E#16;EE#19[X#18,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#2=(\ X#3.S#5);X#9=A#20[(app A#21[(var X#18)] C#22[(var X#2)])];E#16;EE#19[X#18,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(\ X#3.S#5);X#9=A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])];E#16;EE#19[X#18,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#2=(\ X#3.S#5);X#9=A#20[(app A#21[(var X#18)] C#22[(\ X#3.S#5)])];E#16;EE#19[X#18,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] C#24[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#20[X#9,(var X#18)]
       ;EE#21[X#19,(app (letrec {E#11} in S#13) S#12)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#20[X#9,(var X#18)]
       ;EE#21[X#19,(letrec {E#11} in (app S#13 S#12))]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#17,C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),A#22[(app A#23[(var X#19)] C#24)]),
             ((var X#2),A#22[(app A#23[(var X#19)] C#24)]),
             (S#5,A#22[(app A#23[(var X#19)] C#24)]),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),A#22[(app A#23[(var X#19)] C#24[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#20[X#9,(var X#18)];EE#21[X#19,(app (letrec {E#11} in S#13) S#12)]},
           C#8          |->  A#22[(app A#23[(var X#19)] C#24)],
           A#17         |->  A#22[(app A#23 C#24[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#20[X#9,(var X#18)];EE#21[X#19,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(var X#2)])];X#2=(\ X#3.S#5);E#16;EE#20[X#9,(var X#18)];EE#21[X#19,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#20[X#9,(var X#18)];EE#21[X#19,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#20[X#9,(var X#18)];EE#21[X#19,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (letrec {E#11} in C#23[(var X#2)]) S#12)]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {E#11} in (app C#23[(\ X#3.S#5)] S#12))]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#22,C#21,A#17,C#8,A#20}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),A#20[(app (letrec {E#11} in C#23) S#12)]),
             ((var X#2),A#20[(app (letrec {E#11} in C#23) S#12)]),
             (S#5,A#20[(app (letrec {E#11} in C#23) S#12)]),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),A#20[(app (letrec {E#11} in C#23[[.]]) S#12)]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#19[X#9,(var X#18)]},
           A#17         |->  A#20,
           C#8          |->  A#20[(app (letrec {E#11} in C#23) S#12)],
           C#21         |->  (app (letrec {E#11} in C#23) S#12),
           C#22         |->  (letrec {E#11} in C#23),
           S#13         |->  C#23[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (letrec {E#11} in C#23[(\ X#3.S#5)]) S#12)];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=A#20[(app (letrec {E#11} in C#23[(var X#2)]) S#12)];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (letrec {E#11} in C#23[(\ X#3.S#5)]) S#12)];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#18=A#20[(letrec {E#11} in (app C#23[(\ X#3.S#5)] S#12))];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (letrec {X#24=C#23[(var X#2)];E#26} in S#13) S#12)]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {X#24=C#23[(\ X#3.S#5)];E#26} in (app S#13 S#12))]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#22,C#21,A#17,C#8,A#20}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),A#20[(app (letrec {X#24=C#23;E#26} in S#13) S#12)]),
             ((var X#2),A#20[(app (letrec {X#24=C#23;E#26} in S#13) S#12)]),
             (S#5,A#20[(app (letrec {X#24=C#23;E#26} in S#13) S#12)]),
             (S#12,(letrec {X#24=C#23[(\ X#3.S#5)];E#26} in [.])),
             ((var X#2),A#20[(app (letrec {X#24=C#23[[.]];E#26} in S#13) S#12)]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#19[X#9,(var X#18)]},
           A#17         |->  A#20,
           C#8          |->  A#20[(app (letrec {X#24=C#23;E#26} in S#13) S#12)],
           C#21         |->  (app (letrec {X#24=C#23;E#26} in S#13) S#12),
           C#22         |->  (letrec {X#24=C#23;E#26} in S#13),
           E#11         |->  {X#24=C#23[(\ X#3.S#5)];E#26},
           E#25         |->  {E#26}}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (letrec {X#24=C#23[(\ X#3.S#5)];E#26} in S#13) S#12)];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=A#20[(app (letrec {X#24=C#23[(var X#2)];E#26} in S#13) S#12)];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (letrec {X#24=C#23[(\ X#3.S#5)];E#26} in S#13) S#12)];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#18=A#20[(letrec {X#24=C#23[(\ X#3.S#5)];E#26} in (app S#13 S#12))];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (letrec {E#11} in S#13) C#22[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {E#11} in (app S#13 C#22[(\ X#3.S#5)]))]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#21,A#17,C#8,A#20}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),A#20[(app (letrec {E#11} in S#13) C#22)]),
             ((var X#2),A#20[(app (letrec {E#11} in S#13) C#22)]),
             (S#5,A#20[(app (letrec {E#11} in S#13) C#22)]),
             (C#22[(\ X#3.S#5)],(letrec {E#11} in [.])),
             ((var X#2),A#20[(app (letrec {E#11} in S#13) C#22[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#19[X#9,(var X#18)]},
           A#17         |->  A#20,
           C#8          |->  A#20[(app (letrec {E#11} in S#13) C#22)],
           C#21         |->  (app (letrec {E#11} in S#13) C#22),
           S#12         |->  C#22[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (letrec {E#11} in S#13) C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=A#20[(app (letrec {E#11} in S#13) C#22[(var X#2)])];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (letrec {E#11} in S#13) C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#18=A#20[(letrec {E#11} in (app S#13 C#22[(\ X#3.S#5)]))];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(app (letrec {E#11} in S#13) S#12)] C#22[(var X#2)])]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(letrec {E#11} in (app S#13 S#12))] C#22[(\ X#3.S#5)])]
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#17,C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),A#20[(app A#21[(app (letrec {E#11} in S#13) S#12)] C#22)]),
             ((var X#2),A#20[(app A#21[(app (letrec {E#11} in S#13) S#12)] C#22)]),
             (S#5,A#20[(app A#21[(app (letrec {E#11} in S#13) S#12)] C#22)]),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),A#20[(app A#21[(app (letrec {E#11} in S#13) S#12)] C#22[[.]])]),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] C#22[(\ X#3.S#5)])];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#19[X#9,(var X#18)]},
           C#8          |->  A#20[(app A#21[(app (letrec {E#11} in S#13) S#12)] C#22)],
           A#17         |->  A#20[(app A#21 C#22[(\ X#3.S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(app (letrec {E#11} in S#13) S#12)] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=A#20[(app A#21[(app (letrec {E#11} in S#13) S#12)] C#22[(var X#2)])];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(app (letrec {E#11} in S#13) S#12)] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#18=A#20[(app A#21[(letrec {E#11} in (app S#13 S#12))] C#22[(\ X#3.S#5)])];X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (letrec {E#11} in C#21[(var X#2)]) S#12)
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= (letrec {E#11} in (app C#21[(\ X#3.S#5)] S#12))
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#20,C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),(app (letrec {E#11} in C#21) S#12)),
             ((var X#2),(app (letrec {E#11} in C#21) S#12)),
             (S#5,(app (letrec {E#11} in C#21) S#12)),
             (S#12,(letrec {E#11} in [.])),
             ((var X#2),(app (letrec {E#11} in C#21[[.]]) S#12)),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#19[X#9,(var X#18)]},
           A#17         |->  [.],
           C#8          |->  (app (letrec {E#11} in C#21) S#12),
           C#20         |->  (letrec {E#11} in C#21),
           S#13         |->  C#21[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#18=(app (letrec {E#11} in C#21[(\ X#3.S#5)]) S#12);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=(app (letrec {E#11} in C#21[(var X#2)]) S#12);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=(app (letrec {E#11} in C#21[(\ X#3.S#5)]) S#12);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#18=(letrec {E#11} in (app C#21[(\ X#3.S#5)] S#12));X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (letrec {X#22=C#21[(var X#2)];E#24} in S#13) S#12)
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= (letrec {X#22=C#21[(\ X#3.S#5)];E#24} in (app S#13 S#12))
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#20,C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),(app (letrec {X#22=C#21;E#24} in S#13) S#12)),
             ((var X#2),(app (letrec {X#22=C#21;E#24} in S#13) S#12)),
             (S#5,(app (letrec {X#22=C#21;E#24} in S#13) S#12)),
             (S#12,(letrec {X#22=C#21[(\ X#3.S#5)];E#24} in [.])),
             ((var X#2),(app (letrec {X#22=C#21[[.]];E#24} in S#13) S#12)),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#19[X#9,(var X#18)]},
           A#17         |->  [.],
           C#8          |->  (app (letrec {X#22=C#21;E#24} in S#13) S#12),
           C#20         |->  (letrec {X#22=C#21;E#24} in S#13),
           E#11         |->  {X#22=C#21[(\ X#3.S#5)];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#18=(app (letrec {X#22=C#21[(\ X#3.S#5)];E#24} in S#13) S#12);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=(app (letrec {X#22=C#21[(var X#2)];E#24} in S#13) S#12);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=(app (letrec {X#22=C#21[(\ X#3.S#5)];E#24} in S#13) S#12);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#18=(letrec {X#22=C#21[(\ X#3.S#5)];E#24} in (app S#13 S#12));X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (letrec {E#11} in S#13) C#20[(var X#2)])
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= (letrec {E#11} in (app S#13 C#20[(\ X#3.S#5)]))
       ;X#2= (\ X#3.S#5)
       ;E#16
       ;EE#19[X#9,(var X#18)]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {C#8}
   Delta2 = {E#11}
   Delta3 = {((\ X#3.S#5),(app (letrec {E#11} in S#13) C#20)),
             ((var X#2),(app (letrec {E#11} in S#13) C#20)),
             (S#5,(app (letrec {E#11} in S#13) C#20)),
             (C#20[(\ X#3.S#5)],(letrec {E#11} in [.])),
             ((var X#2),(app (letrec {E#11} in S#13) C#20[[.]])),
             ((var X#9),A#14[[.]]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-e1-> . -SR,lapp3-> with input rules:

                                  T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
    -cp-e1->                      T#7[(letrec {X#1=C#8[(var X#2)];X#2=(\ X#3.S#5);E#4} in S#6)]
    and constraints: ((\ X#3.S#5),C#8), ((var X#2),C#8), (S#5,C#8)
    ................................................................................
                                  (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {E#10;EE#15[X#9,(letrec {E#11} in (app S#13 S#12))]} in A#14[(var X#9)])
    and constraints: E#11/= {}, (S#12,(letrec {E#11} in [.]))

and letrec unification problem:

      Gamma ={
        T#7[(letrec {X#1=C#8[(\ X#3.S#5)];X#2=(\ X#3.S#5);E#4} in S#6)]
        =?=
        (letrec {E#10;EE#15[X#9,(app (letrec {E#11} in S#13) S#12)]} in A#14[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#11}
      Delta3=  {((\ X#3.S#5),C#8),((var X#2),C#8),(S#5,C#8),(S#12,(letrec {E#11} in [.])),((var X#2),C#8[[.]]),((var X#9),A#14[[.]]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#7          |->  [.],
           S#6          |->  A#14[(var X#9)],
           E#10         |->  {X#2=(\ X#3.S#5);E#16},
           EE#15[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {E#16;EE#19[X#9,(var X#18)]},
           A#17         |->  [.],
           C#8          |->  (app (letrec {E#11} in S#13) C#20),
           S#12         |->  C#20[(\ X#3.S#5)]}

and instantiated rules:

                                  (letrec {X#18=(app (letrec {E#11} in S#13) C#20[(\ X#3.S#5)]);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -cp-e1->                      (letrec {X#18=(app (letrec {E#11} in S#13) C#20[(var X#2)]);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=(app (letrec {E#11} in S#13) C#20[(\ X#3.S#5)]);X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    -SR,lapp3->                   (letrec {X#18=(letrec {E#11} in (app S#13 C#20[(\ X#3.S#5)]));X#2=(\ X#3.S#5);E#16;EE#19[X#9,(var X#18)]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     A#11[(app (\ X#7.S#9) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
    ,
     A#11[(letrec {X#7=T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#9)]
  )

where

   Delta1 = {T#12,A#10,T#5,A#11}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(\ X#7.[.])),
             (T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {X#7=[.]} in S#9)),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  A#10[(app (\ X#7.S#9) S#8)]
    -SR,lbeta1->                  A#10[(letrec {X#7=S#8} in S#9)]
    and constraints: (S#8,(\ X#7.[.])), (S#8,(letrec {X#7=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        A#10[(app (\ X#7.S#9) S#8)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#8,(\ X#7.[.])),(S#8,(letrec {X#7=[.]} in S#9)),((var X#1),C#6[[.]])}


and found solution:

    Sol = {A#10  |->  A#11,
           T#5   |->  A#11[(app (\ X#7.S#9) T#13)],
           T#12  |->  (app (\ X#7.S#9) T#13),
           S#8   |->  T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  A#11[(app (\ X#7.S#9) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
    -cp-in1->                     A#11[(app (\ X#7.S#9) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
    ................................................................................
                                  A#11[(app (\ X#7.S#9) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
    -SR,lbeta1->                  A#11[(letrec {X#7=T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#9)]
    

================================================================================
Critical Pair:

  (
     A#11[(app A#12[(app (\ X#7.S#9) S#8)] T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
    ,
     A#11[(app A#12[(letrec {X#7=S#8} in S#9)] T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
  )

where

   Delta1 = {A#10,T#5}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#8,(\ X#7.[.])),
             (S#8,(letrec {X#7=[.]} in S#9)),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  A#10[(app (\ X#7.S#9) S#8)]
    -SR,lbeta1->                  A#10[(letrec {X#7=S#8} in S#9)]
    and constraints: (S#8,(\ X#7.[.])), (S#8,(letrec {X#7=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        A#10[(app (\ X#7.S#9) S#8)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#8,(\ X#7.[.])),(S#8,(letrec {X#7=[.]} in S#9)),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  A#11[(app A#12[(app (\ X#7.S#9) S#8)] T#13)],
           A#10  |->  A#11[(app A#12 T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  A#11[(app A#12[(app (\ X#7.S#9) S#8)] T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
    -cp-in1->                     A#11[(app A#12[(app (\ X#7.S#9) S#8)] T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
    ................................................................................
                                  A#11[(app A#12[(app (\ X#7.S#9) S#8)] T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
    -SR,lbeta1->                  A#11[(app A#12[(letrec {X#7=S#8} in S#9)] T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
    

================================================================================
Critical Pair:

  (
     (app (\ X#7.S#9) T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])
    ,
     (letrec {X#7=T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#9)
  )

where

   Delta1 = {T#5}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(\ X#7.[.])),
             (T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {X#7=[.]} in S#9)),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  A#10[(app (\ X#7.S#9) S#8)]
    -SR,lbeta1->                  A#10[(letrec {X#7=S#8} in S#9)]
    and constraints: (S#8,(\ X#7.[.])), (S#8,(letrec {X#7=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        A#10[(app (\ X#7.S#9) S#8)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#8,(\ X#7.[.])),(S#8,(letrec {X#7=[.]} in S#9)),((var X#1),C#6[[.]])}


and found solution:

    Sol = {A#10  |->  [.],
           T#5   |->  (app (\ X#7.S#9) T#11),
           S#8   |->  T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (app (\ X#7.S#9) T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])
    -cp-in1->                     (app (\ X#7.S#9) T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])
    ................................................................................
                                  (app (\ X#7.S#9) T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])
    -SR,lbeta1->                  (letrec {X#7=T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#9)
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#13[(app (\ X#7.S#10) T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
     )
    ,
     (letrec
        E#8
     in
        A#13[(letrec {X#7=T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#10)]
     )
  )

where

   Delta1 = {T#14,A#11,T#12,T#5,A#13}
   Delta2 = {E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(\ X#7.[.])),
             (T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {X#7=[.]} in S#10)),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#8} in A#13[(app (\ X#7.S#10) T#15)]),
           A#11  |->  A#13,
           T#12  |->  A#13[(app (\ X#7.S#10) T#15)],
           T#14  |->  (app (\ X#7.S#10) T#15),
           S#9   |->  T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {E#8} in A#13[(app (\ X#7.S#10) T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -cp-in1->                     (letrec {E#8} in A#13[(app (\ X#7.S#10) T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])])
    ................................................................................
                                  (letrec {E#8} in A#13[(app (\ X#7.S#10) T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -SR,lbeta2->                  (letrec {E#8} in A#13[(letrec {X#7=T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
     )
    ,
     (letrec
        E#8
     in
        A#13[(app A#14[(letrec {X#7=S#9} in S#10)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
     )
  )

where

   Delta1 = {A#11,T#12,T#5}
   Delta2 = {E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#8} in A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15)]),
           T#12  |->  A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {E#8} in A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -cp-in1->                     (letrec {E#8} in A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])])
    ................................................................................
                                  (letrec {E#8} in A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -SR,lbeta2->                  (letrec {E#8} in A#13[(app A#14[(letrec {X#7=S#9} in S#10)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        (app (\ X#7.S#10) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])
     )
    ,
     (letrec
        E#8
     in
        (letrec {X#7=T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#10)
     )
  )

where

   Delta1 = {T#12,T#5}
   Delta2 = {E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(\ X#7.[.])),
             (T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {X#7=[.]} in S#10)),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#8} in (app (\ X#7.S#10) T#13)),
           A#11  |->  [.],
           T#12  |->  (app (\ X#7.S#10) T#13),
           S#9   |->  T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {E#8} in (app (\ X#7.S#10) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]))
    -cp-in1->                     (letrec {E#8} in (app (\ X#7.S#10) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]))
    ................................................................................
                                  (letrec {E#8} in (app (\ X#7.S#10) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]))
    -SR,lbeta2->                  (letrec {E#8} in (letrec {X#7=T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#10))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
       ;E#15
     in
        A#11[(app (\ X#7.S#10) S#9)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;E#15
     in
        A#11[(letrec {X#7=S#9} in S#10)]
     )
  )

where

   Delta1 = {T#5}
   Delta2 = {E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#13=T#12;E#15} in A#11[(app (\ X#7.S#10) S#9)]),
           E#8   |->  {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15} in A#11[(app (\ X#7.S#10) S#9)])
    -cp-in1->                     (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#15} in A#11[(app (\ X#7.S#10) S#9)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15} in A#11[(letrec {X#7=S#9} in S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (\ X#7.C#16[(var X#1)]) S#9)])
    ,
     (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(letrec {X#7=S#9} in C#16[(\ X#2.S#4)])])
  )

where

   Delta1 = {C#15,C#14,A#11,C#6,A#13}
   Delta2 = {E#8}
   Delta3 = {((\ X#2.S#4),A#13[(app (\ X#7.C#16) S#9)]),
             ((var X#1),A#13[(app (\ X#7.C#16) S#9)]),
             (S#4,A#13[(app (\ X#7.C#16) S#9)]),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in C#16[(\ X#2.S#4)])),
             ((var X#1),A#13[(app (\ X#7.C#16[[.]]) S#9)])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#8   |->  {X#1=(\ X#2.S#4);E#12},
           E#3   |->  {E#12},
           A#11  |->  A#13,
           C#6   |->  A#13[(app (\ X#7.C#16) S#9)],
           C#14  |->  (app (\ X#7.C#16) S#9),
           C#15  |->  (\ X#7.C#16),
           S#10  |->  C#16[(\ X#2.S#4)]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (\ X#7.C#16[(\ X#2.S#4)]) S#9)])
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (\ X#7.C#16[(var X#1)]) S#9)])
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (\ X#7.C#16[(\ X#2.S#4)]) S#9)])
    -SR,lbeta2->                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(letrec {X#7=S#9} in C#16[(\ X#2.S#4)])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#7.S#10);E#12} in A#13[(app (var X#1) S#9)])
    ,
     (letrec {X#1=(\ X#7.S#10);E#12} in A#13[(letrec {X#7=S#9} in S#10)])
  )

where

   Delta1 = {C#14,A#11,C#6,A#13}
   Delta2 = {E#8}
   Delta3 = {((\ X#7.S#10),A#13[(app [.] S#9)]),
             ((var X#1),A#13[(app [.] S#9)]),
             (S#10,A#13[(app [.] S#9)]),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),A#13[(app [.] S#9)])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#8   |->  {X#1=(\ X#7.S#10);E#12},
           E#3   |->  {E#12},
           A#11  |->  A#13,
           C#6   |->  A#13[(app [.] S#9)],
           C#14  |->  (app [.] S#9),
           C#15  |->  [.],
           X#2   |->  X#7,
           S#4   |->  S#10}

and instantiated rules:

                                  (letrec {X#1=(\ X#7.S#10);E#12} in A#13[(app (\ X#7.S#10) S#9)])
    -cp-in1->                     (letrec {X#1=(\ X#7.S#10);E#12} in A#13[(app (var X#1) S#9)])
    ................................................................................
                                  (letrec {X#1=(\ X#7.S#10);E#12} in A#13[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {X#1=(\ X#7.S#10);E#12} in A#13[(letrec {X#7=S#9} in S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (\ X#7.S#10) C#15[(var X#1)])])
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;E#12
     in
        A#13[(letrec {X#7=C#15[(\ X#2.S#4)]} in S#10)]
     )
  )

where

   Delta1 = {C#14,A#11,C#6,A#13}
   Delta2 = {E#8}
   Delta3 = {((\ X#2.S#4),A#13[(app (\ X#7.S#10) C#15)]),
             ((var X#1),A#13[(app (\ X#7.S#10) C#15)]),
             (S#4,A#13[(app (\ X#7.S#10) C#15)]),
             (C#15[(\ X#2.S#4)],(\ X#7.[.])),
             (C#15[(\ X#2.S#4)],(letrec {X#7=[.]} in S#10)),
             ((var X#1),A#13[(app (\ X#7.S#10) C#15[[.]])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#8   |->  {X#1=(\ X#2.S#4);E#12},
           E#3   |->  {E#12},
           A#11  |->  A#13,
           C#6   |->  A#13[(app (\ X#7.S#10) C#15)],
           C#14  |->  (app (\ X#7.S#10) C#15),
           S#9   |->  C#15[(\ X#2.S#4)]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (\ X#7.S#10) C#15[(\ X#2.S#4)])])
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (\ X#7.S#10) C#15[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (\ X#7.S#10) C#15[(\ X#2.S#4)])])
    -SR,lbeta2->                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(letrec {X#7=C#15[(\ X#2.S#4)]} in S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#2.S#4)
       ;E#12
     in
        A#13[(app A#14[(app (\ X#7.S#10) S#9)] C#15[(var X#1)])]
     )
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;E#12
     in
        A#13[(app A#14[(letrec {X#7=S#9} in S#10)] C#15[(\ X#2.S#4)])]
     )
  )

where

   Delta1 = {A#11,C#6}
   Delta2 = {E#8}
   Delta3 = {((\ X#2.S#4),A#13[(app A#14[(app (\ X#7.S#10) S#9)] C#15)]),
             ((var X#1),A#13[(app A#14[(app (\ X#7.S#10) S#9)] C#15)]),
             (S#4,A#13[(app A#14[(app (\ X#7.S#10) S#9)] C#15)]),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),A#13[(app A#14[(app (\ X#7.S#10) S#9)] C#15[[.]])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#8   |->  {X#1=(\ X#2.S#4);E#12},
           E#3   |->  {E#12},
           C#6   |->  A#13[(app A#14[(app (\ X#7.S#10) S#9)] C#15)],
           A#11  |->  A#13[(app A#14 C#15[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app A#14[(app (\ X#7.S#10) S#9)] C#15[(\ X#2.S#4)])])
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app A#14[(app (\ X#7.S#10) S#9)] C#15[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app A#14[(app (\ X#7.S#10) S#9)] C#15[(\ X#2.S#4)])])
    -SR,lbeta2->                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app A#14[(letrec {X#7=S#9} in S#10)] C#15[(\ X#2.S#4)])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#2.S#4);E#12} in (app (\ X#7.C#14[(var X#1)]) S#9))
    ,
     (letrec {X#1=(\ X#2.S#4);E#12} in (letrec {X#7=S#9} in C#14[(\ X#2.S#4)]))
  )

where

   Delta1 = {C#13,C#6}
   Delta2 = {E#8}
   Delta3 = {((\ X#2.S#4),(app (\ X#7.C#14) S#9)),
             ((var X#1),(app (\ X#7.C#14) S#9)),
             (S#4,(app (\ X#7.C#14) S#9)),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in C#14[(\ X#2.S#4)])),
             ((var X#1),(app (\ X#7.C#14[[.]]) S#9))}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#8   |->  {X#1=(\ X#2.S#4);E#12},
           E#3   |->  {E#12},
           A#11  |->  [.],
           C#6   |->  (app (\ X#7.C#14) S#9),
           C#13  |->  (\ X#7.C#14),
           S#10  |->  C#14[(\ X#2.S#4)]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#12} in (app (\ X#7.C#14[(\ X#2.S#4)]) S#9))
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#12} in (app (\ X#7.C#14[(var X#1)]) S#9))
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#12} in (app (\ X#7.C#14[(\ X#2.S#4)]) S#9))
    -SR,lbeta2->                  (letrec {X#1=(\ X#2.S#4);E#12} in (letrec {X#7=S#9} in C#14[(\ X#2.S#4)]))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#7.S#10);E#12} in (app (var X#1) S#9))
    ,
     (letrec {X#1=(\ X#7.S#10);E#12} in (letrec {X#7=S#9} in S#10))
  )

where

   Delta1 = {C#6}
   Delta2 = {E#8}
   Delta3 = {((\ X#7.S#10),(app [.] S#9)),
             ((var X#1),(app [.] S#9)),
             (S#10,(app [.] S#9)),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),(app [.] S#9))}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#8   |->  {X#1=(\ X#7.S#10);E#12},
           E#3   |->  {E#12},
           A#11  |->  [.],
           C#6   |->  (app [.] S#9),
           C#13  |->  [.],
           X#2   |->  X#7,
           S#4   |->  S#10}

and instantiated rules:

                                  (letrec {X#1=(\ X#7.S#10);E#12} in (app (\ X#7.S#10) S#9))
    -cp-in1->                     (letrec {X#1=(\ X#7.S#10);E#12} in (app (var X#1) S#9))
    ................................................................................
                                  (letrec {X#1=(\ X#7.S#10);E#12} in (app (\ X#7.S#10) S#9))
    -SR,lbeta2->                  (letrec {X#1=(\ X#7.S#10);E#12} in (letrec {X#7=S#9} in S#10))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#2.S#4);E#12} in (app (\ X#7.S#10) C#13[(var X#1)]))
    ,
     (letrec {X#1=(\ X#2.S#4);E#12} in (letrec {X#7=C#13[(\ X#2.S#4)]} in S#10))
  )

where

   Delta1 = {C#6}
   Delta2 = {E#8}
   Delta3 = {((\ X#2.S#4),(app (\ X#7.S#10) C#13)),
             ((var X#1),(app (\ X#7.S#10) C#13)),
             (S#4,(app (\ X#7.S#10) C#13)),
             (C#13[(\ X#2.S#4)],(\ X#7.[.])),
             (C#13[(\ X#2.S#4)],(letrec {X#7=[.]} in S#10)),
             ((var X#1),(app (\ X#7.S#10) C#13[[.]]))}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#8   |->  {X#1=(\ X#2.S#4);E#12},
           E#3   |->  {E#12},
           A#11  |->  [.],
           C#6   |->  (app (\ X#7.S#10) C#13),
           S#9   |->  C#13[(\ X#2.S#4)]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#12} in (app (\ X#7.S#10) C#13[(\ X#2.S#4)]))
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#12} in (app (\ X#7.S#10) C#13[(var X#1)]))
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#12} in (app (\ X#7.S#10) C#13[(\ X#2.S#4)]))
    -SR,lbeta2->                  (letrec {X#1=(\ X#2.S#4);E#12} in (letrec {X#7=C#13[(\ X#2.S#4)]} in S#10))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
       ;EE#13[X#7,(app (\ X#8.S#11) S#10)]
     in
        A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
     )
    ,
     (letrec
        E#9
       ;EE#13[X#7,(letrec {X#8=S#10} in S#11)]
     in
        A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
     )
  )

where

   Delta1 = {A#12,T#14,T#5}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#15[(app A#16[[.]] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]),
             ((var X#7),A#15[(app A#16[[.]] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#7)] T#17)],
           A#12  |->  A#15[(app A#16 T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -cp-in1->                     (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])])
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
       ;E#17
       ;EE#13[X#7,(app (\ X#8.S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;E#17
       ;EE#13[X#7,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#5}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#15=T#14;E#17;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)]),
           E#9   |->  {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17},
           E#16  |->  {E#17;EE#13[X#7,(app (\ X#8.S#11) S#10)]}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#17;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app (\ X#8.S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#9
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(letrec {X#8=T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#11)]
       ;E#9
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#19,A#17,T#14,T#5,A#18}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(\ X#8.[.])),
             (T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {X#8=[.]} in S#11)),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=A#18[(app (\ X#8.S#11) T#20)];E#9} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#9},
           A#17         |->  A#18,
           T#14         |->  A#18[(app (\ X#8.S#11) T#20)],
           T#19         |->  (app (\ X#8.S#11) T#20),
           S#10         |->  T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#7=A#18[(app (\ X#8.S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#7=A#18[(app (\ X#8.S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#9} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app (\ X#8.S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#7=A#18[(letrec {X#8=T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#11)];E#9} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#9
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(app A#19[(letrec {X#8=S#10} in S#11)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#9
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#5}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20)];E#9} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]},
           X#15         |->  X#7,
           E#16         |->  {E#9},
           T#14         |->  A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20)],
           A#17         |->  A#18[(app A#19 T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#7=A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#9} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#7=A#18[(app A#19[(letrec {X#8=S#10} in S#11)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (app (\ X#8.S#11) T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])
       ;E#9
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= (letrec {X#8=T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#11)
       ;E#9
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#5}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(\ X#8.[.])),
             (T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {X#8=[.]} in S#11)),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=(app (\ X#8.S#11) T#18);E#9} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {E#9},
           A#17         |->  [.],
           T#14         |->  (app (\ X#8.S#11) T#18),
           S#10         |->  T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#7=(app (\ X#8.S#11) T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]);E#9} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#7=(app (\ X#8.S#11) T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]);E#9} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(app (\ X#8.S#11) T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]);E#9} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#7=(letrec {X#8=T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#11);E#9} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#9
       ;EE#19[X#18,(app (\ X#8.S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#9
       ;EE#19[X#18,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#5}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22)];E#9;EE#19[X#18,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];EE#19[X#18,[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#9;EE#19[X#18,(app (\ X#8.S#11) S#10)]},
           T#14         |->  A#20[(app A#21[(var X#18)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9;EE#19[X#18,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#9;EE#19[X#18,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9;EE#19[X#18,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9;EE#19[X#18,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#9
       ;EE#20[X#7,(var X#18)]
       ;EE#21[X#19,(app (\ X#8.S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#9
       ;EE#20[X#7,(var X#18)]
       ;EE#21[X#19,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#5}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24)];E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#15         |->  X#18,
           E#16         |->  {E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(app (\ X#8.S#11) S#10)]},
           T#14         |->  A#22[(app A#23[(var X#19)] T#24)],
           A#17         |->  A#22[(app A#23 T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (\ X#8.S#11) T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {X#8=T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#11)]
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#21,A#17,T#14,T#5,A#20}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(\ X#8.[.])),
             (T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {X#8=[.]} in S#11)),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=A#20[(app (\ X#8.S#11) T#22)];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#9;EE#19[X#7,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[(app (\ X#8.S#11) T#22)],
           T#21         |->  (app (\ X#8.S#11) T#22),
           S#10         |->  T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (\ X#8.S#11) T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#18=A#20[(app (\ X#8.S#11) T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (\ X#8.S#11) T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#18=A#20[(letrec {X#8=T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#11)];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(letrec {X#8=S#10} in S#11)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#5}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22)];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#9;EE#19[X#7,(var X#18)]},
           T#14         |->  A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#18=A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#18=A#20[(app A#21[(letrec {X#8=S#10} in S#11)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (\ X#8.S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= (letrec {X#8=T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#11)
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#5}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(\ X#8.[.])),
             (T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {X#8=[.]} in S#11)),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=(app (\ X#8.S#11) T#20);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#9;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  (app (\ X#8.S#11) T#20),
           S#10         |->  T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#18=(app (\ X#8.S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#18=(app (\ X#8.S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=(app (\ X#8.S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#18=(letrec {X#8=T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]} in S#11);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#2.S#4)
       ;E#14
       ;EE#13[X#7,(app (\ X#8.S#11) S#10)]
     in
        A#15[(app A#16[(var X#7)] C#17[(var X#1)])]
     )
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;E#14
       ;EE#13[X#7,(letrec {X#8=S#10} in S#11)]
     in
        A#15[(app A#16[(var X#7)] C#17[(\ X#2.S#4)])]
     )
  )

where

   Delta1 = {A#12,C#6}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),A#15[(app A#16[(var X#7)] C#17)]),
             ((var X#1),A#15[(app A#16[(var X#7)] C#17)]),
             (S#4,A#15[(app A#16[(var X#7)] C#17)]),
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),A#15[(app A#16[(var X#7)] C#17[[.]])]),
             ((var X#7),A#15[(app A#16[[.]] C#17[(\ X#2.S#4)])]),
             ((var X#7),A#15[(app A#16[[.]] C#17[(\ X#2.S#4)])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lbeta3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#9   |->  {X#1=(\ X#2.S#4);E#14},
           E#3   |->  {E#14;EE#13[X#7,(app (\ X#8.S#11) S#10)]},
           C#6   |->  A#15[(app A#16[(var X#7)] C#17)],
           A#12  |->  A#15[(app A#16 C#17[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#14;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#15[(app A#16[(var X#7)] C#17[(\ X#2.S#4)])])
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#14;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#15[(app A#16[(var X#7)] C#17[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#14;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#15[(app A#16[(var X#7)] C#17[(\ X#2.S#4)])])
    -SR,lbeta3->                  (letrec {X#1=(\ X#2.S#4);E#14;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#15[(app A#16[(var X#7)] C#17[(\ X#2.S#4)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#10)
       ;E#9
     in
        A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
     )
    ,
     (letrec
        X#7= (\ X#8.S#10)
       ;E#9
     in
        A#13[(app A#14[(\ X#8.S#10)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
     )
  )

where

   Delta1 = {A#11,T#12,T#5}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#13[(app A#14[[.]] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-in1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(\ X#8.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#7=(\ X#8.S#10);E#9} in A#13[(app A#14[(var X#7)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#7)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#13[(app A#14[(\ X#8.S#10)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
       ;X#7= (\ X#8.S#10)
       ;E#15
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;X#7= (\ X#8.S#10)
       ;E#15
     in
        A#11[(\ X#8.S#10)]
     )
  )

where

   Delta1 = {T#5}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-in1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(\ X#8.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#13=T#12;X#7=(\ X#8.S#10);E#15} in A#11[(var X#7)]),
           E#9   |->  {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15},
           E#14  |->  {X#7=(\ X#8.S#10);E#15}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(\ X#8.S#10);E#15} in A#11[(var X#7)])
    -cp-in1->                     (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];X#7=(\ X#8.S#10);E#15} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(\ X#8.S#10);E#15} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(\ X#8.S#10);E#15} in A#11[(\ X#8.S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#7=(\ X#8.S#10);E#9} in A#12[(app A#13[(var X#7)] C#14[(var X#7)])])
    ,
     (letrec
        X#7= (\ X#8.S#10)
       ;E#9
     in
        A#12[(app A#13[(\ X#8.S#10)] C#14[(\ X#8.S#10)])]
     )
  )

where

   Delta1 = {A#11,C#6}
   Delta2 = {}
   Delta3 = {((\ X#8.S#10),A#12[(app A#13[(var X#7)] C#14)]),
             ((var X#7),A#12[(app A#13[(var X#7)] C#14)]),
             (S#10,A#12[(app A#13[(var X#7)] C#14)]),
             ((var X#7),A#12[(app A#13[(var X#7)] C#14[[.]])]),
             ((var X#7),A#12[(app A#13[[.]] C#14[(\ X#8.S#10)])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-in1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(\ X#8.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           X#1   |->  X#7,
           X#2   |->  X#8,
           S#4   |->  S#10,
           E#3   |->  {E#9},
           C#6   |->  A#12[(app A#13[(var X#7)] C#14)],
           A#11  |->  A#12[(app A#13 C#14[(\ X#8.S#10)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#12[(app A#13[(var X#7)] C#14[(\ X#8.S#10)])])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#10);E#9} in A#12[(app A#13[(var X#7)] C#14[(var X#7)])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#12[(app A#13[(var X#7)] C#14[(\ X#8.S#10)])])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#12[(app A#13[(\ X#8.S#10)] C#14[(\ X#8.S#10)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#2.S#4)
       ;X#7= (\ X#8.S#10)
       ;E#12
     in
        A#13[(app A#14[(var X#7)] C#15[(var X#1)])]
     )
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;X#7= (\ X#8.S#10)
       ;E#12
     in
        A#13[(app A#14[(\ X#8.S#10)] C#15[(\ X#2.S#4)])]
     )
  )

where

   Delta1 = {A#11,C#6}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),A#13[(app A#14[(var X#7)] C#15)]),
             ((var X#1),A#13[(app A#14[(var X#7)] C#15)]),
             (S#4,A#13[(app A#14[(var X#7)] C#15)]),
             ((var X#1),A#13[(app A#14[(var X#7)] C#15[[.]])]),
             ((var X#7),A#13[(app A#14[[.]] C#15[(\ X#2.S#4)])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-in1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(\ X#8.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#9   |->  {X#1=(\ X#2.S#4);E#12},
           E#3   |->  {X#7=(\ X#8.S#10);E#12},
           C#6   |->  A#13[(app A#14[(var X#7)] C#15)],
           A#11  |->  A#13[(app A#14 C#15[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#10);E#12} in A#13[(app A#14[(var X#7)] C#15[(\ X#2.S#4)])])
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#10);E#12} in A#13[(app A#14[(var X#7)] C#15[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#10);E#12} in A#13[(app A#14[(var X#7)] C#15[(\ X#2.S#4)])])
    -SR,cp-in1->                  (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#10);E#12} in A#13[(app A#14[(\ X#8.S#10)] C#15[(\ X#2.S#4)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;VV#13|X#9,(var X#7)|
     in
        A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;VV#13|X#9,(var X#7)|
     in
        A#15[(app A#16[(\ X#8.S#11)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
     )
  )

where

   Delta1 = {A#12,T#14,T#5}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#15[(app A#16[[.]] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-in2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#5   |->  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(var X#9)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#9)] T#17)],
           A#12  |->  A#15[(app A#16 T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(\ X#8.S#11)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
       ;X#7= (\ X#8.S#11)
       ;E#17
       ;VV#13|X#9,(var X#7)|
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;X#7= (\ X#8.S#11)
       ;E#17
       ;VV#13|X#9,(var X#7)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {T#5}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-in2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#5   |->  (letrec {X#15=T#14;X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|} in A#12[(var X#9)]),
           E#10  |->  {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17},
           E#16  |->  {X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -cp-in1->                     (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;VV#13|X#9,(var X#7)|
     in
        A#14[(app A#15[(var X#9)] C#16[(var X#7)])]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;VV#13|X#9,(var X#7)|
     in
        A#14[(app A#15[(\ X#8.S#11)] C#16[(\ X#8.S#11)])]
     )
  )

where

   Delta1 = {A#12,C#6}
   Delta2 = {}
   Delta3 = {((\ X#8.S#11),A#14[(app A#15[(var X#9)] C#16)]),
             ((var X#7),A#14[(app A#15[(var X#9)] C#16)]),
             (S#11,A#14[(app A#15[(var X#9)] C#16)]),
             ((var X#7),A#14[(app A#15[(var X#9)] C#16[[.]])]),
             ((var X#7),[.]),
             ((var X#9),A#14[(app A#15[[.]] C#16[(\ X#8.S#11)])]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-in2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#5   |->  [.],
           X#1   |->  X#7,
           X#2   |->  X#8,
           S#4   |->  S#11,
           E#3   |->  {E#10;VV#13|X#9,(var X#7)|},
           C#6   |->  A#14[(app A#15[(var X#9)] C#16)],
           A#12  |->  A#14[(app A#15 C#16[(\ X#8.S#11)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#14[(app A#15[(var X#9)] C#16[(\ X#8.S#11)])])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#14[(app A#15[(var X#9)] C#16[(var X#7)])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#14[(app A#15[(var X#9)] C#16[(\ X#8.S#11)])])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#14[(app A#15[(\ X#8.S#11)] C#16[(\ X#8.S#11)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#2.S#4)
       ;X#7= (\ X#8.S#11)
       ;E#14
       ;VV#13|X#9,(var X#7)|
     in
        A#15[(app A#16[(var X#9)] C#17[(var X#1)])]
     )
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;X#7= (\ X#8.S#11)
       ;E#14
       ;VV#13|X#9,(var X#7)|
     in
        A#15[(app A#16[(\ X#8.S#11)] C#17[(\ X#2.S#4)])]
     )
  )

where

   Delta1 = {A#12,C#6}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),A#15[(app A#16[(var X#9)] C#17)]),
             ((var X#1),A#15[(app A#16[(var X#9)] C#17)]),
             (S#4,A#15[(app A#16[(var X#9)] C#17)]),
             ((var X#1),A#15[(app A#16[(var X#9)] C#17[[.]])]),
             ((var X#7),[.]),
             ((var X#9),A#15[(app A#16[[.]] C#17[(\ X#2.S#4)])]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-in2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#5   |->  [.],
           E#10  |->  {X#1=(\ X#2.S#4);E#14},
           E#3   |->  {X#7=(\ X#8.S#11);E#14;VV#13|X#9,(var X#7)|},
           C#6   |->  A#15[(app A#16[(var X#9)] C#17)],
           A#12  |->  A#15[(app A#16 C#17[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#11);E#14;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(var X#9)] C#17[(\ X#2.S#4)])])
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#11);E#14;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(var X#9)] C#17[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#11);E#14;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(var X#9)] C#17[(\ X#2.S#4)])])
    -SR,cp-in2->                  (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#11);E#14;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(\ X#8.S#11)] C#17[(\ X#2.S#4)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;EE#14[X#9,A#12[(var X#7)]]
     in
        A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;EE#14[X#9,A#12[(\ X#8.S#11)]]
     in
        A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
     )
  )

where

   Delta1 = {A#13,T#15,T#5,A#12}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#16[(app A#17[[.]] T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]),
             ((var X#9),A#16[(app A#17[[.]] T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#16[(app A#17[(var X#9)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#9)] T#18)],
           A#13  |->  A#16[(app A#17 T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
       ;X#7= (\ X#8.S#11)
       ;E#18
       ;EE#14[X#9,A#12[(var X#7)]]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;X#7= (\ X#8.S#11)
       ;E#18
       ;EE#14[X#9,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#5,A#12}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#16=T#15;X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)]),
           E#10  |->  {X#16=T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#18},
           E#17  |->  {X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(var X#7)]]}}

and instantiated rules:

                                  (letrec {X#16=T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -cp-in1->                     (letrec {X#16=T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#16=T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]]
       ;E#10
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[A#21[(app A#22[(\ X#8.S#11)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]]
       ;E#10
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#5,A#12,A#19}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#21[(app A#22[[.]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=(\ X#8.S#11);X#9=A#19[A#21[(app A#22[(var X#7)] T#23)]];E#10} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#9,
           E#17         |->  {X#7=(\ X#8.S#11);E#10},
           A#18         |->  A#19,
           T#15         |->  A#19[A#21[(app A#22[(var X#7)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#7)] T#23)],
           A#12         |->  A#21[(app A#22 T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]];E#10} in A#13[(var X#9)])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#11);X#9=A#19[A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]];E#10} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]];E#10} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#19[A#21[(app A#22[(\ X#8.S#11)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]];E#10} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[(app A#20[A#12[(var X#7)]] T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#10
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[(app A#20[A#12[(\ X#8.S#11)]] T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#10
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#5,A#12}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[A#12[(var X#7)]] T#21)];E#10} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]},
           X#16         |->  X#9,
           E#17         |->  {X#7=(\ X#8.S#11);E#10},
           T#15         |->  A#19[(app A#20[A#12[(var X#7)]] T#21)],
           A#18         |->  A#19[(app A#20 T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[A#12[(var X#7)]] T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10} in A#13[(var X#9)])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[A#12[(var X#7)]] T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#10} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[A#12[(var X#7)]] T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[A#12[(\ X#8.S#11)]] T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[(app A#20[(var X#7)] T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#10
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[(app A#20[(\ X#8.S#11)] T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#10
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#15,T#5,A#12}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#19[(app A#20[[.]] T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[(var X#7)] T#21)];E#10} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#9,
           E#17         |->  {X#7=(\ X#8.S#11);E#10},
           A#18         |->  [.],
           T#15         |->  A#19[(app A#20[(var X#7)] T#21)],
           A#12         |->  A#19[(app A#20 T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[(var X#7)] T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10} in A#13[(var X#9)])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[(var X#7)] T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#10} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[(var X#7)] T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[(\ X#8.S#11)] T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#10
       ;EE#20[X#19,A#12[(var X#7)]]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#10
       ;EE#20[X#19,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#5,A#12}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=(\ X#8.S#11);X#9=A#21[(app A#22[(var X#19)] T#23)];E#10;EE#20[X#19,A#12[(var X#7)]]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];EE#20[X#19,[.2]]},
           X#16         |->  X#9,
           E#17         |->  {X#7=(\ X#8.S#11);E#10;EE#20[X#19,A#12[(var X#7)]]},
           T#15         |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10;EE#20[X#19,A#12[(var X#7)]]} in A#13[(var X#9)])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#11);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#10;EE#20[X#19,A#12[(var X#7)]]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10;EE#20[X#19,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10;EE#20[X#19,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#21[X#9,(var X#19)]
       ;EE#22[X#20,A#12[(var X#7)]]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#21[X#9,(var X#19)]
       ;EE#22[X#20,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#5,A#12}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(var X#7)]]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(var X#7)]]},
           T#15         |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(var X#7)]]} in A#13[(var X#9)])
    -cp-in1->                     (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(var X#7)]]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(app A#24[(var X#7)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[(\ X#8.S#11)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#5,A#12,A#21}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#23[(app A#24[[.]] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#19=A#21[A#23[(app A#24[(var X#7)] T#25)]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]},
           A#18         |->  A#21,
           T#15         |->  A#21[A#23[(app A#24[(var X#7)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#7)] T#25)],
           A#12         |->  A#23[(app A#24 T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#7)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -cp-in1->                     (letrec {X#19=A#21[A#23[(app A#24[(var X#7)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#7)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#19=A#21[A#23[(app A#24[(\ X#8.S#11)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[A#12[(var X#7)]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[A#12[(\ X#8.S#11)]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#5,A#12}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#19=A#21[(app A#22[A#12[(var X#7)]] T#23)];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]},
           T#15         |->  A#21[(app A#22[A#12[(var X#7)]] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[A#12[(var X#7)]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -cp-in1->                     (letrec {X#19=A#21[(app A#22[A#12[(var X#7)]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[A#12[(var X#7)]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#19=A#21[(app A#22[A#12[(\ X#8.S#11)]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(\ X#8.S#11)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#15,T#5,A#12}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#21[(app A#22[[.]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#19=A#21[(app A#22[(var X#7)] T#23)];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]},
           A#18         |->  [.],
           T#15         |->  A#21[(app A#22[(var X#7)] T#23)],
           A#12         |->  A#21[(app A#22 T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -cp-in1->                     (letrec {X#19=A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#19=A#21[(app A#22[(\ X#8.S#11)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;EE#14[X#9,A#12[(var X#7)]]
     in
        A#15[(app A#16[(var X#9)] C#17[(var X#7)])]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;EE#14[X#9,A#12[(\ X#8.S#11)]]
     in
        A#15[(app A#16[(var X#9)] C#17[(\ X#8.S#11)])]
     )
  )

where

   Delta1 = {A#13,C#6,A#12}
   Delta2 = {}
   Delta3 = {((\ X#8.S#11),A#15[(app A#16[(var X#9)] C#17)]),
             ((var X#7),A#15[(app A#16[(var X#9)] C#17)]),
             (S#11,A#15[(app A#16[(var X#9)] C#17)]),
             ((var X#7),A#15[(app A#16[(var X#9)] C#17[[.]])]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#15[(app A#16[[.]] C#17[(\ X#8.S#11)])]),
             ((var X#9),A#15[(app A#16[[.]] C#17[(\ X#8.S#11)])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           X#1   |->  X#7,
           X#2   |->  X#8,
           S#4   |->  S#11,
           E#3   |->  {E#10;EE#14[X#9,A#12[(var X#7)]]},
           C#6   |->  A#15[(app A#16[(var X#9)] C#17)],
           A#13  |->  A#15[(app A#16 C#17[(\ X#8.S#11)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#15[(app A#16[(var X#9)] C#17[(\ X#8.S#11)])])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#15[(app A#16[(var X#9)] C#17[(var X#7)])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#15[(app A#16[(var X#9)] C#17[(\ X#8.S#11)])])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#15[(app A#16[(var X#9)] C#17[(\ X#8.S#11)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#2.S#4)
       ;X#7= (\ X#8.S#11)
       ;E#15
       ;EE#14[X#9,A#12[(var X#7)]]
     in
        A#16[(app A#17[(var X#9)] C#18[(var X#1)])]
     )
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;X#7= (\ X#8.S#11)
       ;E#15
       ;EE#14[X#9,A#12[(\ X#8.S#11)]]
     in
        A#16[(app A#17[(var X#9)] C#18[(\ X#2.S#4)])]
     )
  )

where

   Delta1 = {A#13,C#6,A#12}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),A#16[(app A#17[(var X#9)] C#18)]),
             ((var X#1),A#16[(app A#17[(var X#9)] C#18)]),
             (S#4,A#16[(app A#17[(var X#9)] C#18)]),
             ((var X#1),A#16[(app A#17[(var X#9)] C#18[[.]])]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#16[(app A#17[[.]] C#18[(\ X#2.S#4)])]),
             ((var X#9),A#16[(app A#17[[.]] C#18[(\ X#2.S#4)])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#10  |->  {X#1=(\ X#2.S#4);E#15},
           E#3   |->  {X#7=(\ X#8.S#11);E#15;EE#14[X#9,A#12[(var X#7)]]},
           C#6   |->  A#16[(app A#17[(var X#9)] C#18)],
           A#13  |->  A#16[(app A#17 C#18[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#11);E#15;EE#14[X#9,A#12[(var X#7)]]} in A#16[(app A#17[(var X#9)] C#18[(\ X#2.S#4)])])
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#11);E#15;EE#14[X#9,A#12[(var X#7)]]} in A#16[(app A#17[(var X#9)] C#18[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#11);E#15;EE#14[X#9,A#12[(var X#7)]]} in A#16[(app A#17[(var X#9)] C#18[(\ X#2.S#4)])])
    -SR,cp-e1->                   (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#11);E#15;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#16[(app A#17[(var X#9)] C#18[(\ X#2.S#4)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
     )
  )

where

   Delta1 = {A#14,T#17,T#5,A#13}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#18[(app A#19[[.]] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#18[(app A#19[[.]] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] T#20)]),
           T#17  |->  A#18[(app A#19[(var X#9)] T#20)],
           A#14  |->  A#18[(app A#19 T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
       ;X#7= (\ X#8.S#12)
       ;E#20
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;X#7= (\ X#8.S#12)
       ;E#20
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#5,A#13}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#18=T#17;X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           E#11  |->  {X#18=T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#20},
           E#19  |->  {X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#18=T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -cp-in1->                     (letrec {X#18=T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[A#23[(app A#24[(\ X#8.S#12)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#22,A#20,T#17,T#5,A#13,A#21}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#23[(app A#24[[.]] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=(\ X#8.S#12);X#9=A#21[A#23[(app A#24[(var X#10)] T#25)]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#21[[.2]]},
           X#18         |->  X#9,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;VV#16|X#10,(var X#7)|},
           A#20         |->  A#21,
           T#17         |->  A#21[A#23[(app A#24[(var X#10)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#10)] T#25)],
           A#13         |->  A#23[(app A#24 T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#12);X#9=A#21[A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#21[A#23[(app A#24[(\ X#8.S#12)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[(app A#22[A#13[(var X#10)]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[(app A#22[A#13[(\ X#8.S#12)]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#20,T#17,T#5,A#13}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[A#13[(var X#10)]] T#23)];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#21[(app A#22[[.2]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]},
           X#18         |->  X#9,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;VV#16|X#10,(var X#7)|},
           T#17         |->  A#21[(app A#22[A#13[(var X#10)]] T#23)],
           A#20         |->  A#21[(app A#22 T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[A#13[(var X#10)]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[A#13[(var X#10)]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[A#13[(var X#10)]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[A#13[(\ X#8.S#12)]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[(app A#22[(var X#10)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[(app A#22[(\ X#8.S#12)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#17,T#5,A#13}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#21[(app A#22[[.]] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[(var X#10)] T#23)];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#18         |->  X#9,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;VV#16|X#10,(var X#7)|},
           A#20         |->  [.],
           T#17         |->  A#21[(app A#22[(var X#10)] T#23)],
           A#13         |->  A#21[(app A#22 T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[(var X#10)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[(var X#10)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[(var X#10)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[(\ X#8.S#12)] T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#11
       ;EE#22[X#21,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#11
       ;EE#22[X#21,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#20,T#17,T#5,A#13}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=(\ X#8.S#12);X#9=A#23[(app A#24[(var X#21)] T#25)];E#11;EE#22[X#21,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];EE#22[X#21,[.2]]},
           X#18         |->  X#9,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;EE#22[X#21,A#13[(var X#10)]];VV#16|X#10,(var X#7)|},
           T#17         |->  A#23[(app A#24[(var X#21)] T#25)],
           A#20         |->  A#23[(app A#24 T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#11;EE#22[X#21,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#12);X#9=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#11;EE#22[X#21,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#11;EE#22[X#21,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#11;EE#22[X#21,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#23[X#9,(var X#21)]
       ;EE#24[X#22,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#21= A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#23[X#9,(var X#21)]
       ;EE#24[X#22,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#20,T#17,T#5,A#13}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#21=A#25[(app A#26[(var X#22)] T#27)];X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];EE#23[[.1],(var X#21)];EE#24[X#22,[.2]]},
           X#18         |->  X#21,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(var X#10)]];VV#16|X#10,(var X#7)|},
           T#17         |->  A#25[(app A#26[(var X#22)] T#27)],
           A#20         |->  A#25[(app A#26 T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -cp-in1->                     (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#23[A#25[(app A#26[(var X#10)] T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#21= A#23[A#25[(app A#26[(\ X#8.S#12)] T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#24,A#20,T#17,T#5,A#13,A#23}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#25[(app A#26[[.]] T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#21=A#23[A#25[(app A#26[(var X#10)] T#27)]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#21=A#23[[.2]];EE#22[[.1],(var X#21)]},
           X#18         |->  X#21,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|},
           A#20         |->  A#23,
           T#17         |->  A#23[A#25[(app A#26[(var X#10)] T#27)]],
           T#24         |->  A#25[(app A#26[(var X#10)] T#27)],
           A#13         |->  A#25[(app A#26 T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#21=A#23[A#25[(app A#26[(var X#10)] T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -cp-in1->                     (letrec {X#21=A#23[A#25[(app A#26[(var X#10)] T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#21=A#23[A#25[(app A#26[(var X#10)] T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#21=A#23[A#25[(app A#26[(\ X#8.S#12)] T#27[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#23[(app A#24[A#13[(var X#10)]] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#21= A#23[(app A#24[A#13[(\ X#8.S#12)]] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#20,T#17,T#5,A#13}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#21=A#23[(app A#24[A#13[(var X#10)]] T#25)];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#21=A#23[(app A#24[[.2]] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];EE#22[[.1],(var X#21)]},
           X#18         |->  X#21,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|},
           T#17         |->  A#23[(app A#24[A#13[(var X#10)]] T#25)],
           A#20         |->  A#23[(app A#24 T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#21=A#23[(app A#24[A#13[(var X#10)]] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -cp-in1->                     (letrec {X#21=A#23[(app A#24[A#13[(var X#10)]] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#21=A#23[(app A#24[A#13[(var X#10)]] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#21=A#23[(app A#24[A#13[(\ X#8.S#12)]] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#21= A#23[(app A#24[(\ X#8.S#12)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#17,T#5,A#13}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#23[(app A#24[[.]] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#21=A#23[(app A#24[(var X#10)] T#25)];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#21=[.2];EE#22[[.1],(var X#21)]},
           X#18         |->  X#21,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|},
           A#20         |->  [.],
           T#17         |->  A#23[(app A#24[(var X#10)] T#25)],
           A#13         |->  A#23[(app A#24 T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#21=A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -cp-in1->                     (letrec {X#21=A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#21=A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#21=A#23[(app A#24[(\ X#8.S#12)] T#25[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#17[(app A#18[(var X#9)] C#19[(var X#7)])]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#17[(app A#18[(var X#9)] C#19[(\ X#8.S#12)])]
     )
  )

where

   Delta1 = {A#14,C#6,A#13}
   Delta2 = {}
   Delta3 = {((\ X#8.S#12),A#17[(app A#18[(var X#9)] C#19)]),
             ((var X#7),A#17[(app A#18[(var X#9)] C#19)]),
             (S#12,A#17[(app A#18[(var X#9)] C#19)]),
             ((var X#7),A#17[(app A#18[(var X#9)] C#19[[.]])]),
             ((var X#7),[.]),
             ((var X#9),A#17[(app A#18[[.]] C#19[(\ X#8.S#12)])]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#17[(app A#18[[.]] C#19[(\ X#8.S#12)])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           X#1   |->  X#7,
           X#2   |->  X#8,
           S#4   |->  S#12,
           E#3   |->  {E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|},
           C#6   |->  A#17[(app A#18[(var X#9)] C#19)],
           A#14  |->  A#17[(app A#18 C#19[(\ X#8.S#12)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#17[(app A#18[(var X#9)] C#19[(\ X#8.S#12)])])
    -cp-in1->                     (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#17[(app A#18[(var X#9)] C#19[(var X#7)])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#17[(app A#18[(var X#9)] C#19[(\ X#8.S#12)])])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#17[(app A#18[(var X#9)] C#19[(\ X#8.S#12)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#2.S#4)
       ;X#7= (\ X#8.S#12)
       ;E#17
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#18[(app A#19[(var X#9)] C#20[(var X#1)])]
     )
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;X#7= (\ X#8.S#12)
       ;E#17
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#18[(app A#19[(var X#9)] C#20[(\ X#2.S#4)])]
     )
  )

where

   Delta1 = {A#14,C#6,A#13}
   Delta2 = {}
   Delta3 = {((\ X#2.S#4),A#18[(app A#19[(var X#9)] C#20)]),
             ((var X#1),A#18[(app A#19[(var X#9)] C#20)]),
             (S#4,A#18[(app A#19[(var X#9)] C#20)]),
             ((var X#1),A#18[(app A#19[(var X#9)] C#20[[.]])]),
             ((var X#7),[.]),
             ((var X#9),A#18[(app A#19[[.]] C#20[(\ X#2.S#4)])]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#18[(app A#19[[.]] C#20[(\ X#2.S#4)])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,cp-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#1),C#6[[.]]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#11  |->  {X#1=(\ X#2.S#4);E#17},
           E#3   |->  {X#7=(\ X#8.S#12);E#17;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|},
           C#6   |->  A#18[(app A#19[(var X#9)] C#20)],
           A#14  |->  A#18[(app A#19 C#20[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#12);E#17;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] C#20[(\ X#2.S#4)])])
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#12);E#17;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] C#20[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#12);E#17;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] C#20[(\ X#2.S#4)])])
    -SR,cp-e2->                   (letrec {X#1=(\ X#2.S#4);X#7=(\ X#8.S#12);E#17;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] C#20[(\ X#2.S#4)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (letrec {E#8} in T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])
     )
    ,
     (letrec {E#7;E#8} in T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])
  )

where

   Delta1 = {T#10,T#5}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             [{E#7},(letrec {E#8} in [.])],
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-in1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),[{E#7},(letrec {E#8} in [.])],((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#7} in (letrec {E#8} in T#11)),
           T#10  |->  (letrec {E#8} in T#11),
           S#9   |->  T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {E#7} in (letrec {E#8} in T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]))
    -cp-in1->                     (letrec {E#7} in (letrec {E#8} in T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]))
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]))
    -SR,llet-in1->                (letrec {E#7;E#8} in T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (letrec
           X#12= T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
          ;E#14
        in
           S#9
        )
     )
    ,
     (letrec
        X#12= T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;E#14
       ;E#7
     in
        S#9
     )
  )

where

   Delta1 = {T#10,T#5}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             [{E#7},(letrec {X#12=T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#14} in [.])],
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-in1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),[{E#7},(letrec {E#8} in [.])],((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#7} in (letrec {X#12=T#11;E#14} in S#9)),
           T#10  |->  (letrec {X#12=T#11;E#14} in S#9),
           E#8   |->  {X#12=T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#14},
           E#13  |->  {E#14}}

and instantiated rules:

                                  (letrec {E#7} in (letrec {X#12=T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#14} in S#9))
    -cp-in1->                     (letrec {E#7} in (letrec {X#12=T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#14} in S#9))
    ................................................................................
                                  (letrec {E#7} in (letrec {X#12=T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#14} in S#9))
    -SR,llet-in1->                (letrec {X#12=T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#14;E#7} in S#9)
    

================================================================================
Critical Pair:

  (
     (letrec {E#7} in (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]))
    ,
     (letrec {X#1=(\ X#2.S#4);E#3;E#7} in C#6[(\ X#2.S#4)])
  )

where

   Delta1 = {T#5}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             [{E#7},(letrec {X#1=(\ X#2.S#4);E#3} in [.])],
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-in1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),[{E#7},(letrec {E#8} in [.])],((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#7} in [.]),
           T#10  |->  [.],
           S#9   |->  C#6[(\ X#2.S#4)],
           E#8   |->  {X#1=(\ X#2.S#4);E#3}}

and instantiated rules:

                                  (letrec {E#7} in (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]))
    -cp-in1->                     (letrec {E#7} in (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]))
    ................................................................................
                                  (letrec {E#7} in (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]))
    -SR,llet-in1->                (letrec {X#1=(\ X#2.S#4);E#3;E#7} in C#6[(\ X#2.S#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
       ;E#13
     in
        (letrec {E#8} in S#9)
     )
    ,
     (letrec
        X#11= T#10[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;E#13
       ;E#8
     in
        S#9
     )
  )

where

   Delta1 = {T#5}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             [{X#11=T#10[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#13},(letrec {E#8} in [.])],
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-in1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),[{E#7},(letrec {E#8} in [.])],((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#11=T#10;E#13} in (letrec {E#8} in S#9)),
           E#7   |->  {X#11=T#10[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#13} in (letrec {E#8} in S#9))
    -cp-in1->                     (letrec {X#11=T#10[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#13} in (letrec {E#8} in S#9))
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#13} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {X#11=T#10[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#13;E#8} in S#9)
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#2.S#4);E#10} in (letrec {E#8} in C#11[(var X#1)]))
    ,
     (letrec {X#1=(\ X#2.S#4);E#10;E#8} in C#11[(\ X#2.S#4)])
  )

where

   Delta1 = {C#6}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),(letrec {E#8} in C#11)),
             ((var X#1),(letrec {E#8} in C#11)),
             (S#4,(letrec {E#8} in C#11)),
             [{X#1=(\ X#2.S#4);E#10},(letrec {E#8} in [.])],
             ((var X#1),(letrec {E#8} in C#11[[.]]))}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-in1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),[{E#7},(letrec {E#8} in [.])],((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5  |->  [.],
           E#7  |->  {X#1=(\ X#2.S#4);E#10},
           E#3  |->  {E#10},
           C#6  |->  (letrec {E#8} in C#11),
           S#9  |->  C#11[(\ X#2.S#4)]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#10} in (letrec {E#8} in C#11[(\ X#2.S#4)]))
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#10} in (letrec {E#8} in C#11[(var X#1)]))
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#10} in (letrec {E#8} in C#11[(\ X#2.S#4)]))
    -SR,llet-in1->                (letrec {X#1=(\ X#2.S#4);E#10;E#8} in C#11[(\ X#2.S#4)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#2.S#4);E#10} in (letrec {X#12=C#11[(var X#1)];E#14} in S#9))
    ,
     (letrec {X#1=(\ X#2.S#4);X#12=C#11[(\ X#2.S#4)];E#10;E#14} in S#9)
  )

where

   Delta1 = {C#6}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),(letrec {X#12=C#11;E#14} in S#9)),
             ((var X#1),(letrec {X#12=C#11;E#14} in S#9)),
             (S#4,(letrec {X#12=C#11;E#14} in S#9)),
             [{X#1=(\ X#2.S#4);E#10},(letrec {X#12=C#11[(\ X#2.S#4)];E#14} in [.])],
             ((var X#1),(letrec {X#12=C#11[[.]];E#14} in S#9))}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-in1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),[{E#7},(letrec {E#8} in [.])],((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#7   |->  {X#1=(\ X#2.S#4);E#10},
           E#3   |->  {E#10},
           C#6   |->  (letrec {X#12=C#11;E#14} in S#9),
           E#8   |->  {X#12=C#11[(\ X#2.S#4)];E#14},
           E#13  |->  {E#14}}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#10} in (letrec {X#12=C#11[(\ X#2.S#4)];E#14} in S#9))
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#10} in (letrec {X#12=C#11[(var X#1)];E#14} in S#9))
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#10} in (letrec {X#12=C#11[(\ X#2.S#4)];E#14} in S#9))
    -SR,llet-in1->                (letrec {X#1=(\ X#2.S#4);X#12=C#11[(\ X#2.S#4)];E#10;E#14} in S#9)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#8} in S#10)
       ;E#9
     in
        A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
     )
    ,
     (letrec
        X#7= S#10
       ;E#8
       ;E#9
     in
        A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
     )
  )

where

   Delta1 = {A#11,T#12,T#5}
   Delta2 = {E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])],(letrec {E#8} in [.])),
             [{E#9},(letrec {E#8} in [.])],
             ((var X#1),C#6[[.]]),
             ((var X#7),A#13[(app A#14[[.]] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]),
             ((var X#7),A#13[(app A#14[[.]] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#1),C#6[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#13[(app A#14[(var X#7)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#7)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -cp-in1->                     (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])])
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#8} in T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])
       ;E#9
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#7= T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;E#8
       ;E#9
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#12,T#5}
   Delta2 = {E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{E#9},(letrec {E#8} in [.])],
             ((var X#1),C#6[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#1),C#6[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#7=(letrec {E#8} in T#15);E#9} in A#11[(var X#7)]),
           X#13  |->  X#7,
           E#14  |->  {E#9},
           T#12  |->  (letrec {E#8} in T#15),
           S#10  |->  T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#8} in T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]);E#9} in A#11[(var X#7)])
    -cp-in1->                     (letrec {X#7=(letrec {E#8} in T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]);E#9} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#8;E#9} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec
                X#16= T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
               ;E#18
             in
                S#10
             )
       ;E#9
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;X#7= S#10
       ;E#18
       ;E#9
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#12,T#5}
   Delta2 = {E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (A#11[(var X#7)],(letrec {X#16=T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#18} in [.])),
             [{E#9},(letrec {X#16=T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#18} in [.])],
             ((var X#1),C#6[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#1),C#6[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#7=(letrec {X#16=T#15;E#18} in S#10);E#9} in A#11[(var X#7)]),
           X#13  |->  X#7,
           E#14  |->  {E#9},
           T#12  |->  (letrec {X#16=T#15;E#18} in S#10),
           E#8   |->  {X#16=T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {X#7=(letrec {X#16=T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#18} in S#10);E#9} in A#11[(var X#7)])
    -cp-in1->                     (letrec {X#7=(letrec {X#16=T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#18} in S#10);E#9} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(letrec {X#16=T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#18} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#16=T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=S#10;E#18;E#9} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])
       ;E#9
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#1=(\ X#2.S#4);X#7=C#6[(\ X#2.S#4)];E#3;E#9} in A#11[(var X#7)])
  )

where

   Delta1 = {T#5}
   Delta2 = {E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (A#11[(var X#7)],(letrec {X#1=(\ X#2.S#4);E#3} in [.])),
             [{E#9},(letrec {X#1=(\ X#2.S#4);E#3} in [.])],
             ((var X#1),C#6[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#1),C#6[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#7=[.];E#9} in A#11[(var X#7)]),
           X#13  |->  X#7,
           E#14  |->  {E#9},
           T#12  |->  [.],
           S#10  |->  C#6[(\ X#2.S#4)],
           E#8   |->  {X#1=(\ X#2.S#4);E#3}}

and instantiated rules:

                                  (letrec {X#7=(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]);E#9} in A#11[(var X#7)])
    -cp-in1->                     (letrec {X#7=(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]);E#9} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#1=(\ X#2.S#4);X#7=C#6[(\ X#2.S#4)];E#3;E#9} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
       ;X#7= (letrec {E#8} in S#10)
       ;E#15
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;X#7= S#10
       ;E#15
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#5}
   Delta2 = {E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15},(letrec {E#8} in [.])],
             ((var X#1),C#6[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#1),C#6[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#13=T#12;X#7=(letrec {E#8} in S#10);E#15} in A#11[(var X#7)]),
           E#9   |->  {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15},
           E#14  |->  {X#7=(letrec {E#8} in S#10);E#15}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(letrec {E#8} in S#10);E#15} in A#11[(var X#7)])
    -cp-in1->                     (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];X#7=(letrec {E#8} in S#10);E#15} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(letrec {E#8} in S#10);E#15} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=S#10;E#15;E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#2.S#4)
       ;X#7= (letrec {E#8} in S#10)
       ;E#12
     in
        A#13[(app A#14[(var X#7)] C#15[(var X#1)])]
     )
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;X#7= S#10
       ;E#12
       ;E#8
     in
        A#13[(app A#14[(var X#7)] C#15[(\ X#2.S#4)])]
     )
  )

where

   Delta1 = {A#11,C#6}
   Delta2 = {E#8}
   Delta3 = {((\ X#2.S#4),A#13[(app A#14[(var X#7)] C#15)]),
             ((var X#1),A#13[(app A#14[(var X#7)] C#15)]),
             (S#4,A#13[(app A#14[(var X#7)] C#15)]),
             (A#13[(app A#14[(var X#7)] C#15[(\ X#2.S#4)])],(letrec {E#8} in [.])),
             [{X#1=(\ X#2.S#4);E#12},(letrec {E#8} in [.])],
             ((var X#1),A#13[(app A#14[(var X#7)] C#15[[.]])]),
             ((var X#7),A#13[(app A#14[[.]] C#15[(\ X#2.S#4)])]),
             ((var X#7),A#13[(app A#14[[.]] C#15[(\ X#2.S#4)])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#1),C#6[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#9   |->  {X#1=(\ X#2.S#4);E#12},
           E#3   |->  {X#7=(letrec {E#8} in S#10);E#12},
           C#6   |->  A#13[(app A#14[(var X#7)] C#15)],
           A#11  |->  A#13[(app A#14 C#15[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);X#7=(letrec {E#8} in S#10);E#12} in A#13[(app A#14[(var X#7)] C#15[(\ X#2.S#4)])])
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);X#7=(letrec {E#8} in S#10);E#12} in A#13[(app A#14[(var X#7)] C#15[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);X#7=(letrec {E#8} in S#10);E#12} in A#13[(app A#14[(var X#7)] C#15[(\ X#2.S#4)])])
    -SR,llet-e1->                 (letrec {X#1=(\ X#2.S#4);X#7=S#10;E#12;E#8} in A#13[(app A#14[(var X#7)] C#15[(\ X#2.S#4)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#9} in S#11)
       ;E#10
       ;EE#13[X#8,(var X#7)]
     in
        A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
     )
    ,
     (letrec
        X#7= S#11
       ;E#10
       ;E#9
       ;EE#13[X#8,(var X#7)]
     in
        A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
     )
  )

where

   Delta1 = {A#12,T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),
             (A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])],(letrec {E#9} in [.])),
             [{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#15[(app A#16[[.]] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]),
             ((var X#7),[.]),
             ((var X#8),A#15[(app A#16[[.]] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),C#6[[.]]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#8)] T#17)],
           A#12  |->  A#15[(app A#16 T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -cp-in1->                     (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#9} in T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])
       ;E#10
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#7= T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;E#10
       ;E#9
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),C#6[[.]]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#7=(letrec {E#9} in T#17);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)]),
           X#15  |->  X#7,
           E#16  |->  {E#10;EE#13[X#8,(var X#7)]},
           T#14  |->  (letrec {E#9} in T#17),
           S#11  |->  T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -cp-in1->                     (letrec {X#7=(letrec {E#9} in T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec
                X#18= T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
               ;E#20
             in
                S#11
             )
       ;E#10
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;X#7= S#11
       ;E#10
       ;E#20
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#7),(letrec {X#18=T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#10;E#20;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {X#18=T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#20} in [.])),
             [{E#10;EE#13[X#8,(var X#7)]},(letrec {X#18=T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#20} in [.])],
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),C#6[[.]]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#7=(letrec {X#18=T#17;E#20} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)]),
           X#15  |->  X#7,
           E#16  |->  {E#10;EE#13[X#8,(var X#7)]},
           T#14  |->  (letrec {X#18=T#17;E#20} in S#11),
           E#9   |->  {X#18=T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#20},
           E#19  |->  {E#20}}

and instantiated rules:

                                  (letrec {X#7=(letrec {X#18=T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#20} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -cp-in1->                     (letrec {X#7=(letrec {X#18=T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#20} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {X#18=T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#20} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#18=T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=S#11;E#10;E#20;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])
       ;E#10
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;X#7= C#6[(\ X#2.S#4)]
       ;E#10
       ;E#3
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#7),(letrec {X#1=(\ X#2.S#4);E#10;E#3;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {X#1=(\ X#2.S#4);E#3} in [.])),
             [{E#10;EE#13[X#8,(var X#7)]},(letrec {X#1=(\ X#2.S#4);E#3} in [.])],
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),C#6[[.]]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#7=[.];E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)]),
           X#15  |->  X#7,
           E#16  |->  {E#10;EE#13[X#8,(var X#7)]},
           T#14  |->  [.],
           S#11  |->  C#6[(\ X#2.S#4)],
           E#9   |->  {X#1=(\ X#2.S#4);E#3}}

and instantiated rules:

                                  (letrec {X#7=(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -cp-in1->                     (letrec {X#7=(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#1=(\ X#2.S#4);X#7=C#6[(\ X#2.S#4)];E#10;E#3;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
       ;X#7= (letrec {E#9} in S#11)
       ;E#17
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;X#7= S#11
       ;E#17
       ;E#9
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#7),(letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17;E#9;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),C#6[[.]]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#15=T#14;X#7=(letrec {E#9} in S#11);E#17;EE#13[X#8,(var X#7)]} in A#12[(var X#8)]),
           E#10  |->  {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17},
           E#16  |->  {X#7=(letrec {E#9} in S#11);E#17;EE#13[X#8,(var X#7)]}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(letrec {E#9} in S#11);E#17;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -cp-in1->                     (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];X#7=(letrec {E#9} in S#11);E#17;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=(letrec {E#9} in S#11);E#17;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];X#7=S#11;E#17;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#9} in S#11)
       ;X#8= A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#10
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#7= S#11
       ;X#8= A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#10
       ;E#9
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#7),(letrec {X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10;E#9} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10},(letrec {E#9} in [.])],
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),C#6[[.]]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#18[(app A#19[(var X#7)] T#20)];E#10} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]},
           X#15         |->  X#8,
           E#16         |->  {X#7=(letrec {E#9} in S#11);E#10},
           T#14         |->  A#18[(app A#19[(var X#7)] T#20)],
           A#17         |->  A#18[(app A#19 T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10} in A#12[(var X#8)])
    -cp-in1->                     (letrec {X#7=(letrec {E#9} in S#11);X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#10} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#9} in S#11)
       ;X#8= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#10
       ;EE#19[X#18,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#7= S#11
       ;X#8= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#10
       ;E#9
       ;EE#19[X#18,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#7),(letrec {X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10;E#9;EE#19[X#18,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10;EE#19[X#18,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),C#6[[.]]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#20[(app A#21[(var X#18)] T#22)];E#10;EE#19[X#18,(var X#7)]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];EE#19[X#18,[.2]]},
           X#15         |->  X#8,
           E#16         |->  {X#7=(letrec {E#9} in S#11);E#10;EE#19[X#18,(var X#7)]},
           T#14         |->  A#20[(app A#21[(var X#18)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10;EE#19[X#18,(var X#7)]} in A#12[(var X#8)])
    -cp-in1->                     (letrec {X#7=(letrec {E#9} in S#11);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#10;EE#19[X#18,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10;EE#19[X#18,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10;E#9;EE#19[X#18,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;X#7= (letrec {E#9} in S#11)
       ;E#10
       ;EE#20[X#8,(var X#18)]
       ;EE#21[X#19,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;X#7= S#11
       ;E#10
       ;E#9
       ;EE#20[X#8,(var X#18)]
       ;EE#21[X#19,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#7),(letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10;E#9;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),C#6[[.]]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24)];X#7=(letrec {E#9} in S#11);E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#15         |->  X#18,
           E#16         |->  {X#7=(letrec {E#9} in S#11);E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]},
           T#14         |->  A#22[(app A#23[(var X#19)] T#24)],
           A#17         |->  A#22[(app A#23 T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(letrec {E#9} in S#11);E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in A#12[(var X#8)])
    -cp-in1->                     (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];X#7=(letrec {E#9} in S#11);E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(letrec {E#9} in S#11);E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=S#11;E#10;E#9;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;X#7= (letrec {E#9} in S#11)
       ;E#10
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;X#7= S#11
       ;E#10
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             ((var X#7),(letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10;E#9;EE#19[X#8,(var X#18)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#10;EE#19[X#8,(var X#18)]},(letrec {E#9} in [.])],
             ((var X#1),C#6[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),C#6[[.]]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=A#20[(app A#21[(var X#7)] T#22)];X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]},
           T#14         |->  A#20[(app A#21[(var X#7)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -cp-in1->                     (letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];X#7=S#11;E#10;E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#2.S#4)
       ;X#7= (letrec {E#9} in S#11)
       ;E#14
       ;EE#13[X#8,(var X#7)]
     in
        A#15[(app A#16[(var X#8)] C#17[(var X#1)])]
     )
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;X#7= S#11
       ;E#14
       ;E#9
       ;EE#13[X#8,(var X#7)]
     in
        A#15[(app A#16[(var X#8)] C#17[(\ X#2.S#4)])]
     )
  )

where

   Delta1 = {A#12,C#6}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),A#15[(app A#16[(var X#8)] C#17)]),
             ((var X#1),A#15[(app A#16[(var X#8)] C#17)]),
             (S#4,A#15[(app A#16[(var X#8)] C#17)]),
             ((var X#7),(letrec {X#1=(\ X#2.S#4);E#14;E#9;EE#13[X#8,(var X#7)]} in [.])),
             (A#15[(app A#16[(var X#8)] C#17[(\ X#2.S#4)])],(letrec {E#9} in [.])),
             [{X#1=(\ X#2.S#4);E#14;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#1),A#15[(app A#16[(var X#8)] C#17[[.]])]),
             ((var X#7),[.]),
             ((var X#8),A#15[(app A#16[[.]] C#17[(\ X#2.S#4)])]),
             ((var X#7),[.]),
             ((var X#8),A#15[(app A#16[[.]] C#17[(\ X#2.S#4)])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,llet-e2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),C#6[[.]]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#10  |->  {X#1=(\ X#2.S#4);E#14},
           E#3   |->  {X#7=(letrec {E#9} in S#11);E#14;EE#13[X#8,(var X#7)]},
           C#6   |->  A#15[(app A#16[(var X#8)] C#17)],
           A#12  |->  A#15[(app A#16 C#17[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);X#7=(letrec {E#9} in S#11);E#14;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] C#17[(\ X#2.S#4)])])
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);X#7=(letrec {E#9} in S#11);E#14;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] C#17[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);X#7=(letrec {E#9} in S#11);E#14;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] C#17[(\ X#2.S#4)])])
    -SR,llet-e2->                 (letrec {X#1=(\ X#2.S#4);X#7=S#11;E#14;E#9;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] C#17[(\ X#2.S#4)])])
    

================================================================================
Critical Pair:

  (
     A#11[(app (letrec {E#7} in T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#8)]
    ,
     A#11[(letrec
              E#7
           in
              (app T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#8)
           )]
  )

where

   Delta1 = {T#13,T#12,A#10,T#5,A#11}
   Delta2 = {E#7}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#8,(letrec {E#7} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {A#10  |->  A#11,
           T#5   |->  A#11[(app (letrec {E#7} in T#14) S#8)],
           T#12  |->  (app (letrec {E#7} in T#14) S#8),
           T#13  |->  (letrec {E#7} in T#14),
           S#9   |->  T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  A#11[(app (letrec {E#7} in T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#8)]
    -cp-in1->                     A#11[(app (letrec {E#7} in T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#8)]
    ................................................................................
                                  A#11[(app (letrec {E#7} in T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#8)]
    -SR,lapp1->                   A#11[(letrec {E#7} in (app T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#8))]
    

================================================================================
Critical Pair:

  (
     A#11[(app (letrec
                   X#15= T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
                  ;E#17
                in
                   S#9
                ) S#8)]
    ,
     A#11[(letrec
              X#15= T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
             ;E#17
           in
              (app S#9 S#8)
           )]
  )

where

   Delta1 = {T#13,T#12,A#10,T#5,A#11}
   Delta2 = {E#7}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#8,(letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#8,(letrec {E#7} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {A#10  |->  A#11,
           T#5   |->  A#11[(app (letrec {X#15=T#14;E#17} in S#9) S#8)],
           T#12  |->  (app (letrec {X#15=T#14;E#17} in S#9) S#8),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#9),
           E#7   |->  {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  A#11[(app (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17} in S#9) S#8)]
    -cp-in1->                     A#11[(app (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#17} in S#9) S#8)]
    ................................................................................
                                  A#11[(app (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17} in S#9) S#8)]
    -SR,lapp1->                   A#11[(letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17} in (app S#9 S#8))]
    

================================================================================
Critical Pair:

  (
     A#11[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#8)]
    ,
     A#11[(letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#8))]
  )

where

   Delta1 = {T#12,A#10,T#5,A#11}
   Delta2 = {E#7}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#8,(letrec {X#1=(\ X#2.S#4);E#3} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#8,(letrec {E#7} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {A#10  |->  A#11,
           T#5   |->  A#11[(app [.] S#8)],
           T#12  |->  (app [.] S#8),
           T#13  |->  [.],
           S#9   |->  C#6[(\ X#2.S#4)],
           E#7   |->  {X#1=(\ X#2.S#4);E#3}}

and instantiated rules:

                                  A#11[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#8)]
    -cp-in1->                     A#11[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#8)]
    ................................................................................
                                  A#11[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#8)]
    -SR,lapp1->                   A#11[(letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#8))]
    

================================================================================
Critical Pair:

  (
     A#11[(app (letrec {E#7} in S#9) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
    ,
     A#11[(letrec
              E#7
           in
              (app S#9 T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])
           )]
  )

where

   Delta1 = {T#12,A#10,T#5,A#11}
   Delta2 = {E#7}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {E#7} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#8,(letrec {E#7} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {A#10  |->  A#11,
           T#5   |->  A#11[(app (letrec {E#7} in S#9) T#13)],
           T#12  |->  (app (letrec {E#7} in S#9) T#13),
           S#8   |->  T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  A#11[(app (letrec {E#7} in S#9) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
    -cp-in1->                     A#11[(app (letrec {E#7} in S#9) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
    ................................................................................
                                  A#11[(app (letrec {E#7} in S#9) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
    -SR,lapp1->                   A#11[(letrec {E#7} in (app S#9 T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]))]
    

================================================================================
Critical Pair:

  (
     A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
    ,
     A#11[(app A#12[(letrec {E#7} in (app S#9 S#8))] T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
  )

where

   Delta1 = {A#10,T#5}
   Delta2 = {E#7}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#8,(letrec {E#7} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13)],
           A#10  |->  A#11[(app A#12 T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
    -cp-in1->                     A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
    ................................................................................
                                  A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
    -SR,lapp1->                   A#11[(app A#12[(letrec {E#7} in (app S#9 S#8))] T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#7} in T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#8)
    ,
     (letrec
        E#7
     in
        (app T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#8)
     )
  )

where

   Delta1 = {T#11,T#5}
   Delta2 = {E#7}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#8,(letrec {E#7} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {A#10  |->  [.],
           T#5   |->  (app (letrec {E#7} in T#12) S#8),
           T#11  |->  (letrec {E#7} in T#12),
           S#9   |->  T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (app (letrec {E#7} in T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#8)
    -cp-in1->                     (app (letrec {E#7} in T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#8)
    ................................................................................
                                  (app (letrec {E#7} in T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#8)
    -SR,lapp1->                   (letrec {E#7} in (app T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#8))
    

================================================================================
Critical Pair:

  (
     (app (letrec
             X#13= T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
            ;E#15
          in
             S#9
          ) S#8)
    ,
     (letrec
        X#13= T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;E#15
     in
        (app S#9 S#8)
     )
  )

where

   Delta1 = {T#11,T#5}
   Delta2 = {E#7}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#8,(letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#8,(letrec {E#7} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {A#10  |->  [.],
           T#5   |->  (app (letrec {X#13=T#12;E#15} in S#9) S#8),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#9),
           E#7   |->  {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (app (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15} in S#9) S#8)
    -cp-in1->                     (app (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#15} in S#9) S#8)
    ................................................................................
                                  (app (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15} in S#9) S#8)
    -SR,lapp1->                   (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15} in (app S#9 S#8))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#8)
    ,
     (letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#8))
  )

where

   Delta1 = {T#5}
   Delta2 = {E#7}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#8,(letrec {X#1=(\ X#2.S#4);E#3} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#8,(letrec {E#7} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {A#10  |->  [.],
           T#5   |->  (app [.] S#8),
           T#11  |->  [.],
           S#9   |->  C#6[(\ X#2.S#4)],
           E#7   |->  {X#1=(\ X#2.S#4);E#3}}

and instantiated rules:

                                  (app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#8)
    -cp-in1->                     (app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#8)
    ................................................................................
                                  (app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#8)
    -SR,lapp1->                   (letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#8))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#7} in S#9) T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])
    ,
     (letrec
        E#7
     in
        (app S#9 T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])
     )
  )

where

   Delta1 = {T#5}
   Delta2 = {E#7}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {E#7} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp1-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#8,(letrec {E#7} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {A#10  |->  [.],
           T#5   |->  (app (letrec {E#7} in S#9) T#11),
           S#8   |->  T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (app (letrec {E#7} in S#9) T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])
    -cp-in1->                     (app (letrec {E#7} in S#9) T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])
    ................................................................................
                                  (app (letrec {E#7} in S#9) T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])
    -SR,lapp1->                   (letrec {E#7} in (app S#9 T#11[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#13[(app (letrec {E#8} in T#16[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#9)]
     )
    ,
     (letrec
        E#7
     in
        A#13[(letrec
                 E#8
              in
                 (app T#16[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#9)
              )]
     )
  )

where

   Delta1 = {T#15,T#14,A#11,T#12,T#5,A#13}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#7} in A#13[(app (letrec {E#8} in T#16) S#9)]),
           A#11  |->  A#13,
           T#12  |->  A#13[(app (letrec {E#8} in T#16) S#9)],
           T#14  |->  (app (letrec {E#8} in T#16) S#9),
           T#15  |->  (letrec {E#8} in T#16),
           S#10  |->  T#16[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {E#7} in A#13[(app (letrec {E#8} in T#16[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#9)])
    -cp-in1->                     (letrec {E#7} in A#13[(app (letrec {E#8} in T#16[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#9)])
    ................................................................................
                                  (letrec {E#7} in A#13[(app (letrec {E#8} in T#16[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#13[(letrec {E#8} in (app T#16[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#13[(app (letrec
                      X#17= T#16[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
                     ;E#19
                   in
                      S#10
                   ) S#9)]
     )
    ,
     (letrec
        E#7
     in
        A#13[(letrec
                 X#17= T#16[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
                ;E#19
              in
                 (app S#10 S#9)
              )]
     )
  )

where

   Delta1 = {T#15,T#14,A#11,T#12,T#5,A#13}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#9,(letrec {X#17=T#16[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#19} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#7} in A#13[(app (letrec {X#17=T#16;E#19} in S#10) S#9)]),
           A#11  |->  A#13,
           T#12  |->  A#13[(app (letrec {X#17=T#16;E#19} in S#10) S#9)],
           T#14  |->  (app (letrec {X#17=T#16;E#19} in S#10) S#9),
           T#15  |->  (letrec {X#17=T#16;E#19} in S#10),
           E#8   |->  {X#17=T#16[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#19},
           E#18  |->  {E#19}}

and instantiated rules:

                                  (letrec {E#7} in A#13[(app (letrec {X#17=T#16[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#19} in S#10) S#9)])
    -cp-in1->                     (letrec {E#7} in A#13[(app (letrec {X#17=T#16[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#19} in S#10) S#9)])
    ................................................................................
                                  (letrec {E#7} in A#13[(app (letrec {X#17=T#16[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#19} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#13[(letrec {X#17=T#16[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#19} in (app S#10 S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#13[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#9)]
     )
    ,
     (letrec
        E#7
     in
        A#13[(letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#9))]
     )
  )

where

   Delta1 = {T#14,A#11,T#12,T#5,A#13}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#9,(letrec {X#1=(\ X#2.S#4);E#3} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#7} in A#13[(app [.] S#9)]),
           A#11  |->  A#13,
           T#12  |->  A#13[(app [.] S#9)],
           T#14  |->  (app [.] S#9),
           T#15  |->  [.],
           S#10  |->  C#6[(\ X#2.S#4)],
           E#8   |->  {X#1=(\ X#2.S#4);E#3}}

and instantiated rules:

                                  (letrec {E#7} in A#13[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#9)])
    -cp-in1->                     (letrec {E#7} in A#13[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#9)])
    ................................................................................
                                  (letrec {E#7} in A#13[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#13[(letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#13[(app (letrec {E#8} in S#10) T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
     )
    ,
     (letrec
        E#7
     in
        A#13[(letrec
                 E#8
              in
                 (app S#10 T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])
              )]
     )
  )

where

   Delta1 = {T#14,A#11,T#12,T#5,A#13}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {E#8} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#7} in A#13[(app (letrec {E#8} in S#10) T#15)]),
           A#11  |->  A#13,
           T#12  |->  A#13[(app (letrec {E#8} in S#10) T#15)],
           T#14  |->  (app (letrec {E#8} in S#10) T#15),
           S#9   |->  T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {E#7} in A#13[(app (letrec {E#8} in S#10) T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -cp-in1->                     (letrec {E#7} in A#13[(app (letrec {E#8} in S#10) T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])])
    ................................................................................
                                  (letrec {E#7} in A#13[(app (letrec {E#8} in S#10) T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -SR,lapp2->                   (letrec {E#7} in A#13[(letrec {E#8} in (app S#10 T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
     )
    ,
     (letrec
        E#7
     in
        A#13[(app A#14[(letrec {E#8} in (app S#10 S#9))] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
     )
  )

where

   Delta1 = {A#11,T#12,T#5}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#7} in A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15)]),
           T#12  |->  A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {E#7} in A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -cp-in1->                     (letrec {E#7} in A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])])
    ................................................................................
                                  (letrec {E#7} in A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -SR,lapp2->                   (letrec {E#7} in A#13[(app A#14[(letrec {E#8} in (app S#10 S#9))] T#15[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (app (letrec {E#8} in T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#9)
     )
    ,
     (letrec
        E#7
     in
        (letrec
           E#8
        in
           (app T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#9)
        )
     )
  )

where

   Delta1 = {T#13,T#12,T#5}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#7} in (app (letrec {E#8} in T#14) S#9)),
           A#11  |->  [.],
           T#12  |->  (app (letrec {E#8} in T#14) S#9),
           T#13  |->  (letrec {E#8} in T#14),
           S#10  |->  T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {E#7} in (app (letrec {E#8} in T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#9))
    -cp-in1->                     (letrec {E#7} in (app (letrec {E#8} in T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#9))
    ................................................................................
                                  (letrec {E#7} in (app (letrec {E#8} in T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#9))
    -SR,lapp2->                   (letrec {E#7} in (letrec {E#8} in (app T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#9)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (app (letrec
                X#15= T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
               ;E#17
             in
                S#10
             ) S#9)
     )
    ,
     (letrec
        E#7
     in
        (letrec
           X#15= T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
          ;E#17
        in
           (app S#10 S#9)
        )
     )
  )

where

   Delta1 = {T#13,T#12,T#5}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#9,(letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#7} in (app (letrec {X#15=T#14;E#17} in S#10) S#9)),
           A#11  |->  [.],
           T#12  |->  (app (letrec {X#15=T#14;E#17} in S#10) S#9),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#10),
           E#8   |->  {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {E#7} in (app (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17} in S#10) S#9))
    -cp-in1->                     (letrec {E#7} in (app (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#17} in S#10) S#9))
    ................................................................................
                                  (letrec {E#7} in (app (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17} in S#10) S#9))
    -SR,lapp2->                   (letrec {E#7} in (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17} in (app S#10 S#9)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#7} in (app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#9))
    ,
     (letrec {E#7} in (letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#9)))
  )

where

   Delta1 = {T#12,T#5}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#9,(letrec {X#1=(\ X#2.S#4);E#3} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#7} in (app [.] S#9)),
           A#11  |->  [.],
           T#12  |->  (app [.] S#9),
           T#13  |->  [.],
           S#10  |->  C#6[(\ X#2.S#4)],
           E#8   |->  {X#1=(\ X#2.S#4);E#3}}

and instantiated rules:

                                  (letrec {E#7} in (app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#9))
    -cp-in1->                     (letrec {E#7} in (app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#9))
    ................................................................................
                                  (letrec {E#7} in (app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#9))
    -SR,lapp2->                   (letrec {E#7} in (letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#9)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (app (letrec {E#8} in S#10) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])
     )
    ,
     (letrec
        E#7
     in
        (letrec
           E#8
        in
           (app S#10 T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])
        )
     )
  )

where

   Delta1 = {T#12,T#5}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {E#8} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#7} in (app (letrec {E#8} in S#10) T#13)),
           A#11  |->  [.],
           T#12  |->  (app (letrec {E#8} in S#10) T#13),
           S#9   |->  T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {E#7} in (app (letrec {E#8} in S#10) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]))
    -cp-in1->                     (letrec {E#7} in (app (letrec {E#8} in S#10) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]))
    ................................................................................
                                  (letrec {E#7} in (app (letrec {E#8} in S#10) T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]))
    -SR,lapp2->                   (letrec {E#7} in (letrec {E#8} in (app S#10 T#13[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
       ;E#15
     in
        A#11[(app (letrec {E#8} in S#10) S#9)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;E#15
     in
        A#11[(letrec {E#8} in (app S#10 S#9))]
     )
  )

where

   Delta1 = {T#5}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),C#6[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#13=T#12;E#15} in A#11[(app (letrec {E#8} in S#10) S#9)]),
           E#7   |->  {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -cp-in1->                     (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#15} in A#11[(app (letrec {E#8} in S#10) S#9)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {X#13=T#12[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#15} in A#11[(letrec {E#8} in (app S#10 S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#2.S#4)
       ;E#12
     in
        A#13[(app (letrec {E#8} in C#16[(var X#1)]) S#9)]
     )
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;E#12
     in
        A#13[(letrec {E#8} in (app C#16[(\ X#2.S#4)] S#9))]
     )
  )

where

   Delta1 = {C#15,C#14,A#11,C#6,A#13}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),A#13[(app (letrec {E#8} in C#16) S#9)]),
             ((var X#1),A#13[(app (letrec {E#8} in C#16) S#9)]),
             (S#4,A#13[(app (letrec {E#8} in C#16) S#9)]),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),A#13[(app (letrec {E#8} in C#16[[.]]) S#9)])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#7   |->  {X#1=(\ X#2.S#4);E#12},
           E#3   |->  {E#12},
           A#11  |->  A#13,
           C#6   |->  A#13[(app (letrec {E#8} in C#16) S#9)],
           C#14  |->  (app (letrec {E#8} in C#16) S#9),
           C#15  |->  (letrec {E#8} in C#16),
           S#10  |->  C#16[(\ X#2.S#4)]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (letrec {E#8} in C#16[(\ X#2.S#4)]) S#9)])
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (letrec {E#8} in C#16[(var X#1)]) S#9)])
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (letrec {E#8} in C#16[(\ X#2.S#4)]) S#9)])
    -SR,lapp2->                   (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(letrec {E#8} in (app C#16[(\ X#2.S#4)] S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#2.S#4)
       ;E#12
     in
        A#13[(app (letrec {X#17=C#16[(var X#1)];E#19} in S#10) S#9)]
     )
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;E#12
     in
        A#13[(letrec {X#17=C#16[(\ X#2.S#4)];E#19} in (app S#10 S#9))]
     )
  )

where

   Delta1 = {C#15,C#14,A#11,C#6,A#13}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),A#13[(app (letrec {X#17=C#16;E#19} in S#10) S#9)]),
             ((var X#1),A#13[(app (letrec {X#17=C#16;E#19} in S#10) S#9)]),
             (S#4,A#13[(app (letrec {X#17=C#16;E#19} in S#10) S#9)]),
             (S#9,(letrec {X#17=C#16[(\ X#2.S#4)];E#19} in [.])),
             ((var X#1),A#13[(app (letrec {X#17=C#16[[.]];E#19} in S#10) S#9)])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#7   |->  {X#1=(\ X#2.S#4);E#12},
           E#3   |->  {E#12},
           A#11  |->  A#13,
           C#6   |->  A#13[(app (letrec {X#17=C#16;E#19} in S#10) S#9)],
           C#14  |->  (app (letrec {X#17=C#16;E#19} in S#10) S#9),
           C#15  |->  (letrec {X#17=C#16;E#19} in S#10),
           E#8   |->  {X#17=C#16[(\ X#2.S#4)];E#19},
           E#18  |->  {E#19}}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (letrec {X#17=C#16[(\ X#2.S#4)];E#19} in S#10) S#9)])
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (letrec {X#17=C#16[(var X#1)];E#19} in S#10) S#9)])
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (letrec {X#17=C#16[(\ X#2.S#4)];E#19} in S#10) S#9)])
    -SR,lapp2->                   (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(letrec {X#17=C#16[(\ X#2.S#4)];E#19} in (app S#10 S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#2.S#4)
       ;E#12
     in
        A#13[(app (letrec {E#8} in S#10) C#15[(var X#1)])]
     )
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;E#12
     in
        A#13[(letrec {E#8} in (app S#10 C#15[(\ X#2.S#4)]))]
     )
  )

where

   Delta1 = {C#14,A#11,C#6,A#13}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),A#13[(app (letrec {E#8} in S#10) C#15)]),
             ((var X#1),A#13[(app (letrec {E#8} in S#10) C#15)]),
             (S#4,A#13[(app (letrec {E#8} in S#10) C#15)]),
             (C#15[(\ X#2.S#4)],(letrec {E#8} in [.])),
             ((var X#1),A#13[(app (letrec {E#8} in S#10) C#15[[.]])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#7   |->  {X#1=(\ X#2.S#4);E#12},
           E#3   |->  {E#12},
           A#11  |->  A#13,
           C#6   |->  A#13[(app (letrec {E#8} in S#10) C#15)],
           C#14  |->  (app (letrec {E#8} in S#10) C#15),
           S#9   |->  C#15[(\ X#2.S#4)]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (letrec {E#8} in S#10) C#15[(\ X#2.S#4)])])
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (letrec {E#8} in S#10) C#15[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app (letrec {E#8} in S#10) C#15[(\ X#2.S#4)])])
    -SR,lapp2->                   (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(letrec {E#8} in (app S#10 C#15[(\ X#2.S#4)]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#2.S#4)
       ;E#12
     in
        A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] C#15[(var X#1)])]
     )
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;E#12
     in
        A#13[(app A#14[(letrec {E#8} in (app S#10 S#9))] C#15[(\ X#2.S#4)])]
     )
  )

where

   Delta1 = {A#11,C#6}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] C#15)]),
             ((var X#1),A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] C#15)]),
             (S#4,A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] C#15)]),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] C#15[[.]])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#7   |->  {X#1=(\ X#2.S#4);E#12},
           E#3   |->  {E#12},
           C#6   |->  A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] C#15)],
           A#11  |->  A#13[(app A#14 C#15[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] C#15[(\ X#2.S#4)])])
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] C#15[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] C#15[(\ X#2.S#4)])])
    -SR,lapp2->                   (letrec {X#1=(\ X#2.S#4);E#12} in A#13[(app A#14[(letrec {E#8} in (app S#10 S#9))] C#15[(\ X#2.S#4)])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#2.S#4);E#12} in (app (letrec {E#8} in C#14[(var X#1)]) S#9))
    ,
     (letrec {X#1=(\ X#2.S#4);E#12} in (letrec {E#8} in (app C#14[(\ X#2.S#4)] S#9)))
  )

where

   Delta1 = {C#13,C#6}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),(app (letrec {E#8} in C#14) S#9)),
             ((var X#1),(app (letrec {E#8} in C#14) S#9)),
             (S#4,(app (letrec {E#8} in C#14) S#9)),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),(app (letrec {E#8} in C#14[[.]]) S#9))}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#7   |->  {X#1=(\ X#2.S#4);E#12},
           E#3   |->  {E#12},
           A#11  |->  [.],
           C#6   |->  (app (letrec {E#8} in C#14) S#9),
           C#13  |->  (letrec {E#8} in C#14),
           S#10  |->  C#14[(\ X#2.S#4)]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#12} in (app (letrec {E#8} in C#14[(\ X#2.S#4)]) S#9))
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#12} in (app (letrec {E#8} in C#14[(var X#1)]) S#9))
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#12} in (app (letrec {E#8} in C#14[(\ X#2.S#4)]) S#9))
    -SR,lapp2->                   (letrec {X#1=(\ X#2.S#4);E#12} in (letrec {E#8} in (app C#14[(\ X#2.S#4)] S#9)))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#2.S#4)
       ;E#12
     in
        (app (letrec {X#15=C#14[(var X#1)];E#17} in S#10) S#9)
     )
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;E#12
     in
        (letrec {X#15=C#14[(\ X#2.S#4)];E#17} in (app S#10 S#9))
     )
  )

where

   Delta1 = {C#13,C#6}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),(app (letrec {X#15=C#14;E#17} in S#10) S#9)),
             ((var X#1),(app (letrec {X#15=C#14;E#17} in S#10) S#9)),
             (S#4,(app (letrec {X#15=C#14;E#17} in S#10) S#9)),
             (S#9,(letrec {X#15=C#14[(\ X#2.S#4)];E#17} in [.])),
             ((var X#1),(app (letrec {X#15=C#14[[.]];E#17} in S#10) S#9))}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#7   |->  {X#1=(\ X#2.S#4);E#12},
           E#3   |->  {E#12},
           A#11  |->  [.],
           C#6   |->  (app (letrec {X#15=C#14;E#17} in S#10) S#9),
           C#13  |->  (letrec {X#15=C#14;E#17} in S#10),
           E#8   |->  {X#15=C#14[(\ X#2.S#4)];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#12} in (app (letrec {X#15=C#14[(\ X#2.S#4)];E#17} in S#10) S#9))
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#12} in (app (letrec {X#15=C#14[(var X#1)];E#17} in S#10) S#9))
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#12} in (app (letrec {X#15=C#14[(\ X#2.S#4)];E#17} in S#10) S#9))
    -SR,lapp2->                   (letrec {X#1=(\ X#2.S#4);E#12} in (letrec {X#15=C#14[(\ X#2.S#4)];E#17} in (app S#10 S#9)))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#2.S#4);E#12} in (app (letrec {E#8} in S#10) C#13[(var X#1)]))
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;E#12
     in
        (letrec {E#8} in (app S#10 C#13[(\ X#2.S#4)]))
     )
  )

where

   Delta1 = {C#6}
   Delta2 = {E#7,E#8}
   Delta3 = {((\ X#2.S#4),(app (letrec {E#8} in S#10) C#13)),
             ((var X#1),(app (letrec {E#8} in S#10) C#13)),
             (S#4,(app (letrec {E#8} in S#10) C#13)),
             (C#13[(\ X#2.S#4)],(letrec {E#8} in [.])),
             ((var X#1),(app (letrec {E#8} in S#10) C#13[[.]]))}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp2-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#9,(letrec {E#8} in [.])),((var X#1),C#6[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#7   |->  {X#1=(\ X#2.S#4);E#12},
           E#3   |->  {E#12},
           A#11  |->  [.],
           C#6   |->  (app (letrec {E#8} in S#10) C#13),
           S#9   |->  C#13[(\ X#2.S#4)]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#12} in (app (letrec {E#8} in S#10) C#13[(\ X#2.S#4)]))
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#12} in (app (letrec {E#8} in S#10) C#13[(var X#1)]))
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#12} in (app (letrec {E#8} in S#10) C#13[(\ X#2.S#4)]))
    -SR,lapp2->                   (letrec {X#1=(\ X#2.S#4);E#12} in (letrec {E#8} in (app S#10 C#13[(\ X#2.S#4)])))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
       ;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]
     in
        A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
     )
    ,
     (letrec
        E#8
       ;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]
     in
        A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
     )
  )

where

   Delta1 = {A#12,T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {E#9} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#15[(app A#16[[.]] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]),
             ((var X#7),A#15[(app A#16[[.]] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#7)] T#17)],
           A#12  |->  A#15[(app A#16 T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -cp-in1->                     (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])])
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
       ;E#17
       ;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
       ;E#17
       ;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {E#9} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5   |->  (letrec {X#15=T#14;E#17;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)]),
           E#8   |->  {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17},
           E#16  |->  {E#17;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#17;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#15=T#14[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#17;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app (letrec {E#9} in T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#10)]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(letrec
                      E#9
                   in
                      (app T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#10)
                   )]
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,T#19,A#17,T#14,T#5,A#18}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {E#9} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=A#18[(app (letrec {E#9} in T#21) S#10)];E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  A#18,
           T#14         |->  A#18[(app (letrec {E#9} in T#21) S#10)],
           T#19         |->  (app (letrec {E#9} in T#21) S#10),
           T#20         |->  (letrec {E#9} in T#21),
           S#11         |->  T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#7=A#18[(app (letrec {E#9} in T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#10)];E#8} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#7=A#18[(app (letrec {E#9} in T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#10)];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app (letrec {E#9} in T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#10)];E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#18[(letrec {E#9} in (app T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#10))];E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app (letrec
                           X#22= T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
                          ;E#24
                        in
                           S#11
                        ) S#10)]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(letrec
                      X#22= T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
                     ;E#24
                   in
                      (app S#11 S#10)
                   )]
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,T#19,A#17,T#14,T#5,A#18}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {X#22=T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#24} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=A#18[(app (letrec {X#22=T#21;E#24} in S#11) S#10)];E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  A#18,
           T#14         |->  A#18[(app (letrec {X#22=T#21;E#24} in S#11) S#10)],
           T#19         |->  (app (letrec {X#22=T#21;E#24} in S#11) S#10),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#11),
           E#9          |->  {X#22=T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#7=A#18[(app (letrec {X#22=T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#24} in S#11) S#10)];E#8} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#7=A#18[(app (letrec {X#22=T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#24} in S#11) S#10)];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app (letrec {X#22=T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#24} in S#11) S#10)];E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#18[(letrec {X#22=T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#24} in (app S#11 S#10))];E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#10)]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#10))]
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#19,A#17,T#14,T#5,A#18}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {X#1=(\ X#2.S#4);E#3} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=A#18[(app [.] S#10)];E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  A#18,
           T#14         |->  A#18[(app [.] S#10)],
           T#19         |->  (app [.] S#10),
           T#20         |->  [.],
           S#11         |->  C#6[(\ X#2.S#4)],
           E#9          |->  {X#1=(\ X#2.S#4);E#3}}

and instantiated rules:

                                  (letrec {X#7=A#18[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#10)];E#8} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#7=A#18[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#10)];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#10)];E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#18[(letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#10))];E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app (letrec {E#9} in S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(letrec
                      E#9
                   in
                      (app S#11 T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])
                   )]
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#19,A#17,T#14,T#5,A#18}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {E#9} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=A#18[(app (letrec {E#9} in S#11) T#20)];E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  A#18,
           T#14         |->  A#18[(app (letrec {E#9} in S#11) T#20)],
           T#19         |->  (app (letrec {E#9} in S#11) T#20),
           S#10         |->  T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#7=A#18[(app (letrec {E#9} in S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#7=A#18[(app (letrec {E#9} in S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app (letrec {E#9} in S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#18[(letrec {E#9} in (app S#11 T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]))];E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(app A#19[(letrec {E#9} in (app S#11 S#10))] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {E#9} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20)];E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           T#14         |->  A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20)],
           A#17         |->  A#18[(app A#19 T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#7=A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#18[(app A#19[(letrec {E#9} in (app S#11 S#10))] T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (app (letrec {E#9} in T#19[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#10)
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= (letrec
                E#9
             in
                (app T#19[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#10)
             )
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#18,T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {E#9} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=(app (letrec {E#9} in T#19) S#10);E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  [.],
           T#14         |->  (app (letrec {E#9} in T#19) S#10),
           T#18         |->  (letrec {E#9} in T#19),
           S#11         |->  T#19[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#7=(app (letrec {E#9} in T#19[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#10);E#8} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#7=(app (letrec {E#9} in T#19[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#10);E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(app (letrec {E#9} in T#19[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#10);E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=(letrec {E#9} in (app T#19[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#10));E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (app (letrec
                     X#20= T#19[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
                    ;E#22
                  in
                     S#11
                  ) S#10)
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= (letrec
                X#20= T#19[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
               ;E#22
             in
                (app S#11 S#10)
             )
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#18,T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {X#20=T#19[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#22} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=(app (letrec {X#20=T#19;E#22} in S#11) S#10);E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  [.],
           T#14         |->  (app (letrec {X#20=T#19;E#22} in S#11) S#10),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#11),
           E#9          |->  {X#20=T#19[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#7=(app (letrec {X#20=T#19[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#22} in S#11) S#10);E#8} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#7=(app (letrec {X#20=T#19[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#22} in S#11) S#10);E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(app (letrec {X#20=T#19[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#22} in S#11) S#10);E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=(letrec {X#20=T#19[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#22} in (app S#11 S#10));E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#10)
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= (letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#10))
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {X#1=(\ X#2.S#4);E#3} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=(app [.] S#10);E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  [.],
           T#14         |->  (app [.] S#10),
           T#18         |->  [.],
           S#11         |->  C#6[(\ X#2.S#4)],
           E#9          |->  {X#1=(\ X#2.S#4);E#3}}

and instantiated rules:

                                  (letrec {X#7=(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#10);E#8} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#7=(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#10);E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#10);E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=(letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#10));E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (app (letrec {E#9} in S#11) T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= (letrec
                E#9
             in
                (app S#11 T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])
             )
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {E#9} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=(app (letrec {E#9} in S#11) T#18);E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  [.],
           T#14         |->  (app (letrec {E#9} in S#11) T#18),
           S#10         |->  T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#7=(app (letrec {E#9} in S#11) T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]);E#8} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#7=(app (letrec {E#9} in S#11) T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]);E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(app (letrec {E#9} in S#11) T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]);E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=(letrec {E#9} in (app S#11 T#18[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]));E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#8
       ;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#8
       ;EE#19[X#18,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {E#9} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22)];E#8;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];EE#19[X#18,[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#8;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]},
           T#14         |->  A#20[(app A#21[(var X#18)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#8;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8;EE#19[X#18,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#8
       ;EE#20[X#7,(var X#18)]
       ;EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#8
       ;EE#20[X#7,(var X#18)]
       ;EE#21[X#19,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {E#9} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24)];E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]},
           T#14         |->  A#22[(app A#23[(var X#19)] T#24)],
           A#17         |->  A#22[(app A#23 T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (letrec {E#9} in T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#10)]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(letrec
                       E#9
                    in
                       (app T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#10)
                    )]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,T#21,A#17,T#14,T#5,A#20}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {E#9} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=A#20[(app (letrec {E#9} in T#23) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[(app (letrec {E#9} in T#23) S#10)],
           T#21         |->  (app (letrec {E#9} in T#23) S#10),
           T#22         |->  (letrec {E#9} in T#23),
           S#11         |->  T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (letrec {E#9} in T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#18=A#20[(app (letrec {E#9} in T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (letrec {E#9} in T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#20[(letrec {E#9} in (app T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#10))];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (letrec
                            X#24= T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
                           ;E#26
                         in
                            S#11
                         ) S#10)]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(letrec
                       X#24= T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
                      ;E#26
                    in
                       (app S#11 S#10)
                    )]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,T#21,A#17,T#14,T#5,A#20}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {X#24=T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#26} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=A#20[(app (letrec {X#24=T#23;E#26} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[(app (letrec {X#24=T#23;E#26} in S#11) S#10)],
           T#21         |->  (app (letrec {X#24=T#23;E#26} in S#11) S#10),
           T#22         |->  (letrec {X#24=T#23;E#26} in S#11),
           E#9          |->  {X#24=T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#26},
           E#25         |->  {E#26}}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (letrec {X#24=T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#26} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#18=A#20[(app (letrec {X#24=T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#26} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (letrec {X#24=T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#26} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#20[(letrec {X#24=T#23[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#26} in (app S#11 S#10))];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#10)]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#10))]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#21,A#17,T#14,T#5,A#20}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {X#1=(\ X#2.S#4);E#3} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=A#20[(app [.] S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[(app [.] S#10)],
           T#21         |->  (app [.] S#10),
           T#22         |->  [.],
           S#11         |->  C#6[(\ X#2.S#4)],
           E#9          |->  {X#1=(\ X#2.S#4);E#3}}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#18=A#20[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#20[(letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#10))];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (letrec {E#9} in S#11) T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(letrec
                       E#9
                    in
                       (app S#11 T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])
                    )]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#21,A#17,T#14,T#5,A#20}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {E#9} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=A#20[(app (letrec {E#9} in S#11) T#22)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[(app (letrec {E#9} in S#11) T#22)],
           T#21         |->  (app (letrec {E#9} in S#11) T#22),
           S#10         |->  T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (letrec {E#9} in S#11) T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#18=A#20[(app (letrec {E#9} in S#11) T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (letrec {E#9} in S#11) T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#20[(letrec {E#9} in (app S#11 T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]))];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(letrec {E#9} in (app S#11 S#10))] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {E#9} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           T#14         |->  A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#18=A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#20[(app A#21[(letrec {E#9} in (app S#11 S#10))] T#22[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (letrec {E#9} in T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#10)
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= (letrec
                 E#9
              in
                 (app T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#10)
              )
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {E#9} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=(app (letrec {E#9} in T#21) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  (app (letrec {E#9} in T#21) S#10),
           T#20         |->  (letrec {E#9} in T#21),
           S#11         |->  T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#18=(app (letrec {E#9} in T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#18=(app (letrec {E#9} in T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=(app (letrec {E#9} in T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=(letrec {E#9} in (app T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])] S#10));E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (letrec
                      X#22= T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
                     ;E#24
                   in
                      S#11
                   ) S#10)
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= (letrec
                 X#22= T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
                ;E#24
              in
                 (app S#11 S#10)
              )
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {X#22=T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#24} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=(app (letrec {X#22=T#21;E#24} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  (app (letrec {X#22=T#21;E#24} in S#11) S#10),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#11),
           E#9          |->  {X#22=T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#18=(app (letrec {X#22=T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#24} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#18=(app (letrec {X#22=T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])];E#24} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=(app (letrec {X#22=T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#24} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=(letrec {X#22=T#21[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])];E#24} in (app S#11 S#10));E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#10)
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= (letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#10))
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (S#10,(letrec {X#1=(\ X#2.S#4);E#3} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=(app [.] S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  (app [.] S#10),
           T#20         |->  [.],
           S#11         |->  C#6[(\ X#2.S#4)],
           E#9          |->  {X#1=(\ X#2.S#4);E#3}}

and instantiated rules:

                                  (letrec {X#18=(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#18=(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)]) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=(app (letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)]) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=(letrec {X#1=(\ X#2.S#4);E#3} in (app C#6[(\ X#2.S#4)] S#10));E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (letrec {E#9} in S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])])
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= (letrec
                 E#9
              in
                 (app S#11 T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])])
              )
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#5}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),C#6),
             ((var X#1),C#6),
             (S#4,C#6),
             (T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])],(letrec {E#9} in [.])),
             ((var X#1),C#6[[.]]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5          |->  (letrec {X#18=(app (letrec {E#9} in S#11) T#20);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  (app (letrec {E#9} in S#11) T#20),
           S#10         |->  T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#18=(app (letrec {E#9} in S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -cp-in1->                     (letrec {X#18=(app (letrec {E#9} in S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=(app (letrec {E#9} in S#11) T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=(letrec {E#9} in (app S#11 T#20[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]));E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#2.S#4)
       ;E#14
       ;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]
     in
        A#15[(app A#16[(var X#7)] C#17[(var X#1)])]
     )
    ,
     (letrec
        X#1= (\ X#2.S#4)
       ;E#14
       ;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]
     in
        A#15[(app A#16[(var X#7)] C#17[(\ X#2.S#4)])]
     )
  )

where

   Delta1 = {A#12,C#6}
   Delta2 = {E#9}
   Delta3 = {((\ X#2.S#4),A#15[(app A#16[(var X#7)] C#17)]),
             ((var X#1),A#15[(app A#16[(var X#7)] C#17)]),
             (S#4,A#15[(app A#16[(var X#7)] C#17)]),
             (S#10,(letrec {E#9} in [.])),
             ((var X#1),A#15[(app A#16[(var X#7)] C#17[[.]])]),
             ((var X#7),A#15[(app A#16[[.]] C#17[(\ X#2.S#4)])]),
             ((var X#7),A#15[(app A#16[[.]] C#17[(\ X#2.S#4)])])}
   Delta4=  {}

from overlapping -cp-in1-> . -SR,lapp3-> with input rules:

                                  T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
    -cp-in1->                     T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(var X#1)])]
    and constraints: ((\ X#2.S#4),C#6), ((var X#1),C#6), (S#4,C#6)
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#5[(letrec {X#1=(\ X#2.S#4);E#3} in C#6[(\ X#2.S#4)])]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((\ X#2.S#4),C#6),((var X#1),C#6),(S#4,C#6),(S#10,(letrec {E#9} in [.])),((var X#1),C#6[[.]]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#5   |->  [.],
           E#8   |->  {X#1=(\ X#2.S#4);E#14},
           E#3   |->  {E#14;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]},
           C#6   |->  A#15[(app A#16[(var X#7)] C#17)],
           A#12  |->  A#15[(app A#16 C#17[(\ X#2.S#4)])]}

and instantiated rules:

                                  (letrec {X#1=(\ X#2.S#4);E#14;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#15[(app A#16[(var X#7)] C#17[(\ X#2.S#4)])])
    -cp-in1->                     (letrec {X#1=(\ X#2.S#4);E#14;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#15[(app A#16[(var X#7)] C#17[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(\ X#2.S#4);E#14;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#15[(app A#16[(var X#7)] C#17[(\ X#2.S#4)])])
    -SR,lapp3->                   (letrec {X#1=(\ X#2.S#4);E#14;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#15[(app A#16[(var X#7)] C#17[(\ X#2.S#4)])])
    

================================================================================
Critical Pair:

  (
     A#9[(app (\ X#5.S#7) T#11[(app (\ X#1.S#3) S#2)])]
    ,
     A#9[(letrec {X#5=T#11[(letrec {X#1=S#2} in S#3)]} in S#7)]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#11[(letrec {X#1=S#2} in S#3)],(\ X#5.[.])),
             (T#11[(letrec {X#1=S#2} in S#3)],(letrec {X#5=[.]} in S#7))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (\ X#5.S#7) T#11)],
           T#10  |->  (app (\ X#5.S#7) T#11),
           S#6   |->  T#11[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  A#9[(app (\ X#5.S#7) T#11[(letrec {X#1=S#2} in S#3)])]
    -lbeta1->                     A#9[(app (\ X#5.S#7) T#11[(app (\ X#1.S#3) S#2)])]
    ................................................................................
                                  A#9[(app (\ X#5.S#7) T#11[(letrec {X#1=S#2} in S#3)])]
    -SR,lbeta1->                  A#9[(letrec {X#5=T#11[(letrec {X#1=S#2} in S#3)]} in S#7)]
    

================================================================================
Critical Pair:

  (
     A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(app (\ X#1.S#3) S#2)])]
    ,
     A#9[(app A#10[(letrec {X#5=S#6} in S#7)] T#11[(letrec {X#1=S#2} in S#3)])]
  )

where

   Delta1 = {A#8,T#4}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7))}


and found solution:

    Sol = {T#4  |->  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11)],
           A#8  |->  A#9[(app A#10 T#11[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(letrec {X#1=S#2} in S#3)])]
    -lbeta1->                     A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(app (\ X#1.S#3) S#2)])]
    ................................................................................
                                  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(letrec {X#1=S#2} in S#3)])]
    -SR,lbeta1->                  A#9[(app A#10[(letrec {X#5=S#6} in S#7)] T#11[(letrec {X#1=S#2} in S#3)])]
    

================================================================================
Critical Pair:

  (
     (app (\ X#5.S#7) T#9[(app (\ X#1.S#3) S#2)])
    ,
     (letrec {X#5=T#9[(letrec {X#1=S#2} in S#3)]} in S#7)
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#9[(letrec {X#1=S#2} in S#3)],(\ X#5.[.])),
             (T#9[(letrec {X#1=S#2} in S#3)],(letrec {X#5=[.]} in S#7))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7))}


and found solution:

    Sol = {A#8  |->  [.],
           T#4  |->  (app (\ X#5.S#7) T#9),
           S#6  |->  T#9[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (app (\ X#5.S#7) T#9[(letrec {X#1=S#2} in S#3)])
    -lbeta1->                     (app (\ X#5.S#7) T#9[(app (\ X#1.S#3) S#2)])
    ................................................................................
                                  (app (\ X#5.S#7) T#9[(letrec {X#1=S#2} in S#3)])
    -SR,lbeta1->                  (letrec {X#5=T#9[(letrec {X#1=S#2} in S#3)]} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(app (\ X#1.S#3) S#2)])])
    ,
     (letrec {E#6} in A#11[(letrec {X#5=T#13[(letrec {X#1=S#2} in S#3)]} in S#8)])
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#13[(letrec {X#1=S#2} in S#3)],(\ X#5.[.])),
             (T#13[(letrec {X#1=S#2} in S#3)],(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (\ X#5.S#8) T#13)],
           T#12  |->  (app (\ X#5.S#8) T#13),
           S#7   |->  T#13[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(letrec {X#1=S#2} in S#3)])])
    -lbeta1->                     (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(app (\ X#1.S#3) S#2)])])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(letrec {X#1=S#2} in S#3)])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=T#13[(letrec {X#1=S#2} in S#3)]} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(app (\ X#1.S#3) S#2)])]
     )
    ,
     (letrec
        E#6
     in
        A#11[(app A#12[(letrec {X#5=S#7} in S#8)] T#13[(letrec {X#1=S#2} in S#3)])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)]),
           T#10  |->  A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(letrec {X#1=S#2} in S#3)])])
    -lbeta1->                     (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(app (\ X#1.S#3) S#2)])])
    ................................................................................
                                  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(letrec {X#1=S#2} in S#3)])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(app A#12[(letrec {X#5=S#7} in S#8)] T#13[(letrec {X#1=S#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (app (\ X#5.S#8) T#11[(app (\ X#1.S#3) S#2)]))
    ,
     (letrec {E#6} in (letrec {X#5=T#11[(letrec {X#1=S#2} in S#3)]} in S#8))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#11[(letrec {X#1=S#2} in S#3)],(\ X#5.[.])),
             (T#11[(letrec {X#1=S#2} in S#3)],(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in (app (\ X#5.S#8) T#11)),
           A#9   |->  [.],
           T#10  |->  (app (\ X#5.S#8) T#11),
           S#7   |->  T#11[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {E#6} in (app (\ X#5.S#8) T#11[(letrec {X#1=S#2} in S#3)]))
    -lbeta1->                     (letrec {E#6} in (app (\ X#5.S#8) T#11[(app (\ X#1.S#3) S#2)]))
    ................................................................................
                                  (letrec {E#6} in (app (\ X#5.S#8) T#11[(letrec {X#1=S#2} in S#3)]))
    -SR,lbeta2->                  (letrec {E#6} in (letrec {X#5=T#11[(letrec {X#1=S#2} in S#3)]} in S#8))
    

================================================================================
Critical Pair:

  (
     (letrec {X#11=T#10[(app (\ X#1.S#3) S#2)];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    ,
     (letrec
        X#11= T#10[(letrec {X#1=S#2} in S#3)]
       ;E#13
     in
        A#9[(letrec {X#5=S#7} in S#8)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;E#13} in A#9[(app (\ X#5.S#8) S#7)]),
           E#6   |->  {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    -lbeta1->                     (letrec {X#11=T#10[(app (\ X#1.S#3) S#2)];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13} in A#9[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (app (\ X#1.A#9[(app (\ X#5.S#8) S#7)]) S#2)
    ,
     (letrec {X#1=S#2} in A#9[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  [.],
           S#3   |->  A#9[(app (\ X#5.S#8) S#7)],
           E#6   |->  {X#1=S#2},
           E#10  |->  {}}

and instantiated rules:

                                  (letrec {X#1=S#2} in A#9[(app (\ X#5.S#8) S#7)])
    -lbeta1->                     (app (\ X#1.A#9[(app (\ X#5.S#8) S#7)]) S#2)
    ................................................................................
                                  (letrec {X#1=S#2} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {X#1=S#2} in A#9[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        A#13[(app A#14[(var X#5)] T#15[(app (\ X#1.S#3) S#2)])]
     )
    ,
     (letrec
        E#7
       ;EE#11[X#5,(letrec {X#6=S#8} in S#9)]
     in
        A#13[(app A#14[(var X#5)] T#15[(letrec {X#1=S#2} in S#3)])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {X#1=S#2} in S#3)])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {X#1=S#2} in S#3)])])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#5)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {X#1=S#2} in S#3)])])
    -lbeta1->                     (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(app (\ X#1.S#3) S#2)])])
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {X#1=S#2} in S#3)])])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {X#1=S#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(app (\ X#1.S#3) S#2)]
       ;E#15
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=S#2} in S#3)]
       ;E#15
       ;EE#11[X#5,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           E#7   |->  {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15},
           E#14  |->  {E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#13=T#12[(app (\ X#1.S#3) S#2)];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (\ X#6.S#9) T#18[(app (\ X#1.S#3) S#2)])]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {X#6=T#18[(letrec {X#1=S#2} in S#3)]} in S#9)]
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#18[(letrec {X#1=S#2} in S#3)],(\ X#6.[.])),
             (T#18[(letrec {X#1=S#2} in S#3)],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18)];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (\ X#6.S#9) T#18)],
           T#17         |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(letrec {X#1=S#2} in S#3)])];E#7} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(app (\ X#1.S#3) S#2)])];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(letrec {X#1=S#2} in S#3)])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=T#18[(letrec {X#1=S#2} in S#3)]} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(app (\ X#1.S#3) S#2)])]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(app A#17[(letrec {X#6=S#8} in S#9)] T#18[(letrec {X#1=S#2} in S#3)])]
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[(letrec {X#1=S#2} in S#3)])]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           T#12         |->  A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(letrec {X#1=S#2} in S#3)])];E#7} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(app (\ X#1.S#3) S#2)])];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(letrec {X#1=S#2} in S#3)])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(app A#17[(letrec {X#6=S#8} in S#9)] T#18[(letrec {X#1=S#2} in S#3)])];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (\ X#6.S#9) T#16[(app (\ X#1.S#3) S#2)])
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {X#6=T#16[(letrec {X#1=S#2} in S#3)]} in S#9)
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#16[(letrec {X#1=S#2} in S#3)],(\ X#6.[.])),
             (T#16[(letrec {X#1=S#2} in S#3)],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (\ X#6.S#9) T#16);E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  [.],
           T#12         |->  (app (\ X#6.S#9) T#16),
           S#8          |->  T#16[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=(app (\ X#6.S#9) T#16[(letrec {X#1=S#2} in S#3)]);E#7} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#5=(app (\ X#6.S#9) T#16[(app (\ X#1.S#3) S#2)]);E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (\ X#6.S#9) T#16[(letrec {X#1=S#2} in S#3)]);E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=(letrec {X#6=T#16[(letrec {X#1=S#2} in S#3)]} in S#9);E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(app (\ X#1.S#3) S#2)])]
       ;E#7
       ;EE#17[X#16,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])]
       ;E#7
       ;EE#17[X#16,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(app (\ X#1.S#3) S#2)])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])];E#7;EE#17[X#16,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(app (\ X#1.S#3) S#2)])]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(app (\ X#1.S#3) S#2)])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (\ X#6.S#9) T#20[(app (\ X#1.S#3) S#2)])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=T#20[(letrec {X#1=S#2} in S#3)]} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#20[(letrec {X#1=S#2} in S#3)],(\ X#6.[.])),
             (T#20[(letrec {X#1=S#2} in S#3)],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (\ X#6.S#9) T#20)],
           T#19         |->  (app (\ X#6.S#9) T#20),
           S#8          |->  T#20[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[(letrec {X#1=S#2} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[(app (\ X#1.S#3) S#2)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[(letrec {X#1=S#2} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=T#20[(letrec {X#1=S#2} in S#3)]} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(app (\ X#1.S#3) S#2)])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[(letrec {X#1=S#2} in S#3)])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[(letrec {X#1=S#2} in S#3)])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           T#12         |->  A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(letrec {X#1=S#2} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(app (\ X#1.S#3) S#2)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(letrec {X#1=S#2} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[(letrec {X#1=S#2} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (\ X#6.S#9) T#18[(app (\ X#1.S#3) S#2)])
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#6=T#18[(letrec {X#1=S#2} in S#3)]} in S#9)
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#18[(letrec {X#1=S#2} in S#3)],(\ X#6.[.])),
             (T#18[(letrec {X#1=S#2} in S#3)],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (\ X#6.S#9) T#18);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=(app (\ X#6.S#9) T#18[(letrec {X#1=S#2} in S#3)]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#16=(app (\ X#6.S#9) T#18[(app (\ X#1.S#3) S#2)]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (\ X#6.S#9) T#18[(letrec {X#1=S#2} in S#3)]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=(letrec {X#6=T#18[(letrec {X#1=S#2} in S#3)]} in S#9);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (app (\ X#5.A#10[(var X#5)]) A#12[(app (\ X#6.S#9) S#8)])
    ,
     (letrec {X#5=A#12[(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {(A#12[(app (\ X#6.S#9) S#8)],(\ X#5.[.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           S#3          |->  A#10[(var X#5)],
           EE#11[.1,.2] |-> {[.1]=A#12[[.2]]},
           X#1          |->  X#5,
           S#2          |->  A#12[(app (\ X#6.S#9) S#8)],
           E#7          |->  {}}

and instantiated rules:

                                  (letrec {X#5=A#12[(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -lbeta1->                     (app (\ X#5.A#10[(var X#5)]) A#12[(app (\ X#6.S#9) S#8)])
    ................................................................................
                                  (letrec {X#5=A#12[(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#12[(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#8)
       ;E#7
     in
        A#11[(app A#12[(var X#5)] T#13[(app (\ X#1.S#3) S#2)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#8)
       ;E#7
     in
        A#11[(app A#12[(\ X#6.S#8)] T#13[(letrec {X#1=S#2} in S#3)])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),A#11[(app A#12[[.]] T#13[(letrec {X#1=S#2} in S#3)])])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)]),
           T#10  |->  A#11[(app A#12[(var X#5)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {X#1=S#2} in S#3)])])
    -lbeta1->                     (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(app (\ X#1.S#3) S#2)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {X#1=S#2} in S#3)])])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(\ X#6.S#8)] T#13[(letrec {X#1=S#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(app (\ X#1.S#3) S#2)]
       ;X#5= (\ X#6.S#8)
       ;E#13
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#11= T#10[(letrec {X#1=S#2} in S#3)]
       ;X#5= (\ X#6.S#8)
       ;E#13
     in
        A#9[(\ X#6.S#8)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)]),
           E#7   |->  {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13},
           E#12  |->  {X#5=(\ X#6.S#8);E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    -lbeta1->                     (letrec {X#11=T#10[(app (\ X#1.S#3) S#2)];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];X#5=(\ X#6.S#8);E#13} in A#9[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (app (\ X#5.A#9[(var X#5)]) (\ X#6.S#8))
    ,
     (letrec {X#5=(\ X#6.S#8)} in A#9[(\ X#6.S#8)])
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((\ X#6.S#8),(\ X#5.[.])),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#9[(var X#5)],
           X#1  |->  X#5,
           S#2  |->  (\ X#6.S#8),
           E#7  |->  {}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8)} in A#9[(var X#5)])
    -lbeta1->                     (app (\ X#5.A#9[(var X#5)]) (\ X#6.S#8))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8)} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8)} in A#9[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(app A#14[(var X#7)] T#15[(app (\ X#1.S#3) S#2)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(app A#14[(\ X#6.S#9)] T#15[(letrec {X#1=S#2} in S#3)])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),[.]),
             ((var X#7),A#13[(app A#14[[.]] T#15[(letrec {X#1=S#2} in S#3)])]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#7)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=S#2} in S#3)])])
    -lbeta1->                     (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[(app (\ X#1.S#3) S#2)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=S#2} in S#3)])])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(\ X#6.S#9)] T#15[(letrec {X#1=S#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(app (\ X#1.S#3) S#2)]
       ;X#5= (\ X#6.S#9)
       ;E#15
       ;VV#11|X#7,(var X#5)|
     in
        A#10[(var X#7)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=S#2} in S#3)]
       ;X#5= (\ X#6.S#9)
       ;E#15
       ;VV#11|X#7,(var X#5)|
     in
        A#10[(\ X#6.S#9)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)]),
           E#8   |->  {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15},
           E#14  |->  {X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -lbeta1->                     (letrec {X#13=T#12[(app (\ X#1.S#3) S#2)];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#14[(app A#15[(var X#7)] T#16[(app (\ X#1.S#3) S#2)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#14[(app A#15[(var X#7)] T#16[(letrec {X#1=S#2} in S#3)])]
     )
  )

where

   Delta1 = {A#11,T#13,T#4,A#10}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#14[(app A#15[[.]] T#16[(letrec {X#1=S#2} in S#3)])]),
             ((var X#7),A#14[(app A#15[[.]] T#16[(letrec {X#1=S#2} in S#3)])])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#7)] T#16)],
           A#11  |->  A#14[(app A#15 T#16[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[(letrec {X#1=S#2} in S#3)])])
    -lbeta1->                     (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[(app (\ X#1.S#3) S#2)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[(letrec {X#1=S#2} in S#3)])])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[(app A#15[(var X#7)] T#16[(letrec {X#1=S#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(app (\ X#1.S#3) S#2)]
       ;X#5= (\ X#6.S#9)
       ;E#16
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {X#1=S#2} in S#3)]
       ;X#5= (\ X#6.S#9)
       ;E#16
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#10}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#14=T#13;X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)]),
           E#8   |->  {X#14=T#13[(letrec {X#1=S#2} in S#3)];E#16},
           E#15  |->  {X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {X#1=S#2} in S#3)];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -lbeta1->                     (letrec {X#14=T#13[(app (\ X#1.S#3) S#2)];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {X#1=S#2} in S#3)];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#14=T#13[(letrec {X#1=S#2} in S#3)];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[(var X#5)] T#21[(app (\ X#1.S#3) S#2)])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {X#1=S#2} in S#3)])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#18,A#16,T#13,T#4,A#10,A#17}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),A#19[(app A#20[[.]] T#21[(letrec {X#1=S#2} in S#3)])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21)]];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[A#19[(app A#20[(var X#5)] T#21)]],
           T#18         |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[(letrec {X#1=S#2} in S#3)])]];E#8} in A#11[(var X#7)])
    -lbeta1->                     (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[(app (\ X#1.S#3) S#2)])]];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[(letrec {X#1=S#2} in S#3)])]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {X#1=S#2} in S#3)])]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[A#10[(var X#5)]] T#19[(app (\ X#1.S#3) S#2)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[A#10[(\ X#6.S#9)]] T#19[(letrec {X#1=S#2} in S#3)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19)];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] T#19[(letrec {X#1=S#2} in S#3)])]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  A#17[(app A#18[A#10[(var X#5)]] T#19)],
           A#16         |->  A#17[(app A#18 T#19[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[(letrec {X#1=S#2} in S#3)])];E#8} in A#11[(var X#7)])
    -lbeta1->                     (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[(app (\ X#1.S#3) S#2)])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[(letrec {X#1=S#2} in S#3)])];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(\ X#6.S#9)]] T#19[(letrec {X#1=S#2} in S#3)])];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[(var X#5)] T#19[(app (\ X#1.S#3) S#2)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[(\ X#6.S#9)] T#19[(letrec {X#1=S#2} in S#3)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#4,A#10}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),A#17[(app A#18[[.]] T#19[(letrec {X#1=S#2} in S#3)])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19)];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  [.],
           T#13         |->  A#17[(app A#18[(var X#5)] T#19)],
           A#10         |->  A#17[(app A#18 T#19[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[(letrec {X#1=S#2} in S#3)])];E#8} in A#11[(var X#7)])
    -lbeta1->                     (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[(app (\ X#1.S#3) S#2)])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[(letrec {X#1=S#2} in S#3)])];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(\ X#6.S#9)] T#19[(letrec {X#1=S#2} in S#3)])];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(app A#20[(var X#17)] T#21[(app (\ X#1.S#3) S#2)])]
       ;E#8
       ;EE#18[X#17,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=S#2} in S#3)])]
       ;E#8
       ;EE#18[X#17,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21)];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=S#2} in S#3)])];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#17,A#10[(var X#5)]]},
           T#13         |->  A#19[(app A#20[(var X#17)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=S#2} in S#3)])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -lbeta1->                     (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(app (\ X#1.S#3) S#2)])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=S#2} in S#3)])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=S#2} in S#3)])];E#8;EE#18[X#17,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(app (\ X#1.S#3) S#2)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=S#2} in S#3)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=S#2} in S#3)])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]},
           T#13         |->  A#21[(app A#22[(var X#18)] T#23)],
           A#16         |->  A#21[(app A#22 T#23[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -lbeta1->                     (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(app (\ X#1.S#3) S#2)])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[A#21[(app A#22[(var X#5)] T#23[(app (\ X#1.S#3) S#2)])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[(letrec {X#1=S#2} in S#3)])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#16,T#13,T#4,A#10,A#19}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),A#21[(app A#22[[.]] T#23[(letrec {X#1=S#2} in S#3)])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[A#21[(app A#22[(var X#5)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#5)] T#23)],
           A#10         |->  A#21[(app A#22 T#23[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[(letrec {X#1=S#2} in S#3)])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -lbeta1->                     (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[(app (\ X#1.S#3) S#2)])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[(letrec {X#1=S#2} in S#3)])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[(letrec {X#1=S#2} in S#3)])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[A#10[(var X#5)]] T#21[(app (\ X#1.S#3) S#2)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[(letrec {X#1=S#2} in S#3)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] T#21[(letrec {X#1=S#2} in S#3)])];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  A#19[(app A#20[A#10[(var X#5)]] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -lbeta1->                     (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[(app (\ X#1.S#3) S#2)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[(var X#5)] T#21[(app (\ X#1.S#3) S#2)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {X#1=S#2} in S#3)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#4,A#10}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),A#19[(app A#20[[.]] T#21[(letrec {X#1=S#2} in S#3)])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -lbeta1->                     (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[(app (\ X#1.S#3) S#2)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(app A#17[(var X#7)] T#18[(app (\ X#1.S#3) S#2)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(app A#17[(var X#7)] T#18[(letrec {X#1=S#2} in S#3)])]
     )
  )

where

   Delta1 = {A#12,T#15,T#4,A#11}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),[.]),
             ((var X#7),A#16[(app A#17[[.]] T#18[(letrec {X#1=S#2} in S#3)])]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[(app A#17[[.]] T#18[(letrec {X#1=S#2} in S#3)])])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#7)] T#18)],
           A#12  |->  A#16[(app A#17 T#18[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(letrec {X#1=S#2} in S#3)])])
    -lbeta1->                     (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(app (\ X#1.S#3) S#2)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(letrec {X#1=S#2} in S#3)])])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(letrec {X#1=S#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(app (\ X#1.S#3) S#2)]
       ;X#5= (\ X#6.S#10)
       ;E#18
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=S#2} in S#3)]
       ;X#5= (\ X#6.S#10)
       ;E#18
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#11}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#16=T#15;X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           E#9   |->  {X#16=T#15[(letrec {X#1=S#2} in S#3)];E#18},
           E#17  |->  {X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|}}

and instantiated rules:

                                  (letrec {X#16=T#15[(letrec {X#1=S#2} in S#3)];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lbeta1->                     (letrec {X#16=T#15[(app (\ X#1.S#3) S#2)];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#16=T#15[(letrec {X#1=S#2} in S#3)];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#16=T#15[(letrec {X#1=S#2} in S#3)];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[(var X#8)] T#23[(app (\ X#1.S#3) S#2)])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {X#1=S#2} in S#3)])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#4,A#11,A#19}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[(letrec {X#1=S#2} in S#3)])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19,
           T#15         |->  A#19[A#21[(app A#22[(var X#8)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=S#2} in S#3)])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lbeta1->                     (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[(app (\ X#1.S#3) S#2)])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=S#2} in S#3)])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {X#1=S#2} in S#3)])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[A#11[(var X#8)]] T#21[(app (\ X#1.S#3) S#2)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[A#11[(\ X#6.S#10)]] T#21[(letrec {X#1=S#2} in S#3)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[(letrec {X#1=S#2} in S#3)])]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  A#19[(app A#20[A#11[(var X#8)]] T#21)],
           A#18         |->  A#19[(app A#20 T#21[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[(letrec {X#1=S#2} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lbeta1->                     (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[(app (\ X#1.S#3) S#2)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[(letrec {X#1=S#2} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(\ X#6.S#10)]] T#21[(letrec {X#1=S#2} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[(var X#8)] T#21[(app (\ X#1.S#3) S#2)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[(\ X#6.S#10)] T#21[(letrec {X#1=S#2} in S#3)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#4,A#11}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#19[(app A#20[[.]] T#21[(letrec {X#1=S#2} in S#3)])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           T#15         |->  A#19[(app A#20[(var X#8)] T#21)],
           A#11         |->  A#19[(app A#20 T#21[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=S#2} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lbeta1->                     (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[(app (\ X#1.S#3) S#2)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=S#2} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(\ X#6.S#10)] T#21[(letrec {X#1=S#2} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(app A#22[(var X#19)] T#23[(app (\ X#1.S#3) S#2)])]
       ;E#9
       ;EE#20[X#19,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=S#2} in S#3)])]
       ;E#9
       ;EE#20[X#19,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23)];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=S#2} in S#3)])];EE#20[X#19,[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=S#2} in S#3)])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lbeta1->                     (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(app (\ X#1.S#3) S#2)])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=S#2} in S#3)])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=S#2} in S#3)])];E#9;EE#20[X#19,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(app (\ X#1.S#3) S#2)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=S#2} in S#3)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=S#2} in S#3)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lbeta1->                     (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(app (\ X#1.S#3) S#2)])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(app A#24[(var X#8)] T#25[(app (\ X#1.S#3) S#2)])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[(letrec {X#1=S#2} in S#3)])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#4,A#11,A#21}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[(app A#24[[.]] T#25[(letrec {X#1=S#2} in S#3)])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[A#23[(app A#24[(var X#8)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#8)] T#25)],
           A#11         |->  A#23[(app A#24 T#25[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[(letrec {X#1=S#2} in S#3)])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lbeta1->                     (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[(app (\ X#1.S#3) S#2)])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[(letrec {X#1=S#2} in S#3)])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[(letrec {X#1=S#2} in S#3)])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[A#11[(var X#8)]] T#23[(app (\ X#1.S#3) S#2)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[(letrec {X#1=S#2} in S#3)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[(letrec {X#1=S#2} in S#3)])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  A#21[(app A#22[A#11[(var X#8)]] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lbeta1->                     (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[(app (\ X#1.S#3) S#2)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(var X#8)] T#23[(app (\ X#1.S#3) S#2)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {X#1=S#2} in S#3)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#4,A#11}
   Delta2 = {}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[(letrec {X#1=S#2} in S#3)])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           T#15         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lbeta1->                     (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(app (\ X#1.S#3) S#2)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {X#1=S#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (letrec {E#6} in T#9[(app (\ X#1.S#3) S#2)]))
    ,
     (letrec {E#5;E#6} in T#9[(letrec {X#1=S#2} in S#3)])
  )

where

   Delta1 = {T#8,T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             [{E#5},(letrec {E#6} in [.])]}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4  |->  (letrec {E#5} in (letrec {E#6} in T#9)),
           T#8  |->  (letrec {E#6} in T#9),
           S#7  |->  T#9[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {E#5} in (letrec {E#6} in T#9[(letrec {X#1=S#2} in S#3)]))
    -lbeta1->                     (letrec {E#5} in (letrec {E#6} in T#9[(app (\ X#1.S#3) S#2)]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in T#9[(letrec {X#1=S#2} in S#3)]))
    -SR,llet-in1->                (letrec {E#5;E#6} in T#9[(letrec {X#1=S#2} in S#3)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (letrec {X#10=T#9[(app (\ X#1.S#3) S#2)];E#12} in S#7))
    ,
     (letrec {X#10=T#9[(letrec {X#1=S#2} in S#3)];E#12;E#5} in S#7)
  )

where

   Delta1 = {T#8,T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             [{E#5},(letrec {X#10=T#9[(letrec {X#1=S#2} in S#3)];E#12} in [.])]}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (letrec {X#10=T#9;E#12} in S#7)),
           T#8   |->  (letrec {X#10=T#9;E#12} in S#7),
           E#6   |->  {X#10=T#9[(letrec {X#1=S#2} in S#3)];E#12},
           E#11  |->  {E#12}}

and instantiated rules:

                                  (letrec {E#5} in (letrec {X#10=T#9[(letrec {X#1=S#2} in S#3)];E#12} in S#7))
    -lbeta1->                     (letrec {E#5} in (letrec {X#10=T#9[(app (\ X#1.S#3) S#2)];E#12} in S#7))
    ................................................................................
                                  (letrec {E#5} in (letrec {X#10=T#9[(letrec {X#1=S#2} in S#3)];E#12} in S#7))
    -SR,llet-in1->                (letrec {X#10=T#9[(letrec {X#1=S#2} in S#3)];E#12;E#5} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (app (\ X#1.S#7) S#2))
    ,
     (letrec {X#1=S#2;E#5} in S#7)
  )

where

   Delta1 = {T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             [{E#5},(letrec {X#1=S#2} in [.])]}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4  |->  (letrec {E#5} in [.]),
           T#8  |->  [.],
           S#3  |->  S#7,
           E#6  |->  {X#1=S#2},
           E#9  |->  {}}

and instantiated rules:

                                  (letrec {E#5} in (letrec {X#1=S#2} in S#7))
    -lbeta1->                     (letrec {E#5} in (app (\ X#1.S#7) S#2))
    ................................................................................
                                  (letrec {E#5} in (letrec {X#1=S#2} in S#7))
    -SR,llet-in1->                (letrec {X#1=S#2;E#5} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {X#9=T#8[(app (\ X#1.S#3) S#2)];E#11} in (letrec {E#6} in S#7))
    ,
     (letrec {X#9=T#8[(letrec {X#1=S#2} in S#3)];E#11;E#6} in S#7)
  )

where

   Delta1 = {T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             [{X#9=T#8[(letrec {X#1=S#2} in S#3)];E#11},(letrec {E#6} in [.])]}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4   |->  (letrec {X#9=T#8;E#11} in (letrec {E#6} in S#7)),
           E#5   |->  {X#9=T#8[(letrec {X#1=S#2} in S#3)];E#11},
           E#10  |->  {E#11}}

and instantiated rules:

                                  (letrec {X#9=T#8[(letrec {X#1=S#2} in S#3)];E#11} in (letrec {E#6} in S#7))
    -lbeta1->                     (letrec {X#9=T#8[(app (\ X#1.S#3) S#2)];E#11} in (letrec {E#6} in S#7))
    ................................................................................
                                  (letrec {X#9=T#8[(letrec {X#1=S#2} in S#3)];E#11} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {X#9=T#8[(letrec {X#1=S#2} in S#3)];E#11;E#6} in S#7)
    

================================================================================
Critical Pair:

  (
     (app (\ X#1.(letrec {E#6} in S#7)) S#2)
    ,
     (letrec {X#1=S#2;E#6} in S#7)
  )

where

   Delta1 = {}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             [{X#1=S#2},(letrec {E#6} in [.])]}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  (letrec {E#6} in S#7),
           E#5  |->  {X#1=S#2},
           E#8  |->  {}}

and instantiated rules:

                                  (letrec {X#1=S#2} in (letrec {E#6} in S#7))
    -lbeta1->                     (app (\ X#1.(letrec {E#6} in S#7)) S#2)
    ................................................................................
                                  (letrec {X#1=S#2} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {X#1=S#2;E#6} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in S#8)
       ;E#7
     in
        A#11[(app A#12[(var X#5)] T#13[(app (\ X#1.S#3) S#2)])]
     )
    ,
     (letrec
        X#5= S#8
       ;E#6
       ;E#7
     in
        A#11[(app A#12[(var X#5)] T#13[(letrec {X#1=S#2} in S#3)])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (A#11[(app A#12[(var X#5)] T#13[(letrec {X#1=S#2} in S#3)])],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#5),A#11[(app A#12[[.]] T#13[(letrec {X#1=S#2} in S#3)])]),
             ((var X#5),A#11[(app A#12[[.]] T#13[(letrec {X#1=S#2} in S#3)])])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)]),
           T#10  |->  A#11[(app A#12[(var X#5)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {X#1=S#2} in S#3)])])
    -lbeta1->                     (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(app (\ X#1.S#3) S#2)])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {X#1=S#2} in S#3)])])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {X#1=S#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in T#13[(app (\ X#1.S#3) S#2)])
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#5=T#13[(letrec {X#1=S#2} in S#3)];E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#6} in T#13);E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  (letrec {E#6} in T#13),
           S#8   |->  T#13[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in T#13[(letrec {X#1=S#2} in S#3)]);E#7} in A#9[(var X#5)])
    -lbeta1->                     (letrec {X#5=(letrec {E#6} in T#13[(app (\ X#1.S#3) S#2)]);E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in T#13[(letrec {X#1=S#2} in S#3)]);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=T#13[(letrec {X#1=S#2} in S#3)];E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#14=T#13[(app (\ X#1.S#3) S#2)];E#16} in S#8)
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {X#1=S#2} in S#3)]
       ;X#5= S#8
       ;E#16
       ;E#7
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (A#9[(var X#5)],(letrec {X#14=T#13[(letrec {X#1=S#2} in S#3)];E#16} in [.])),
             [{E#7},(letrec {X#14=T#13[(letrec {X#1=S#2} in S#3)];E#16} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {X#14=T#13;E#16} in S#8);E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  (letrec {X#14=T#13;E#16} in S#8),
           E#6   |->  {X#14=T#13[(letrec {X#1=S#2} in S#3)];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#14=T#13[(letrec {X#1=S#2} in S#3)];E#16} in S#8);E#7} in A#9[(var X#5)])
    -lbeta1->                     (letrec {X#5=(letrec {X#14=T#13[(app (\ X#1.S#3) S#2)];E#16} in S#8);E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {X#14=T#13[(letrec {X#1=S#2} in S#3)];E#16} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#14=T#13[(letrec {X#1=S#2} in S#3)];X#5=S#8;E#16;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(app (\ X#1.S#8) S#2);E#7} in A#9[(var X#5)])
    ,
     (letrec {X#1=S#2;X#5=S#8;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (A#9[(var X#5)],(letrec {X#1=S#2} in [.])),
             [{E#7},(letrec {X#1=S#2} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=[.];E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  [.],
           S#3   |->  S#8,
           E#6   |->  {X#1=S#2},
           E#13  |->  {}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#1=S#2} in S#8);E#7} in A#9[(var X#5)])
    -lbeta1->                     (letrec {X#5=(app (\ X#1.S#8) S#2);E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {X#1=S#2} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#1=S#2;X#5=S#8;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(app (\ X#1.S#3) S#2)]
       ;X#5= (letrec {E#6} in S#8)
       ;E#13
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#11= T#10[(letrec {X#1=S#2} in S#3)]
       ;X#5= S#8
       ;E#13
       ;E#6
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13},(letrec {E#6} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)]),
           E#7   |->  {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13},
           E#12  |->  {X#5=(letrec {E#6} in S#8);E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    -lbeta1->                     (letrec {X#11=T#10[(app (\ X#1.S#3) S#2)];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];X#5=S#8;E#13;E#6} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (app (\ X#5.A#9[(var X#5)]) (letrec {E#6} in S#8))
    ,
     (letrec {X#5=S#8;E#6} in A#9[(var X#5)])
  )

where

   Delta1 = {}
   Delta2 = {E#6}
   Delta3 = {((letrec {E#6} in S#8),(\ X#5.[.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{},(letrec {E#6} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#9[(var X#5)],
           X#1  |->  X#5,
           S#2  |->  (letrec {E#6} in S#8),
           E#7  |->  {}}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8)} in A#9[(var X#5)])
    -lbeta1->                     (app (\ X#5.A#9[(var X#5)]) (letrec {E#6} in S#8))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8)} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(app A#14[(var X#6)] T#15[(app (\ X#1.S#3) S#2)])]
     )
    ,
     (letrec
        X#5= S#9
       ;E#7
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(app A#14[(var X#6)] T#15[(letrec {X#1=S#2} in S#3)])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#13[(app A#14[(var X#6)] T#15[(letrec {X#1=S#2} in S#3)])],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#13[(app A#14[[.]] T#15[(letrec {X#1=S#2} in S#3)])]),
             ((var X#5),[.]),
             ((var X#6),A#13[(app A#14[[.]] T#15[(letrec {X#1=S#2} in S#3)])])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#6)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(letrec {X#1=S#2} in S#3)])])
    -lbeta1->                     (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(app (\ X#1.S#3) S#2)])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(letrec {X#1=S#2} in S#3)])])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(letrec {X#1=S#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in T#15[(app (\ X#1.S#3) S#2)])
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= T#15[(letrec {X#1=S#2} in S#3)]
       ;E#7
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#7} in T#15);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  (letrec {E#7} in T#15),
           S#9   |->  T#15[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in T#15[(letrec {X#1=S#2} in S#3)]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -lbeta1->                     (letrec {X#5=(letrec {E#7} in T#15[(app (\ X#1.S#3) S#2)]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in T#15[(letrec {X#1=S#2} in S#3)]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=T#15[(letrec {X#1=S#2} in S#3)];E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#16=T#15[(app (\ X#1.S#3) S#2)];E#18} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=S#2} in S#3)]
       ;X#5= S#9
       ;E#18
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),(letrec {X#16=T#15[(letrec {X#1=S#2} in S#3)];E#18;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {X#16=T#15[(letrec {X#1=S#2} in S#3)];E#18} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {X#16=T#15[(letrec {X#1=S#2} in S#3)];E#18} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {X#16=T#15;E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  (letrec {X#16=T#15;E#18} in S#9),
           E#7   |->  {X#16=T#15[(letrec {X#1=S#2} in S#3)];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#16=T#15[(letrec {X#1=S#2} in S#3)];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -lbeta1->                     (letrec {X#5=(letrec {X#16=T#15[(app (\ X#1.S#3) S#2)];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {X#16=T#15[(letrec {X#1=S#2} in S#3)];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=T#15[(letrec {X#1=S#2} in S#3)];X#5=S#9;E#18;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(app (\ X#1.S#9) S#2);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ,
     (letrec {X#1=S#2;X#5=S#9;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),(letrec {X#1=S#2;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {X#1=S#2} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {X#1=S#2} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=[.];E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  [.],
           S#3   |->  S#9,
           E#7   |->  {X#1=S#2},
           E#15  |->  {}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#1=S#2} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -lbeta1->                     (letrec {X#5=(app (\ X#1.S#9) S#2);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {X#1=S#2} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#1=S#2;X#5=S#9;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(app (\ X#1.S#3) S#2)]
       ;X#5= (letrec {E#7} in S#9)
       ;E#15
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=S#2} in S#3)]
       ;X#5= S#9
       ;E#15
       ;E#7
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),(letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15;E#7;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           E#8   |->  {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15},
           E#14  |->  {X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -lbeta1->                     (letrec {X#13=T#12[(app (\ X#1.S#3) S#2)];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];X#5=S#9;E#15;E#7;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#16[(app A#17[(var X#5)] T#18[(app (\ X#1.S#3) S#2)])]
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#16[(app A#17[(var X#5)] T#18[(letrec {X#1=S#2} in S#3)])]
       ;E#7
       ;E#8
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),(letrec {X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {X#1=S#2} in S#3)])];E#7;E#8} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {X#1=S#2} in S#3)])];E#8},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18)];E#8} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[(letrec {X#1=S#2} in S#3)])]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8},
           T#12         |->  A#16[(app A#17[(var X#5)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {X#1=S#2} in S#3)])];E#8} in A#10[(var X#6)])
    -lbeta1->                     (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[(app (\ X#1.S#3) S#2)])];E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {X#1=S#2} in S#3)])];E#8} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {X#1=S#2} in S#3)])];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#18[(app A#19[(var X#16)] T#20[(app (\ X#1.S#3) S#2)])]
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])]
       ;E#7
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),(letrec {X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])];E#7;E#8;EE#17[X#16,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])];E#8;EE#17[X#16,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20)];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#16,(var X#5)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -lbeta1->                     (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[(app (\ X#1.S#3) S#2)])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])];E#7;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(app (\ X#1.S#3) S#2)])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),(letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])];E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])];E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -lbeta1->                     (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(app (\ X#1.S#3) S#2)])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])];X#5=S#9;E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(var X#5)] T#20[(app (\ X#1.S#3) S#2)])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(var X#5)] T#20[(letrec {X#1=S#2} in S#3)])]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             ((var X#5),(letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {X#1=S#2} in S#3)])];E#7;E#8;EE#17[X#6,(var X#16)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {X#1=S#2} in S#3)])];E#8;EE#17[X#6,(var X#16)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20)];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[(letrec {X#1=S#2} in S#3)])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]},
           T#12         |->  A#18[(app A#19[(var X#5)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {X#1=S#2} in S#3)])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -lbeta1->                     (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(app (\ X#1.S#3) S#2)])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {X#1=S#2} in S#3)])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {X#1=S#2} in S#3)])];X#5=S#9;E#7;E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {E#5} in T#12[(app (\ X#1.S#3) S#2)]) S#6)]
    ,
     A#9[(letrec {E#5} in (app T#12[(letrec {X#1=S#2} in S#3)] S#6))]
  )

where

   Delta1 = {T#11,T#10,A#8,T#4,A#9}
   Delta2 = {E#5}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {(S#2,(\ X#1.[.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (letrec {E#5} in T#12) S#6)],
           T#10  |->  (app (letrec {E#5} in T#12) S#6),
           T#11  |->  (letrec {E#5} in T#12),
           S#7   |->  T#12[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in T#12[(letrec {X#1=S#2} in S#3)]) S#6)]
    -lbeta1->                     A#9[(app (letrec {E#5} in T#12[(app (\ X#1.S#3) S#2)]) S#6)]
    ................................................................................
                                  A#9[(app (letrec {E#5} in T#12[(letrec {X#1=S#2} in S#3)]) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app T#12[(letrec {X#1=S#2} in S#3)] S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {X#13=T#12[(app (\ X#1.S#3) S#2)];E#15} in S#7) S#6)]
    ,
     A#9[(letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15} in (app S#7 S#6))]
  )

where

   Delta1 = {T#11,T#10,A#8,T#4,A#9}
   Delta2 = {E#5}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#6,(letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {(S#2,(\ X#1.[.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (letrec {X#13=T#12;E#15} in S#7) S#6)],
           T#10  |->  (app (letrec {X#13=T#12;E#15} in S#7) S#6),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#7),
           E#5   |->  {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  A#9[(app (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15} in S#7) S#6)]
    -lbeta1->                     A#9[(app (letrec {X#13=T#12[(app (\ X#1.S#3) S#2)];E#15} in S#7) S#6)]
    ................................................................................
                                  A#9[(app (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (app (\ X#1.S#7) S#2) S#6)]
    ,
     A#9[(letrec {X#1=S#2} in (app S#7 S#6))]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {E#5}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#6,(letrec {X#1=S#2} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {(S#2,(\ X#1.[.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app [.] S#6)],
           T#10  |->  (app [.] S#6),
           T#11  |->  [.],
           S#3   |->  S#7,
           E#5   |->  {X#1=S#2},
           E#12  |->  {}}

and instantiated rules:

                                  A#9[(app (letrec {X#1=S#2} in S#7) S#6)]
    -lbeta1->                     A#9[(app (app (\ X#1.S#7) S#2) S#6)]
    ................................................................................
                                  A#9[(app (letrec {X#1=S#2} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {X#1=S#2} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {E#5} in S#7) T#11[(app (\ X#1.S#3) S#2)])]
    ,
     A#9[(letrec {E#5} in (app S#7 T#11[(letrec {X#1=S#2} in S#3)]))]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {E#5}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#11[(letrec {X#1=S#2} in S#3)],(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {(S#2,(\ X#1.[.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (letrec {E#5} in S#7) T#11)],
           T#10  |->  (app (letrec {E#5} in S#7) T#11),
           S#6   |->  T#11[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in S#7) T#11[(letrec {X#1=S#2} in S#3)])]
    -lbeta1->                     A#9[(app (letrec {E#5} in S#7) T#11[(app (\ X#1.S#3) S#2)])]
    ................................................................................
                                  A#9[(app (letrec {E#5} in S#7) T#11[(letrec {X#1=S#2} in S#3)])]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app S#7 T#11[(letrec {X#1=S#2} in S#3)]))]
    

================================================================================
Critical Pair:

  (
     A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(app (\ X#1.S#3) S#2)])]
    ,
     A#9[(app A#10[(letrec {E#5} in (app S#7 S#6))] T#11[(letrec {X#1=S#2} in S#3)])]
  )

where

   Delta1 = {A#8,T#4}
   Delta2 = {E#5}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {(S#2,(\ X#1.[.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#4  |->  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11)],
           A#8  |->  A#9[(app A#10 T#11[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(letrec {X#1=S#2} in S#3)])]
    -lbeta1->                     A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(app (\ X#1.S#3) S#2)])]
    ................................................................................
                                  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(letrec {X#1=S#2} in S#3)])]
    -SR,lapp1->                   A#9[(app A#10[(letrec {E#5} in (app S#7 S#6))] T#11[(letrec {X#1=S#2} in S#3)])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#5} in T#10[(app (\ X#1.S#3) S#2)]) S#6)
    ,
     (letrec {E#5} in (app T#10[(letrec {X#1=S#2} in S#3)] S#6))
  )

where

   Delta1 = {T#9,T#4}
   Delta2 = {E#5}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {(S#2,(\ X#1.[.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8  |->  [.],
           T#4  |->  (app (letrec {E#5} in T#10) S#6),
           T#9  |->  (letrec {E#5} in T#10),
           S#7  |->  T#10[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (app (letrec {E#5} in T#10[(letrec {X#1=S#2} in S#3)]) S#6)
    -lbeta1->                     (app (letrec {E#5} in T#10[(app (\ X#1.S#3) S#2)]) S#6)
    ................................................................................
                                  (app (letrec {E#5} in T#10[(letrec {X#1=S#2} in S#3)]) S#6)
    -SR,lapp1->                   (letrec {E#5} in (app T#10[(letrec {X#1=S#2} in S#3)] S#6))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#11=T#10[(app (\ X#1.S#3) S#2)];E#13} in S#7) S#6)
    ,
     (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13} in (app S#7 S#6))
  )

where

   Delta1 = {T#9,T#4}
   Delta2 = {E#5}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#6,(letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {(S#2,(\ X#1.[.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  [.],
           T#4   |->  (app (letrec {X#11=T#10;E#13} in S#7) S#6),
           T#9   |->  (letrec {X#11=T#10;E#13} in S#7),
           E#5   |->  {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (app (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13} in S#7) S#6)
    -lbeta1->                     (app (letrec {X#11=T#10[(app (\ X#1.S#3) S#2)];E#13} in S#7) S#6)
    ................................................................................
                                  (app (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13} in S#7) S#6)
    -SR,lapp1->                   (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13} in (app S#7 S#6))
    

================================================================================
Critical Pair:

  (
     (app (app (\ X#1.S#7) S#2) S#6)
    ,
     (letrec {X#1=S#2} in (app S#7 S#6))
  )

where

   Delta1 = {T#4}
   Delta2 = {E#5}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#6,(letrec {X#1=S#2} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {(S#2,(\ X#1.[.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  [.],
           T#4   |->  (app [.] S#6),
           T#9   |->  [.],
           S#3   |->  S#7,
           E#5   |->  {X#1=S#2},
           E#10  |->  {}}

and instantiated rules:

                                  (app (letrec {X#1=S#2} in S#7) S#6)
    -lbeta1->                     (app (app (\ X#1.S#7) S#2) S#6)
    ................................................................................
                                  (app (letrec {X#1=S#2} in S#7) S#6)
    -SR,lapp1->                   (letrec {X#1=S#2} in (app S#7 S#6))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#5} in S#7) T#9[(app (\ X#1.S#3) S#2)])
    ,
     (letrec {E#5} in (app S#7 T#9[(letrec {X#1=S#2} in S#3)]))
  )

where

   Delta1 = {T#4}
   Delta2 = {E#5}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#9[(letrec {X#1=S#2} in S#3)],(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {(S#2,(\ X#1.[.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8  |->  [.],
           T#4  |->  (app (letrec {E#5} in S#7) T#9),
           S#6  |->  T#9[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (app (letrec {E#5} in S#7) T#9[(letrec {X#1=S#2} in S#3)])
    -lbeta1->                     (app (letrec {E#5} in S#7) T#9[(app (\ X#1.S#3) S#2)])
    ................................................................................
                                  (app (letrec {E#5} in S#7) T#9[(letrec {X#1=S#2} in S#3)])
    -SR,lapp1->                   (letrec {E#5} in (app S#7 T#9[(letrec {X#1=S#2} in S#3)]))
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(app (\ X#1.S#3) S#2)]) S#7)])
    ,
     (letrec
        E#5
     in
        A#11[(letrec {E#6} in (app T#14[(letrec {X#1=S#2} in S#3)] S#7))]
     )
  )

where

   Delta1 = {T#13,T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14) S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {E#6} in T#14) S#7)],
           T#12  |->  (app (letrec {E#6} in T#14) S#7),
           T#13  |->  (letrec {E#6} in T#14),
           S#8   |->  T#14[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(letrec {X#1=S#2} in S#3)]) S#7)])
    -lbeta1->                     (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(app (\ X#1.S#3) S#2)]) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(letrec {X#1=S#2} in S#3)]) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[(letrec {X#1=S#2} in S#3)] S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {X#15=T#14[(app (\ X#1.S#3) S#2)];E#17} in S#8) S#7)]
     )
    ,
     (letrec
        E#5
     in
        A#11[(letrec {X#15=T#14[(letrec {X#1=S#2} in S#3)];E#17} in (app S#8 S#7))]
     )
  )

where

   Delta1 = {T#13,T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#7,(letrec {X#15=T#14[(letrec {X#1=S#2} in S#3)];E#17} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)],
           T#12  |->  (app (letrec {X#15=T#14;E#17} in S#8) S#7),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#8),
           E#6   |->  {X#15=T#14[(letrec {X#1=S#2} in S#3)];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[(letrec {X#1=S#2} in S#3)];E#17} in S#8) S#7)])
    -lbeta1->                     (letrec {E#5} in A#11[(app (letrec {X#15=T#14[(app (\ X#1.S#3) S#2)];E#17} in S#8) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[(letrec {X#1=S#2} in S#3)];E#17} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {X#15=T#14[(letrec {X#1=S#2} in S#3)];E#17} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in A#11[(app (app (\ X#1.S#8) S#2) S#7)])
    ,
     (letrec {E#5} in A#11[(letrec {X#1=S#2} in (app S#8 S#7))])
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#7,(letrec {X#1=S#2} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app [.] S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app [.] S#7)],
           T#12  |->  (app [.] S#7),
           T#13  |->  [.],
           S#3   |->  S#8,
           E#6   |->  {X#1=S#2},
           E#14  |->  {}}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {X#1=S#2} in S#8) S#7)])
    -lbeta1->                     (letrec {E#5} in A#11[(app (app (\ X#1.S#8) S#2) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {X#1=S#2} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {X#1=S#2} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(app (\ X#1.S#3) S#2)])])
    ,
     (letrec
        E#5
     in
        A#11[(letrec {E#6} in (app S#8 T#13[(letrec {X#1=S#2} in S#3)]))]
     )
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#13[(letrec {X#1=S#2} in S#3)],(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {E#6} in S#8) T#13)],
           T#12  |->  (app (letrec {E#6} in S#8) T#13),
           S#7   |->  T#13[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(letrec {X#1=S#2} in S#3)])])
    -lbeta1->                     (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(app (\ X#1.S#3) S#2)])])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(letrec {X#1=S#2} in S#3)])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 T#13[(letrec {X#1=S#2} in S#3)]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(app (\ X#1.S#3) S#2)])]
     )
    ,
     (letrec
        E#5
     in
        A#11[(app A#12[(letrec {E#6} in (app S#8 S#7))] T#13[(letrec {X#1=S#2} in S#3)])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)]),
           T#10  |->  A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(letrec {X#1=S#2} in S#3)])])
    -lbeta1->                     (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(app (\ X#1.S#3) S#2)])])
    ................................................................................
                                  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(letrec {X#1=S#2} in S#3)])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(app A#12[(letrec {E#6} in (app S#8 S#7))] T#13[(letrec {X#1=S#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (app (letrec {E#6} in T#12[(app (\ X#1.S#3) S#2)]) S#7))
    ,
     (letrec {E#5} in (letrec {E#6} in (app T#12[(letrec {X#1=S#2} in S#3)] S#7)))
  )

where

   Delta1 = {T#11,T#10,T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app (letrec {E#6} in T#12) S#7)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {E#6} in T#12) S#7),
           T#11  |->  (letrec {E#6} in T#12),
           S#8   |->  T#12[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in T#12[(letrec {X#1=S#2} in S#3)]) S#7))
    -lbeta1->                     (letrec {E#5} in (app (letrec {E#6} in T#12[(app (\ X#1.S#3) S#2)]) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in T#12[(letrec {X#1=S#2} in S#3)]) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app T#12[(letrec {X#1=S#2} in S#3)] S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (app (letrec {X#13=T#12[(app (\ X#1.S#3) S#2)];E#15} in S#8) S#7)
     )
    ,
     (letrec
        E#5
     in
        (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15} in (app S#8 S#7))
     )
  )

where

   Delta1 = {T#11,T#10,T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#7,(letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app (letrec {X#13=T#12;E#15} in S#8) S#7)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {X#13=T#12;E#15} in S#8) S#7),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#8),
           E#6   |->  {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15} in S#8) S#7))
    -lbeta1->                     (letrec {E#5} in (app (letrec {X#13=T#12[(app (\ X#1.S#3) S#2)];E#15} in S#8) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15} in S#8) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15} in (app S#8 S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (app (app (\ X#1.S#8) S#2) S#7))
    ,
     (letrec {E#5} in (letrec {X#1=S#2} in (app S#8 S#7)))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#7,(letrec {X#1=S#2} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app [.] S#7)),
           A#9   |->  [.],
           T#10  |->  (app [.] S#7),
           T#11  |->  [.],
           S#3   |->  S#8,
           E#6   |->  {X#1=S#2},
           E#12  |->  {}}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {X#1=S#2} in S#8) S#7))
    -lbeta1->                     (letrec {E#5} in (app (app (\ X#1.S#8) S#2) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {X#1=S#2} in S#8) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {X#1=S#2} in (app S#8 S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(app (\ X#1.S#3) S#2)]))
    ,
     (letrec {E#5} in (letrec {E#6} in (app S#8 T#11[(letrec {X#1=S#2} in S#3)])))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#11[(letrec {X#1=S#2} in S#3)],(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {E#6} in S#8) T#11),
           S#7   |->  T#11[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(letrec {X#1=S#2} in S#3)]))
    -lbeta1->                     (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(app (\ X#1.S#3) S#2)]))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(letrec {X#1=S#2} in S#3)]))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app S#8 T#11[(letrec {X#1=S#2} in S#3)])))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(app (\ X#1.S#3) S#2)]
       ;E#13
     in
        A#9[(app (letrec {E#6} in S#8) S#7)]
     )
    ,
     (letrec
        X#11= T#10[(letrec {X#1=S#2} in S#3)]
       ;E#13
     in
        A#9[(letrec {E#6} in (app S#8 S#7))]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;E#13} in A#9[(app (letrec {E#6} in S#8) S#7)]),
           E#5   |->  {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -lbeta1->                     (letrec {X#11=T#10[(app (\ X#1.S#3) S#2)];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {X#11=T#10[(letrec {X#1=S#2} in S#3)];E#13} in A#9[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (app (\ X#1.A#9[(app (letrec {E#6} in S#8) S#7)]) S#2)
    ,
     (letrec {X#1=S#2} in A#9[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {}
   Delta2 = {E#5,E#6}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {(S#2,(\ X#1.[.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  [.],
           S#3   |->  A#9[(app (letrec {E#6} in S#8) S#7)],
           E#5   |->  {X#1=S#2},
           E#10  |->  {}}

and instantiated rules:

                                  (letrec {X#1=S#2} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -lbeta1->                     (app (\ X#1.A#9[(app (letrec {E#6} in S#8) S#7)]) S#2)
    ................................................................................
                                  (letrec {X#1=S#2} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {X#1=S#2} in A#9[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        A#13[(app A#14[(var X#5)] T#15[(app (\ X#1.S#3) S#2)])]
     )
    ,
     (letrec
        E#6
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#13[(app A#14[(var X#5)] T#15[(letrec {X#1=S#2} in S#3)])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {X#1=S#2} in S#3)])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {X#1=S#2} in S#3)])])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#5)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {X#1=S#2} in S#3)])])
    -lbeta1->                     (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(app (\ X#1.S#3) S#2)])])
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {X#1=S#2} in S#3)])])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[(app A#14[(var X#5)] T#15[(letrec {X#1=S#2} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(app (\ X#1.S#3) S#2)]
       ;E#15
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=S#2} in S#3)]
       ;E#15
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           E#6   |->  {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15},
           E#14  |->  {E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#13=T#12[(app (\ X#1.S#3) S#2)];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#13=T#12[(letrec {X#1=S#2} in S#3)];E#15;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {E#7} in T#19[(app (\ X#1.S#3) S#2)]) S#8)]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app T#19[(letrec {X#1=S#2} in S#3)] S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (letrec {E#7} in T#19) S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {E#7} in T#19) S#8)],
           T#17         |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[(letrec {X#1=S#2} in S#3)]) S#8)];E#6} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#5=A#16[(app (letrec {E#7} in T#19[(app (\ X#1.S#3) S#2)]) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[(letrec {X#1=S#2} in S#3)]) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app T#19[(letrec {X#1=S#2} in S#3)] S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {X#20=T#19[(app (\ X#1.S#3) S#2)];E#22} in S#9) S#8)]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {X#20=T#19[(letrec {X#1=S#2} in S#3)];E#22} in (app S#9 S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {X#20=T#19[(letrec {X#1=S#2} in S#3)];E#22} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)],
           T#17         |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[(letrec {X#1=S#2} in S#3)];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[(letrec {X#1=S#2} in S#3)];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#5=A#16[(app (letrec {X#20=T#19[(app (\ X#1.S#3) S#2)];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[(letrec {X#1=S#2} in S#3)];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {X#20=T#19[(letrec {X#1=S#2} in S#3)];E#22} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=A#16[(app (app (\ X#1.S#9) S#2) S#8)];E#6} in A#10[(var X#5)])
    ,
     (letrec {X#5=A#16[(letrec {X#1=S#2} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {X#1=S#2} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app [.] S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app [.] S#8)],
           T#17         |->  (app [.] S#8),
           T#18         |->  [.],
           S#3          |->  S#9,
           E#7          |->  {X#1=S#2},
           E#19         |->  {}}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {X#1=S#2} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#5=A#16[(app (app (\ X#1.S#9) S#2) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {X#1=S#2} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {X#1=S#2} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {E#7} in S#9) T#18[(app (\ X#1.S#3) S#2)])]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app S#9 T#18[(letrec {X#1=S#2} in S#3)]))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#18[(letrec {X#1=S#2} in S#3)],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {E#7} in S#9) T#18)],
           T#17         |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[(letrec {X#1=S#2} in S#3)])];E#6} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[(app (\ X#1.S#3) S#2)])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[(letrec {X#1=S#2} in S#3)])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 T#18[(letrec {X#1=S#2} in S#3)]))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(app (\ X#1.S#3) S#2)])]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(app A#17[(letrec {E#7} in (app S#9 S#8))] T#18[(letrec {X#1=S#2} in S#3)])]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[(letrec {X#1=S#2} in S#3)])]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(letrec {X#1=S#2} in S#3)])];E#6} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(app (\ X#1.S#3) S#2)])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(letrec {X#1=S#2} in S#3)])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(app A#17[(letrec {E#7} in (app S#9 S#8))] T#18[(letrec {X#1=S#2} in S#3)])];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {E#7} in T#17[(app (\ X#1.S#3) S#2)]) S#8)
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {E#7} in (app T#17[(letrec {X#1=S#2} in S#3)] S#8))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#16,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (letrec {E#7} in T#17) S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in T#17) S#8),
           T#16         |->  (letrec {E#7} in T#17),
           S#9          |->  T#17[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in T#17[(letrec {X#1=S#2} in S#3)]) S#8);E#6} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#5=(app (letrec {E#7} in T#17[(app (\ X#1.S#3) S#2)]) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in T#17[(letrec {X#1=S#2} in S#3)]) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app T#17[(letrec {X#1=S#2} in S#3)] S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {X#18=T#17[(app (\ X#1.S#3) S#2)];E#20} in S#9) S#8)
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {X#18=T#17[(letrec {X#1=S#2} in S#3)];E#20} in (app S#9 S#8))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#16,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {X#18=T#17[(letrec {X#1=S#2} in S#3)];E#20} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (letrec {X#18=T#17;E#20} in S#9) S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {X#18=T#17;E#20} in S#9) S#8),
           T#16         |->  (letrec {X#18=T#17;E#20} in S#9),
           E#7          |->  {X#18=T#17[(letrec {X#1=S#2} in S#3)];E#20},
           E#19         |->  {E#20}}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {X#18=T#17[(letrec {X#1=S#2} in S#3)];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#5=(app (letrec {X#18=T#17[(app (\ X#1.S#3) S#2)];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {X#18=T#17[(letrec {X#1=S#2} in S#3)];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {X#18=T#17[(letrec {X#1=S#2} in S#3)];E#20} in (app S#9 S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(app (app (\ X#1.S#9) S#2) S#8);E#6} in A#10[(var X#5)])
    ,
     (letrec {X#5=(letrec {X#1=S#2} in (app S#9 S#8));E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {X#1=S#2} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app [.] S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#16         |->  [.],
           S#3          |->  S#9,
           E#7          |->  {X#1=S#2},
           E#17         |->  {}}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {X#1=S#2} in S#9) S#8);E#6} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#5=(app (app (\ X#1.S#9) S#2) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {X#1=S#2} in S#9) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {X#1=S#2} in (app S#9 S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {E#7} in S#9) T#16[(app (\ X#1.S#3) S#2)])
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {E#7} in (app S#9 T#16[(letrec {X#1=S#2} in S#3)]))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#16[(letrec {X#1=S#2} in S#3)],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (letrec {E#7} in S#9) T#16);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in S#9) T#16),
           S#8          |->  T#16[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in S#9) T#16[(letrec {X#1=S#2} in S#3)]);E#6} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#5=(app (letrec {E#7} in S#9) T#16[(app (\ X#1.S#3) S#2)]);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in S#9) T#16[(letrec {X#1=S#2} in S#3)]);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app S#9 T#16[(letrec {X#1=S#2} in S#3)]));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(app (\ X#1.S#3) S#2)])]
       ;E#6
       ;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])]
       ;E#6
       ;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(app (\ X#1.S#3) S#2)])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in S#3)])];E#6;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(app (\ X#1.S#3) S#2)])]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(app (\ X#1.S#3) S#2)])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in S#3)])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {E#7} in T#21[(app (\ X#1.S#3) S#2)]) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app T#21[(letrec {X#1=S#2} in S#3)] S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (letrec {E#7} in T#21) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {E#7} in T#21) S#8)],
           T#19         |->  (app (letrec {E#7} in T#21) S#8),
           T#20         |->  (letrec {E#7} in T#21),
           S#9          |->  T#21[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[(letrec {X#1=S#2} in S#3)]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#16=A#18[(app (letrec {E#7} in T#21[(app (\ X#1.S#3) S#2)]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[(letrec {X#1=S#2} in S#3)]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app T#21[(letrec {X#1=S#2} in S#3)] S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {X#22=T#21[(app (\ X#1.S#3) S#2)];E#24} in S#9) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#22=T#21[(letrec {X#1=S#2} in S#3)];E#24} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {X#22=T#21[(letrec {X#1=S#2} in S#3)];E#24} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)],
           T#19         |->  (app (letrec {X#22=T#21;E#24} in S#9) S#8),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#9),
           E#7          |->  {X#22=T#21[(letrec {X#1=S#2} in S#3)];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[(letrec {X#1=S#2} in S#3)];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#16=A#18[(app (letrec {X#22=T#21[(app (\ X#1.S#3) S#2)];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[(letrec {X#1=S#2} in S#3)];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {X#22=T#21[(letrec {X#1=S#2} in S#3)];E#24} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (app (\ X#1.S#9) S#2) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#1=S#2} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {X#1=S#2} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app [.] S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app [.] S#8)],
           T#19         |->  (app [.] S#8),
           T#20         |->  [.],
           S#3          |->  S#9,
           E#7          |->  {X#1=S#2},
           E#21         |->  {}}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {X#1=S#2} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#16=A#18[(app (app (\ X#1.S#9) S#2) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {X#1=S#2} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {X#1=S#2} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {E#7} in S#9) T#20[(app (\ X#1.S#3) S#2)])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 T#20[(letrec {X#1=S#2} in S#3)]))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#20[(letrec {X#1=S#2} in S#3)],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {E#7} in S#9) T#20)],
           T#19         |->  (app (letrec {E#7} in S#9) T#20),
           S#8          |->  T#20[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[(letrec {X#1=S#2} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[(app (\ X#1.S#3) S#2)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[(letrec {X#1=S#2} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 T#20[(letrec {X#1=S#2} in S#3)]))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(app (\ X#1.S#3) S#2)])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[(letrec {X#1=S#2} in S#3)])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[(letrec {X#1=S#2} in S#3)])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {X#1=S#2} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(letrec {X#1=S#2} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(app (\ X#1.S#3) S#2)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(letrec {X#1=S#2} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[(letrec {X#1=S#2} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {E#7} in T#19[(app (\ X#1.S#3) S#2)]) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app T#19[(letrec {X#1=S#2} in S#3)] S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (letrec {E#7} in T#19) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in T#19[(letrec {X#1=S#2} in S#3)]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#16=(app (letrec {E#7} in T#19[(app (\ X#1.S#3) S#2)]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in T#19[(letrec {X#1=S#2} in S#3)]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app T#19[(letrec {X#1=S#2} in S#3)] S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {X#20=T#19[(app (\ X#1.S#3) S#2)];E#22} in S#9) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#20=T#19[(letrec {X#1=S#2} in S#3)];E#22} in (app S#9 S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {X#20=T#19[(letrec {X#1=S#2} in S#3)];E#22} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (letrec {X#20=T#19;E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[(letrec {X#1=S#2} in S#3)];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {X#20=T#19[(letrec {X#1=S#2} in S#3)];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#16=(app (letrec {X#20=T#19[(app (\ X#1.S#3) S#2)];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {X#20=T#19[(letrec {X#1=S#2} in S#3)];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {X#20=T#19[(letrec {X#1=S#2} in S#3)];E#22} in (app S#9 S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (app (\ X#1.S#9) S#2) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#1=S#2} in (app S#9 S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (S#8,(letrec {X#1=S#2} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app [.] S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#18         |->  [.],
           S#3          |->  S#9,
           E#7          |->  {X#1=S#2},
           E#19         |->  {}}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {X#1=S#2} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#16=(app (app (\ X#1.S#9) S#2) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {X#1=S#2} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {X#1=S#2} in (app S#9 S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {E#7} in S#9) T#18[(app (\ X#1.S#3) S#2)])
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app S#9 T#18[(letrec {X#1=S#2} in S#3)]))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {(S#2,(\ X#1.[.])),
             (T#18[(letrec {X#1=S#2} in S#3)],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (letrec {E#7} in S#9) T#18);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[(letrec {X#1=S#2} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in S#9) T#18[(letrec {X#1=S#2} in S#3)]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lbeta1->                     (letrec {X#16=(app (letrec {E#7} in S#9) T#18[(app (\ X#1.S#3) S#2)]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in S#9) T#18[(letrec {X#1=S#2} in S#3)]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app S#9 T#18[(letrec {X#1=S#2} in S#3)]));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (app (\ X#5.A#10[(var X#5)]) A#12[(app (letrec {E#7} in S#9) S#8)])
    ,
     (letrec {X#5=A#12[(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
  )

where

   Delta1 = {}
   Delta2 = {E#7}
   Delta3 = {(A#12[(app (letrec {E#7} in S#9) S#8)],(\ X#5.[.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lbeta1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=S#2} in S#3)]
    -lbeta1->                     T#4[(app (\ X#1.S#3) S#2)]
    and constraints: (S#2,(\ X#1.[.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=S#2} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#2,(\ X#1.[.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           S#3          |->  A#10[(var X#5)],
           EE#11[.1,.2] |-> {[.1]=A#12[[.2]]},
           X#1          |->  X#5,
           S#2          |->  A#12[(app (letrec {E#7} in S#9) S#8)],
           E#6          |->  {}}

and instantiated rules:

                                  (letrec {X#5=A#12[(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -lbeta1->                     (app (\ X#5.A#10[(var X#5)]) A#12[(app (letrec {E#7} in S#9) S#8)])
    ................................................................................
                                  (letrec {X#5=A#12[(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#12[(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     A#9[(app (\ X#5.S#7) T#11[(app (letrec {E#1} in S#3) S#2)])]
    ,
     A#9[(letrec {X#5=T#11[(letrec {E#1} in (app S#3 S#2))]} in S#7)]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#11[(letrec {E#1} in (app S#3 S#2))],(\ X#5.[.])),
             (T#11[(letrec {E#1} in (app S#3 S#2))],(letrec {X#5=[.]} in S#7))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (\ X#5.S#7) T#11)],
           T#10  |->  (app (\ X#5.S#7) T#11),
           S#6   |->  T#11[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  A#9[(app (\ X#5.S#7) T#11[(letrec {E#1} in (app S#3 S#2))])]
    -lapp1->                      A#9[(app (\ X#5.S#7) T#11[(app (letrec {E#1} in S#3) S#2)])]
    ................................................................................
                                  A#9[(app (\ X#5.S#7) T#11[(letrec {E#1} in (app S#3 S#2))])]
    -SR,lbeta1->                  A#9[(letrec {X#5=T#11[(letrec {E#1} in (app S#3 S#2))]} in S#7)]
    

================================================================================
Critical Pair:

  (
     A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(app (letrec {E#1} in S#3) S#2)])]
    ,
     A#9[(app A#10[(letrec {X#5=S#6} in S#7)] T#11[(letrec {E#1} in (app S#3 S#2))])]
  )

where

   Delta1 = {A#8,T#4}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7))}


and found solution:

    Sol = {T#4  |->  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11)],
           A#8  |->  A#9[(app A#10 T#11[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(letrec {E#1} in (app S#3 S#2))])]
    -lapp1->                      A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(app (letrec {E#1} in S#3) S#2)])]
    ................................................................................
                                  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(letrec {E#1} in (app S#3 S#2))])]
    -SR,lbeta1->                  A#9[(app A#10[(letrec {X#5=S#6} in S#7)] T#11[(letrec {E#1} in (app S#3 S#2))])]
    

================================================================================
Critical Pair:

  (
     (app (\ X#5.S#7) T#9[(app (letrec {E#1} in S#3) S#2)])
    ,
     (letrec {X#5=T#9[(letrec {E#1} in (app S#3 S#2))]} in S#7)
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#9[(letrec {E#1} in (app S#3 S#2))],(\ X#5.[.])),
             (T#9[(letrec {E#1} in (app S#3 S#2))],(letrec {X#5=[.]} in S#7))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7))}


and found solution:

    Sol = {A#8  |->  [.],
           T#4  |->  (app (\ X#5.S#7) T#9),
           S#6  |->  T#9[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (app (\ X#5.S#7) T#9[(letrec {E#1} in (app S#3 S#2))])
    -lapp1->                      (app (\ X#5.S#7) T#9[(app (letrec {E#1} in S#3) S#2)])
    ................................................................................
                                  (app (\ X#5.S#7) T#9[(letrec {E#1} in (app S#3 S#2))])
    -SR,lbeta1->                  (letrec {X#5=T#9[(letrec {E#1} in (app S#3 S#2))]} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(app (letrec {E#1} in S#3) S#2)])])
    ,
     (letrec
        E#6
     in
        A#11[(letrec {X#5=T#13[(letrec {E#1} in (app S#3 S#2))]} in S#8)]
     )
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#13[(letrec {E#1} in (app S#3 S#2))],(\ X#5.[.])),
             (T#13[(letrec {E#1} in (app S#3 S#2))],(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (\ X#5.S#8) T#13)],
           T#12  |->  (app (\ X#5.S#8) T#13),
           S#7   |->  T#13[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(letrec {E#1} in (app S#3 S#2))])])
    -lapp1->                      (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(app (letrec {E#1} in S#3) S#2)])])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(letrec {E#1} in (app S#3 S#2))])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=T#13[(letrec {E#1} in (app S#3 S#2))]} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(app (letrec {E#1} in S#3) S#2)])]
     )
    ,
     (letrec
        E#6
     in
        A#11[(app A#12[(letrec {X#5=S#7} in S#8)] T#13[(letrec {E#1} in (app S#3 S#2))])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)]),
           T#10  |->  A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(letrec {E#1} in (app S#3 S#2))])])
    -lapp1->                      (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(app (letrec {E#1} in S#3) S#2)])])
    ................................................................................
                                  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(letrec {E#1} in (app S#3 S#2))])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(app A#12[(letrec {X#5=S#7} in S#8)] T#13[(letrec {E#1} in (app S#3 S#2))])])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (app (\ X#5.S#8) T#11[(app (letrec {E#1} in S#3) S#2)]))
    ,
     (letrec {E#6} in (letrec {X#5=T#11[(letrec {E#1} in (app S#3 S#2))]} in S#8))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#11[(letrec {E#1} in (app S#3 S#2))],(\ X#5.[.])),
             (T#11[(letrec {E#1} in (app S#3 S#2))],(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in (app (\ X#5.S#8) T#11)),
           A#9   |->  [.],
           T#10  |->  (app (\ X#5.S#8) T#11),
           S#7   |->  T#11[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {E#6} in (app (\ X#5.S#8) T#11[(letrec {E#1} in (app S#3 S#2))]))
    -lapp1->                      (letrec {E#6} in (app (\ X#5.S#8) T#11[(app (letrec {E#1} in S#3) S#2)]))
    ................................................................................
                                  (letrec {E#6} in (app (\ X#5.S#8) T#11[(letrec {E#1} in (app S#3 S#2))]))
    -SR,lbeta2->                  (letrec {E#6} in (letrec {X#5=T#11[(letrec {E#1} in (app S#3 S#2))]} in S#8))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(app (letrec {E#1} in S#3) S#2)]
       ;E#13
     in
        A#9[(app (\ X#5.S#8) S#7)]
     )
    ,
     (letrec
        X#11= T#10[(letrec {E#1} in (app S#3 S#2))]
       ;E#13
     in
        A#9[(letrec {X#5=S#7} in S#8)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;E#13} in A#9[(app (\ X#5.S#8) S#7)]),
           E#6   |->  {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    -lapp1->                      (letrec {X#11=T#10[(app (letrec {E#1} in S#3) S#2)];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13} in A#9[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#6} in A#10[(app (\ X#5.S#8) S#7)]) S#2)
    ,
     (letrec {E#6} in (app A#10[(letrec {X#5=S#7} in S#8)] S#2))
  )

where

   Delta1 = {A#9}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#6} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4  |->  [.],
           E#1  |->  {E#6},
           A#9  |->  (app A#10 S#2),
           S#3  |->  A#10[(app (\ X#5.S#8) S#7)]}

and instantiated rules:

                                  (letrec {E#6} in (app A#10[(app (\ X#5.S#8) S#7)] S#2))
    -lapp1->                      (app (letrec {E#6} in A#10[(app (\ X#5.S#8) S#7)]) S#2)
    ................................................................................
                                  (letrec {E#6} in (app A#10[(app (\ X#5.S#8) S#7)] S#2))
    -SR,lbeta2->                  (letrec {E#6} in (app A#10[(letrec {X#5=S#7} in S#8)] S#2))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#6} in (\ X#5.S#8)) S#2)
    ,
     (letrec {E#6} in (letrec {X#5=S#2} in S#8))
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#6} in [.])),
             (S#2,(\ X#5.[.])),
             (S#2,(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4  |->  [.],
           E#1  |->  {E#6},
           A#9  |->  [.],
           S#7  |->  S#2,
           S#3  |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {E#6} in (app (\ X#5.S#8) S#2))
    -lapp1->                      (app (letrec {E#6} in (\ X#5.S#8)) S#2)
    ................................................................................
                                  (letrec {E#6} in (app (\ X#5.S#8) S#2))
    -SR,lbeta2->                  (letrec {E#6} in (letrec {X#5=S#2} in S#8))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        A#13[(app A#14[(var X#5)] T#15[(app (letrec {E#1} in S#3) S#2)])]
     )
    ,
     (letrec
        E#7
       ;EE#11[X#5,(letrec {X#6=S#8} in S#9)]
     in
        A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in (app S#3 S#2))])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {E#1} in (app S#3 S#2))])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {E#1} in (app S#3 S#2))])])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#5)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in (app S#3 S#2))])])
    -lapp1->                      (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(app (letrec {E#1} in S#3) S#2)])])
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in (app S#3 S#2))])])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in (app S#3 S#2))])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(app (letrec {E#1} in S#3) S#2)]
       ;E#15
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {E#1} in (app S#3 S#2))]
       ;E#15
       ;EE#11[X#5,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           E#7   |->  {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15},
           E#14  |->  {E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#13=T#12[(app (letrec {E#1} in S#3) S#2)];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (\ X#6.S#9) T#18[(app (letrec {E#1} in S#3) S#2)])]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {X#6=T#18[(letrec {E#1} in (app S#3 S#2))]} in S#9)]
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#18[(letrec {E#1} in (app S#3 S#2))],(\ X#6.[.])),
             (T#18[(letrec {E#1} in (app S#3 S#2))],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18)];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (\ X#6.S#9) T#18)],
           T#17         |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(letrec {E#1} in (app S#3 S#2))])];E#7} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(app (letrec {E#1} in S#3) S#2)])];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(letrec {E#1} in (app S#3 S#2))])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=T#18[(letrec {E#1} in (app S#3 S#2))]} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(app (letrec {E#1} in S#3) S#2)])]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(app A#17[(letrec {X#6=S#8} in S#9)] T#18[(letrec {E#1} in (app S#3 S#2))])]
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[(letrec {E#1} in (app S#3 S#2))])]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           T#12         |->  A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(letrec {E#1} in (app S#3 S#2))])];E#7} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(app (letrec {E#1} in S#3) S#2)])];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(letrec {E#1} in (app S#3 S#2))])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(app A#17[(letrec {X#6=S#8} in S#9)] T#18[(letrec {E#1} in (app S#3 S#2))])];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (\ X#6.S#9) T#16[(app (letrec {E#1} in S#3) S#2)])
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {X#6=T#16[(letrec {E#1} in (app S#3 S#2))]} in S#9)
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#16[(letrec {E#1} in (app S#3 S#2))],(\ X#6.[.])),
             (T#16[(letrec {E#1} in (app S#3 S#2))],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (\ X#6.S#9) T#16);E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  [.],
           T#12         |->  (app (\ X#6.S#9) T#16),
           S#8          |->  T#16[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {X#5=(app (\ X#6.S#9) T#16[(letrec {E#1} in (app S#3 S#2))]);E#7} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#5=(app (\ X#6.S#9) T#16[(app (letrec {E#1} in S#3) S#2)]);E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (\ X#6.S#9) T#16[(letrec {E#1} in (app S#3 S#2))]);E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=(letrec {X#6=T#16[(letrec {E#1} in (app S#3 S#2))]} in S#9);E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(app (letrec {E#1} in S#3) S#2)])]
       ;E#7
       ;EE#17[X#16,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])]
       ;E#7
       ;EE#17[X#16,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(app (letrec {E#1} in S#3) S#2)])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#7;EE#17[X#16,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(app (letrec {E#1} in S#3) S#2)])]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(app (letrec {E#1} in S#3) S#2)])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (\ X#6.S#9) T#20[(app (letrec {E#1} in S#3) S#2)])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=T#20[(letrec {E#1} in (app S#3 S#2))]} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#20[(letrec {E#1} in (app S#3 S#2))],(\ X#6.[.])),
             (T#20[(letrec {E#1} in (app S#3 S#2))],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (\ X#6.S#9) T#20)],
           T#19         |->  (app (\ X#6.S#9) T#20),
           S#8          |->  T#20[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[(letrec {E#1} in (app S#3 S#2))])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[(app (letrec {E#1} in S#3) S#2)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[(letrec {E#1} in (app S#3 S#2))])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=T#20[(letrec {E#1} in (app S#3 S#2))]} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(app (letrec {E#1} in S#3) S#2)])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[(letrec {E#1} in (app S#3 S#2))])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[(letrec {E#1} in (app S#3 S#2))])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           T#12         |->  A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(app (letrec {E#1} in S#3) S#2)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (\ X#6.S#9) T#18[(app (letrec {E#1} in S#3) S#2)])
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#6=T#18[(letrec {E#1} in (app S#3 S#2))]} in S#9)
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#18[(letrec {E#1} in (app S#3 S#2))],(\ X#6.[.])),
             (T#18[(letrec {E#1} in (app S#3 S#2))],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (\ X#6.S#9) T#18);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {X#16=(app (\ X#6.S#9) T#18[(letrec {E#1} in (app S#3 S#2))]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#16=(app (\ X#6.S#9) T#18[(app (letrec {E#1} in S#3) S#2)]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (\ X#6.S#9) T#18[(letrec {E#1} in (app S#3 S#2))]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=(letrec {X#6=T#18[(letrec {E#1} in (app S#3 S#2))]} in S#9);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#12[(var X#5)]) S#2)
    ,
     (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in (app A#12[(var X#5)] S#2))
  )

where

   Delta1 = {A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),(app A#12[[.]] S#2)),
             ((var X#5),(app A#12[[.]] S#2))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#1   |->  {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]},
           A#10  |->  (app A#12 S#2),
           S#3   |->  A#12[(var X#5)]}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in (app A#12[(var X#5)] S#2))
    -lapp1->                      (app (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#12[(var X#5)]) S#2)
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in (app A#12[(var X#5)] S#2))
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in (app A#12[(var X#5)] S#2))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#8)
       ;E#7
     in
        A#11[(app A#12[(var X#5)] T#13[(app (letrec {E#1} in S#3) S#2)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#8)
       ;E#7
     in
        A#11[(app A#12[(\ X#6.S#8)] T#13[(letrec {E#1} in (app S#3 S#2))])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),A#11[(app A#12[[.]] T#13[(letrec {E#1} in (app S#3 S#2))])])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)]),
           T#10  |->  A#11[(app A#12[(var X#5)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in (app S#3 S#2))])])
    -lapp1->                      (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(app (letrec {E#1} in S#3) S#2)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in (app S#3 S#2))])])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(\ X#6.S#8)] T#13[(letrec {E#1} in (app S#3 S#2))])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(app (letrec {E#1} in S#3) S#2)]
       ;X#5= (\ X#6.S#8)
       ;E#13
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#11= T#10[(letrec {E#1} in (app S#3 S#2))]
       ;X#5= (\ X#6.S#8)
       ;E#13
     in
        A#9[(\ X#6.S#8)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)]),
           E#7   |->  {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13},
           E#12  |->  {X#5=(\ X#6.S#8);E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    -lapp1->                      (letrec {X#11=T#10[(app (letrec {E#1} in S#3) S#2)];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];X#5=(\ X#6.S#8);E#13} in A#9[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#5=(\ X#6.S#8);E#7} in A#10[(var X#5)]) S#2)
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in (app A#10[(\ X#6.S#8)] S#2))
  )

where

   Delta1 = {A#9}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {X#5=(\ X#6.S#8);E#7} in [.])),
             ((var X#5),(app A#10[[.]] S#2))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           E#1  |->  {X#5=(\ X#6.S#8);E#7},
           A#9  |->  (app A#10 S#2),
           S#3  |->  A#10[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in (app A#10[(var X#5)] S#2))
    -lapp1->                      (app (letrec {X#5=(\ X#6.S#8);E#7} in A#10[(var X#5)]) S#2)
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in (app A#10[(var X#5)] S#2))
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in (app A#10[(\ X#6.S#8)] S#2))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(app A#14[(var X#7)] T#15[(app (letrec {E#1} in S#3) S#2)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(app A#14[(\ X#6.S#9)] T#15[(letrec {E#1} in (app S#3 S#2))])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),[.]),
             ((var X#7),A#13[(app A#14[[.]] T#15[(letrec {E#1} in (app S#3 S#2))])]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#7)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[(letrec {E#1} in (app S#3 S#2))])])
    -lapp1->                      (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[(app (letrec {E#1} in S#3) S#2)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[(letrec {E#1} in (app S#3 S#2))])])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(\ X#6.S#9)] T#15[(letrec {E#1} in (app S#3 S#2))])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(app (letrec {E#1} in S#3) S#2)]
       ;X#5= (\ X#6.S#9)
       ;E#15
       ;VV#11|X#7,(var X#5)|
     in
        A#10[(var X#7)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {E#1} in (app S#3 S#2))]
       ;X#5= (\ X#6.S#9)
       ;E#15
       ;VV#11|X#7,(var X#5)|
     in
        A#10[(\ X#6.S#9)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)]),
           E#8   |->  {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15},
           E#14  |->  {X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -lapp1->                      (letrec {X#13=T#12[(app (letrec {E#1} in S#3) S#2)];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#12[(var X#7)]) S#2)
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        (app A#12[(\ X#6.S#9)] S#2)
     )
  )

where

   Delta1 = {A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in [.])),
             ((var X#5),[.]),
             ((var X#7),(app A#12[[.]] S#2)),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#4   |->  [.],
           E#1   |->  {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|},
           A#10  |->  (app A#12 S#2),
           S#3   |->  A#12[(var X#7)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in (app A#12[(var X#7)] S#2))
    -lapp1->                      (app (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#12[(var X#7)]) S#2)
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in (app A#12[(var X#7)] S#2))
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in (app A#12[(\ X#6.S#9)] S#2))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#14[(app A#15[(var X#7)] T#16[(app (letrec {E#1} in S#3) S#2)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#14[(app A#15[(var X#7)] T#16[(letrec {E#1} in (app S#3 S#2))])]
     )
  )

where

   Delta1 = {A#11,T#13,T#4,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#14[(app A#15[[.]] T#16[(letrec {E#1} in (app S#3 S#2))])]),
             ((var X#7),A#14[(app A#15[[.]] T#16[(letrec {E#1} in (app S#3 S#2))])])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#7)] T#16)],
           A#11  |->  A#14[(app A#15 T#16[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[(letrec {E#1} in (app S#3 S#2))])])
    -lapp1->                      (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[(app (letrec {E#1} in S#3) S#2)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[(letrec {E#1} in (app S#3 S#2))])])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[(app A#15[(var X#7)] T#16[(letrec {E#1} in (app S#3 S#2))])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(app (letrec {E#1} in S#3) S#2)]
       ;X#5= (\ X#6.S#9)
       ;E#16
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {E#1} in (app S#3 S#2))]
       ;X#5= (\ X#6.S#9)
       ;E#16
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#14=T#13;X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)]),
           E#8   |->  {X#14=T#13[(letrec {E#1} in (app S#3 S#2))];E#16},
           E#15  |->  {X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {E#1} in (app S#3 S#2))];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -lapp1->                      (letrec {X#14=T#13[(app (letrec {E#1} in S#3) S#2)];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {E#1} in (app S#3 S#2))];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#14=T#13[(letrec {E#1} in (app S#3 S#2))];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[(var X#5)] T#21[(app (letrec {E#1} in S#3) S#2)])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {E#1} in (app S#3 S#2))])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#18,A#16,T#13,T#4,A#10,A#17}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),A#19[(app A#20[[.]] T#21[(letrec {E#1} in (app S#3 S#2))])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21)]];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[A#19[(app A#20[(var X#5)] T#21)]],
           T#18         |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[(letrec {E#1} in (app S#3 S#2))])]];E#8} in A#11[(var X#7)])
    -lapp1->                      (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[(app (letrec {E#1} in S#3) S#2)])]];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[(letrec {E#1} in (app S#3 S#2))])]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {E#1} in (app S#3 S#2))])]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[A#10[(var X#5)]] T#19[(app (letrec {E#1} in S#3) S#2)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[A#10[(\ X#6.S#9)]] T#19[(letrec {E#1} in (app S#3 S#2))])]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19)];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] T#19[(letrec {E#1} in (app S#3 S#2))])]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  A#17[(app A#18[A#10[(var X#5)]] T#19)],
           A#16         |->  A#17[(app A#18 T#19[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[(letrec {E#1} in (app S#3 S#2))])];E#8} in A#11[(var X#7)])
    -lapp1->                      (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[(app (letrec {E#1} in S#3) S#2)])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[(letrec {E#1} in (app S#3 S#2))])];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(\ X#6.S#9)]] T#19[(letrec {E#1} in (app S#3 S#2))])];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[(var X#5)] T#19[(app (letrec {E#1} in S#3) S#2)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[(\ X#6.S#9)] T#19[(letrec {E#1} in (app S#3 S#2))])]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#4,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),A#17[(app A#18[[.]] T#19[(letrec {E#1} in (app S#3 S#2))])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19)];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  [.],
           T#13         |->  A#17[(app A#18[(var X#5)] T#19)],
           A#10         |->  A#17[(app A#18 T#19[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[(letrec {E#1} in (app S#3 S#2))])];E#8} in A#11[(var X#7)])
    -lapp1->                      (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[(app (letrec {E#1} in S#3) S#2)])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[(letrec {E#1} in (app S#3 S#2))])];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(\ X#6.S#9)] T#19[(letrec {E#1} in (app S#3 S#2))])];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(app A#20[(var X#17)] T#21[(app (letrec {E#1} in S#3) S#2)])]
       ;E#8
       ;EE#18[X#17,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(app A#20[(var X#17)] T#21[(letrec {E#1} in (app S#3 S#2))])]
       ;E#8
       ;EE#18[X#17,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21)];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] T#21[(letrec {E#1} in (app S#3 S#2))])];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#17,A#10[(var X#5)]]},
           T#13         |->  A#19[(app A#20[(var X#17)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#1} in (app S#3 S#2))])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -lapp1->                      (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(app (letrec {E#1} in S#3) S#2)])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#1} in (app S#3 S#2))])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#1} in (app S#3 S#2))])];E#8;EE#18[X#17,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(app (letrec {E#1} in S#3) S#2)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {E#1} in (app S#3 S#2))])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#1} in (app S#3 S#2))])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]},
           T#13         |->  A#21[(app A#22[(var X#18)] T#23)],
           A#16         |->  A#21[(app A#22 T#23[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -lapp1->                      (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(app (letrec {E#1} in S#3) S#2)])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[A#21[(app A#22[(var X#5)] T#23[(app (letrec {E#1} in S#3) S#2)])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[(letrec {E#1} in (app S#3 S#2))])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#16,T#13,T#4,A#10,A#19}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),A#21[(app A#22[[.]] T#23[(letrec {E#1} in (app S#3 S#2))])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[A#21[(app A#22[(var X#5)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#5)] T#23)],
           A#10         |->  A#21[(app A#22 T#23[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[(letrec {E#1} in (app S#3 S#2))])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -lapp1->                      (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[(app (letrec {E#1} in S#3) S#2)])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[(letrec {E#1} in (app S#3 S#2))])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[(letrec {E#1} in (app S#3 S#2))])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[A#10[(var X#5)]] T#21[(app (letrec {E#1} in S#3) S#2)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[(letrec {E#1} in (app S#3 S#2))])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] T#21[(letrec {E#1} in (app S#3 S#2))])];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  A#19[(app A#20[A#10[(var X#5)]] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -lapp1->                      (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[(app (letrec {E#1} in S#3) S#2)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[(var X#5)] T#21[(app (letrec {E#1} in S#3) S#2)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {E#1} in (app S#3 S#2))])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#4,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),A#19[(app A#20[[.]] T#21[(letrec {E#1} in (app S#3 S#2))])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -lapp1->                      (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[(app (letrec {E#1} in S#3) S#2)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#13[(var X#7)]) S#2)
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        (app A#13[(var X#7)] S#2)
     )
  )

where

   Delta1 = {A#11,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#7),(app A#13[[.]] S#2)),
             ((var X#7),(app A#13[[.]] S#2))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#1   |->  {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]},
           A#11  |->  (app A#13 S#2),
           S#3   |->  A#13[(var X#7)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in (app A#13[(var X#7)] S#2))
    -lapp1->                      (app (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#13[(var X#7)]) S#2)
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in (app A#13[(var X#7)] S#2))
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in (app A#13[(var X#7)] S#2))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(app A#17[(var X#7)] T#18[(app (letrec {E#1} in S#3) S#2)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(app A#17[(var X#7)] T#18[(letrec {E#1} in (app S#3 S#2))])]
     )
  )

where

   Delta1 = {A#12,T#15,T#4,A#11}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),[.]),
             ((var X#7),A#16[(app A#17[[.]] T#18[(letrec {E#1} in (app S#3 S#2))])]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[(app A#17[[.]] T#18[(letrec {E#1} in (app S#3 S#2))])])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#7)] T#18)],
           A#12  |->  A#16[(app A#17 T#18[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(letrec {E#1} in (app S#3 S#2))])])
    -lapp1->                      (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(app (letrec {E#1} in S#3) S#2)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(letrec {E#1} in (app S#3 S#2))])])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(letrec {E#1} in (app S#3 S#2))])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(app (letrec {E#1} in S#3) S#2)]
       ;X#5= (\ X#6.S#10)
       ;E#18
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {E#1} in (app S#3 S#2))]
       ;X#5= (\ X#6.S#10)
       ;E#18
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#11}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#16=T#15;X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           E#9   |->  {X#16=T#15[(letrec {E#1} in (app S#3 S#2))];E#18},
           E#17  |->  {X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|}}

and instantiated rules:

                                  (letrec {X#16=T#15[(letrec {E#1} in (app S#3 S#2))];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lapp1->                      (letrec {X#16=T#15[(app (letrec {E#1} in S#3) S#2)];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#16=T#15[(letrec {E#1} in (app S#3 S#2))];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#16=T#15[(letrec {E#1} in (app S#3 S#2))];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[(var X#8)] T#23[(app (letrec {E#1} in S#3) S#2)])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {E#1} in (app S#3 S#2))])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#4,A#11,A#19}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[(letrec {E#1} in (app S#3 S#2))])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19,
           T#15         |->  A#19[A#21[(app A#22[(var X#8)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[(letrec {E#1} in (app S#3 S#2))])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lapp1->                      (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[(app (letrec {E#1} in S#3) S#2)])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[(letrec {E#1} in (app S#3 S#2))])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {E#1} in (app S#3 S#2))])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[A#11[(var X#8)]] T#21[(app (letrec {E#1} in S#3) S#2)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[A#11[(\ X#6.S#10)]] T#21[(letrec {E#1} in (app S#3 S#2))])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[(letrec {E#1} in (app S#3 S#2))])]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  A#19[(app A#20[A#11[(var X#8)]] T#21)],
           A#18         |->  A#19[(app A#20 T#21[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[(letrec {E#1} in (app S#3 S#2))])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lapp1->                      (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[(app (letrec {E#1} in S#3) S#2)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[(letrec {E#1} in (app S#3 S#2))])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(\ X#6.S#10)]] T#21[(letrec {E#1} in (app S#3 S#2))])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[(var X#8)] T#21[(app (letrec {E#1} in S#3) S#2)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[(\ X#6.S#10)] T#21[(letrec {E#1} in (app S#3 S#2))])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#4,A#11}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#19[(app A#20[[.]] T#21[(letrec {E#1} in (app S#3 S#2))])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           T#15         |->  A#19[(app A#20[(var X#8)] T#21)],
           A#11         |->  A#19[(app A#20 T#21[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[(letrec {E#1} in (app S#3 S#2))])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lapp1->                      (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[(app (letrec {E#1} in S#3) S#2)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[(letrec {E#1} in (app S#3 S#2))])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(\ X#6.S#10)] T#21[(letrec {E#1} in (app S#3 S#2))])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(app A#22[(var X#19)] T#23[(app (letrec {E#1} in S#3) S#2)])]
       ;E#9
       ;EE#20[X#19,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(app A#22[(var X#19)] T#23[(letrec {E#1} in (app S#3 S#2))])]
       ;E#9
       ;EE#20[X#19,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23)];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[(letrec {E#1} in (app S#3 S#2))])];EE#20[X#19,[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(letrec {E#1} in (app S#3 S#2))])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lapp1->                      (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(app (letrec {E#1} in S#3) S#2)])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(letrec {E#1} in (app S#3 S#2))])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(letrec {E#1} in (app S#3 S#2))])];E#9;EE#20[X#19,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(app (letrec {E#1} in S#3) S#2)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {E#1} in (app S#3 S#2))])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {E#1} in (app S#3 S#2))])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lapp1->                      (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(app (letrec {E#1} in S#3) S#2)])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(app A#24[(var X#8)] T#25[(app (letrec {E#1} in S#3) S#2)])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[(letrec {E#1} in (app S#3 S#2))])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#4,A#11,A#21}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[(app A#24[[.]] T#25[(letrec {E#1} in (app S#3 S#2))])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[A#23[(app A#24[(var X#8)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#8)] T#25)],
           A#11         |->  A#23[(app A#24 T#25[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[(letrec {E#1} in (app S#3 S#2))])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lapp1->                      (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[(app (letrec {E#1} in S#3) S#2)])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[(letrec {E#1} in (app S#3 S#2))])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[(letrec {E#1} in (app S#3 S#2))])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[A#11[(var X#8)]] T#23[(app (letrec {E#1} in S#3) S#2)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[(letrec {E#1} in (app S#3 S#2))])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[(letrec {E#1} in (app S#3 S#2))])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  A#21[(app A#22[A#11[(var X#8)]] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lapp1->                      (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[(app (letrec {E#1} in S#3) S#2)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(var X#8)] T#23[(app (letrec {E#1} in S#3) S#2)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {E#1} in (app S#3 S#2))])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#4,A#11}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[(letrec {E#1} in (app S#3 S#2))])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           T#15         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -lapp1->                      (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(app (letrec {E#1} in S#3) S#2)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {E#1} in (app S#3 S#2))])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (app (letrec
             X#5= (\ X#6.S#10)
            ;E#9
            ;EE#13[X#7,A#11[(var X#8)]]
            ;VV#14|X#8,(var X#5)|
          in
             A#15[(var X#7)]
          ) S#2)
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        (app A#15[(var X#7)] S#2)
     )
  )

where

   Delta1 = {A#12,A#11}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in [.])),
             ((var X#5),[.]),
             ((var X#7),(app A#15[[.]] S#2)),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),(app A#15[[.]] S#2))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#1   |->  {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           A#12  |->  (app A#15 S#2),
           S#3   |->  A#15[(var X#7)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in (app A#15[(var X#7)] S#2))
    -lapp1->                      (app (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#15[(var X#7)]) S#2)
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in (app A#15[(var X#7)] S#2))
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in (app A#15[(var X#7)] S#2))
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (letrec {E#6} in T#9[(app (letrec {E#1} in S#3) S#2)]))
    ,
     (letrec {E#5;E#6} in T#9[(letrec {E#1} in (app S#3 S#2))])
  )

where

   Delta1 = {T#8,T#4}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             [{E#5},(letrec {E#6} in [.])]}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4  |->  (letrec {E#5} in (letrec {E#6} in T#9)),
           T#8  |->  (letrec {E#6} in T#9),
           S#7  |->  T#9[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {E#5} in (letrec {E#6} in T#9[(letrec {E#1} in (app S#3 S#2))]))
    -lapp1->                      (letrec {E#5} in (letrec {E#6} in T#9[(app (letrec {E#1} in S#3) S#2)]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in T#9[(letrec {E#1} in (app S#3 S#2))]))
    -SR,llet-in1->                (letrec {E#5;E#6} in T#9[(letrec {E#1} in (app S#3 S#2))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (letrec {X#10=T#9[(app (letrec {E#1} in S#3) S#2)];E#12} in S#7)
     )
    ,
     (letrec {X#10=T#9[(letrec {E#1} in (app S#3 S#2))];E#12;E#5} in S#7)
  )

where

   Delta1 = {T#8,T#4}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             [{E#5},(letrec {X#10=T#9[(letrec {E#1} in (app S#3 S#2))];E#12} in [.])]}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (letrec {X#10=T#9;E#12} in S#7)),
           T#8   |->  (letrec {X#10=T#9;E#12} in S#7),
           E#6   |->  {X#10=T#9[(letrec {E#1} in (app S#3 S#2))];E#12},
           E#11  |->  {E#12}}

and instantiated rules:

                                  (letrec {E#5} in (letrec {X#10=T#9[(letrec {E#1} in (app S#3 S#2))];E#12} in S#7))
    -lapp1->                      (letrec {E#5} in (letrec {X#10=T#9[(app (letrec {E#1} in S#3) S#2)];E#12} in S#7))
    ................................................................................
                                  (letrec {E#5} in (letrec {X#10=T#9[(letrec {E#1} in (app S#3 S#2))];E#12} in S#7))
    -SR,llet-in1->                (letrec {X#10=T#9[(letrec {E#1} in (app S#3 S#2))];E#12;E#5} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (app (letrec {E#1} in S#3) S#2))
    ,
     (letrec {E#1;E#5} in (app S#3 S#2))
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             [{E#5},(letrec {E#1} in [.])]}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4  |->  (letrec {E#5} in [.]),
           T#8  |->  [.],
           S#7  |->  (app S#3 S#2),
           E#6  |->  {E#1}}

and instantiated rules:

                                  (letrec {E#5} in (letrec {E#1} in (app S#3 S#2)))
    -lapp1->                      (letrec {E#5} in (app (letrec {E#1} in S#3) S#2))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#1} in (app S#3 S#2)))
    -SR,llet-in1->                (letrec {E#1;E#5} in (app S#3 S#2))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= T#8[(app (letrec {E#1} in S#3) S#2)]
       ;E#11
     in
        (letrec {E#6} in S#7)
     )
    ,
     (letrec {X#9=T#8[(letrec {E#1} in (app S#3 S#2))];E#11;E#6} in S#7)
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             [{X#9=T#8[(letrec {E#1} in (app S#3 S#2))];E#11},(letrec {E#6} in [.])]}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4   |->  (letrec {X#9=T#8;E#11} in (letrec {E#6} in S#7)),
           E#5   |->  {X#9=T#8[(letrec {E#1} in (app S#3 S#2))];E#11},
           E#10  |->  {E#11}}

and instantiated rules:

                                  (letrec {X#9=T#8[(letrec {E#1} in (app S#3 S#2))];E#11} in (letrec {E#6} in S#7))
    -lapp1->                      (letrec {X#9=T#8[(app (letrec {E#1} in S#3) S#2)];E#11} in (letrec {E#6} in S#7))
    ................................................................................
                                  (letrec {X#9=T#8[(letrec {E#1} in (app S#3 S#2))];E#11} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {X#9=T#8[(letrec {E#1} in (app S#3 S#2))];E#11;E#6} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in S#8)
       ;E#7
     in
        A#11[(app A#12[(var X#5)] T#13[(app (letrec {E#1} in S#3) S#2)])]
     )
    ,
     (letrec
        X#5= S#8
       ;E#6
       ;E#7
     in
        A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in (app S#3 S#2))])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in (app S#3 S#2))])],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#5),A#11[(app A#12[[.]] T#13[(letrec {E#1} in (app S#3 S#2))])]),
             ((var X#5),A#11[(app A#12[[.]] T#13[(letrec {E#1} in (app S#3 S#2))])])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)]),
           T#10  |->  A#11[(app A#12[(var X#5)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in (app S#3 S#2))])])
    -lapp1->                      (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(app (letrec {E#1} in S#3) S#2)])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in (app S#3 S#2))])])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in (app S#3 S#2))])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in T#13[(app (letrec {E#1} in S#3) S#2)])
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#5=T#13[(letrec {E#1} in (app S#3 S#2))];E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#6} in T#13);E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  (letrec {E#6} in T#13),
           S#8   |->  T#13[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in T#13[(letrec {E#1} in (app S#3 S#2))]);E#7} in A#9[(var X#5)])
    -lapp1->                      (letrec {X#5=(letrec {E#6} in T#13[(app (letrec {E#1} in S#3) S#2)]);E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in T#13[(letrec {E#1} in (app S#3 S#2))]);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=T#13[(letrec {E#1} in (app S#3 S#2))];E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#14=T#13[(app (letrec {E#1} in S#3) S#2)];E#16} in S#8)
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {E#1} in (app S#3 S#2))]
       ;X#5= S#8
       ;E#16
       ;E#7
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (A#9[(var X#5)],(letrec {X#14=T#13[(letrec {E#1} in (app S#3 S#2))];E#16} in [.])),
             [{E#7},(letrec {X#14=T#13[(letrec {E#1} in (app S#3 S#2))];E#16} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {X#14=T#13;E#16} in S#8);E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  (letrec {X#14=T#13;E#16} in S#8),
           E#6   |->  {X#14=T#13[(letrec {E#1} in (app S#3 S#2))];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#14=T#13[(letrec {E#1} in (app S#3 S#2))];E#16} in S#8);E#7} in A#9[(var X#5)])
    -lapp1->                      (letrec {X#5=(letrec {X#14=T#13[(app (letrec {E#1} in S#3) S#2)];E#16} in S#8);E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {X#14=T#13[(letrec {E#1} in (app S#3 S#2))];E#16} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#14=T#13[(letrec {E#1} in (app S#3 S#2))];X#5=S#8;E#16;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(app (letrec {E#1} in S#3) S#2);E#7} in A#9[(var X#5)])
    ,
     (letrec {X#5=(app S#3 S#2);E#1;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (A#9[(var X#5)],(letrec {E#1} in [.])),
             [{E#7},(letrec {E#1} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=[.];E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  [.],
           S#8   |->  (app S#3 S#2),
           E#6   |->  {E#1}}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#1} in (app S#3 S#2));E#7} in A#9[(var X#5)])
    -lapp1->                      (letrec {X#5=(app (letrec {E#1} in S#3) S#2);E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#1} in (app S#3 S#2));E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=(app S#3 S#2);E#1;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(app (letrec {E#1} in S#3) S#2)]
       ;X#5= (letrec {E#6} in S#8)
       ;E#13
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#11= T#10[(letrec {E#1} in (app S#3 S#2))]
       ;X#5= S#8
       ;E#13
       ;E#6
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13},(letrec {E#6} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)]),
           E#7   |->  {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13},
           E#12  |->  {X#5=(letrec {E#6} in S#8);E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    -lapp1->                      (letrec {X#11=T#10[(app (letrec {E#1} in S#3) S#2)];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];X#5=S#8;E#13;E#6} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#10[(var X#5)]) S#2)
    ,
     (letrec {X#5=S#8;E#6;E#7} in (app A#10[(var X#5)] S#2))
  )

where

   Delta1 = {A#9}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {X#5=(letrec {E#6} in S#8);E#7} in [.])),
             ((app A#10[(var X#5)] S#2),(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#5),(app A#10[[.]] S#2)),
             ((var X#5),(app A#10[[.]] S#2))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           E#1  |->  {X#5=(letrec {E#6} in S#8);E#7},
           A#9  |->  (app A#10 S#2),
           S#3  |->  A#10[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in (app A#10[(var X#5)] S#2))
    -lapp1->                      (app (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#10[(var X#5)]) S#2)
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in (app A#10[(var X#5)] S#2))
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in (app A#10[(var X#5)] S#2))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(app A#14[(var X#6)] T#15[(app (letrec {E#1} in S#3) S#2)])]
     )
    ,
     (letrec
        X#5= S#9
       ;E#7
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(app A#14[(var X#6)] T#15[(letrec {E#1} in (app S#3 S#2))])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#13[(app A#14[(var X#6)] T#15[(letrec {E#1} in (app S#3 S#2))])],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#13[(app A#14[[.]] T#15[(letrec {E#1} in (app S#3 S#2))])]),
             ((var X#5),[.]),
             ((var X#6),A#13[(app A#14[[.]] T#15[(letrec {E#1} in (app S#3 S#2))])])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#6)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(letrec {E#1} in (app S#3 S#2))])])
    -lapp1->                      (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(app (letrec {E#1} in S#3) S#2)])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(letrec {E#1} in (app S#3 S#2))])])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(letrec {E#1} in (app S#3 S#2))])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in T#15[(app (letrec {E#1} in S#3) S#2)])
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= T#15[(letrec {E#1} in (app S#3 S#2))]
       ;E#7
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#7} in T#15);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  (letrec {E#7} in T#15),
           S#9   |->  T#15[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in T#15[(letrec {E#1} in (app S#3 S#2))]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -lapp1->                      (letrec {X#5=(letrec {E#7} in T#15[(app (letrec {E#1} in S#3) S#2)]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in T#15[(letrec {E#1} in (app S#3 S#2))]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=T#15[(letrec {E#1} in (app S#3 S#2))];E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#16=T#15[(app (letrec {E#1} in S#3) S#2)];E#18} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {E#1} in (app S#3 S#2))]
       ;X#5= S#9
       ;E#18
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),(letrec {X#16=T#15[(letrec {E#1} in (app S#3 S#2))];E#18;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {X#16=T#15[(letrec {E#1} in (app S#3 S#2))];E#18} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {X#16=T#15[(letrec {E#1} in (app S#3 S#2))];E#18} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {X#16=T#15;E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  (letrec {X#16=T#15;E#18} in S#9),
           E#7   |->  {X#16=T#15[(letrec {E#1} in (app S#3 S#2))];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#16=T#15[(letrec {E#1} in (app S#3 S#2))];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -lapp1->                      (letrec {X#5=(letrec {X#16=T#15[(app (letrec {E#1} in S#3) S#2)];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {X#16=T#15[(letrec {E#1} in (app S#3 S#2))];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=T#15[(letrec {E#1} in (app S#3 S#2))];X#5=S#9;E#18;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {E#1} in S#3) S#2)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#5=(app S#3 S#2);E#1;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),(letrec {E#1;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#1} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#1} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=[.];E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  [.],
           S#9   |->  (app S#3 S#2),
           E#7   |->  {E#1}}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#1} in (app S#3 S#2));E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -lapp1->                      (letrec {X#5=(app (letrec {E#1} in S#3) S#2);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#1} in (app S#3 S#2));E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=(app S#3 S#2);E#1;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(app (letrec {E#1} in S#3) S#2)]
       ;X#5= (letrec {E#7} in S#9)
       ;E#15
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {E#1} in (app S#3 S#2))]
       ;X#5= S#9
       ;E#15
       ;E#7
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),(letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15;E#7;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           E#8   |->  {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15},
           E#14  |->  {X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -lapp1->                      (letrec {X#13=T#12[(app (letrec {E#1} in S#3) S#2)];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];X#5=S#9;E#15;E#7;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#16[(app A#17[(var X#5)] T#18[(app (letrec {E#1} in S#3) S#2)])]
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#16[(app A#17[(var X#5)] T#18[(letrec {E#1} in (app S#3 S#2))])]
       ;E#7
       ;E#8
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),(letrec {X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1} in (app S#3 S#2))])];E#7;E#8} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1} in (app S#3 S#2))])];E#8},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18)];E#8} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[(letrec {E#1} in (app S#3 S#2))])]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8},
           T#12         |->  A#16[(app A#17[(var X#5)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1} in (app S#3 S#2))])];E#8} in A#10[(var X#6)])
    -lapp1->                      (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[(app (letrec {E#1} in S#3) S#2)])];E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1} in (app S#3 S#2))])];E#8} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1} in (app S#3 S#2))])];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#18[(app A#19[(var X#16)] T#20[(app (letrec {E#1} in S#3) S#2)])]
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])]
       ;E#7
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),(letrec {X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#7;E#8;EE#17[X#16,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#8;EE#17[X#16,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20)];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#16,(var X#5)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -lapp1->                      (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[(app (letrec {E#1} in S#3) S#2)])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#7;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(app (letrec {E#1} in S#3) S#2)])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),(letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])];E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])];E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -lapp1->                      (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(app (letrec {E#1} in S#3) S#2)])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])];X#5=S#9;E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(var X#5)] T#20[(app (letrec {E#1} in S#3) S#2)])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(var X#5)] T#20[(letrec {E#1} in (app S#3 S#2))])]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#5),(letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#7;E#8;EE#17[X#6,(var X#16)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#8;EE#17[X#6,(var X#16)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20)];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[(letrec {E#1} in (app S#3 S#2))])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]},
           T#12         |->  A#18[(app A#19[(var X#5)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1} in (app S#3 S#2))])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -lapp1->                      (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(app (letrec {E#1} in S#3) S#2)])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1} in (app S#3 S#2))])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1} in (app S#3 S#2))])];X#5=S#9;E#7;E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#12[(var X#6)]) S#2)
    ,
     (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in (app A#12[(var X#6)] S#2))
  )

where

   Delta1 = {A#10}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             ((app A#12[(var X#6)] S#2),(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),(app A#12[[.]] S#2)),
             ((var X#5),[.]),
             ((var X#6),(app A#12[[.]] S#2))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#1   |->  {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]},
           A#10  |->  (app A#12 S#2),
           S#3   |->  A#12[(var X#6)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in (app A#12[(var X#6)] S#2))
    -lapp1->                      (app (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#12[(var X#6)]) S#2)
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in (app A#12[(var X#6)] S#2))
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in (app A#12[(var X#6)] S#2))
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {E#5} in T#12[(app (letrec {E#1} in S#3) S#2)]) S#6)]
    ,
     A#9[(letrec {E#5} in (app T#12[(letrec {E#1} in (app S#3 S#2))] S#6))]
  )

where

   Delta1 = {T#11,T#10,A#8,T#4,A#9}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (letrec {E#5} in T#12) S#6)],
           T#10  |->  (app (letrec {E#5} in T#12) S#6),
           T#11  |->  (letrec {E#5} in T#12),
           S#7   |->  T#12[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in T#12[(letrec {E#1} in (app S#3 S#2))]) S#6)]
    -lapp1->                      A#9[(app (letrec {E#5} in T#12[(app (letrec {E#1} in S#3) S#2)]) S#6)]
    ................................................................................
                                  A#9[(app (letrec {E#5} in T#12[(letrec {E#1} in (app S#3 S#2))]) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app T#12[(letrec {E#1} in (app S#3 S#2))] S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {X#13=T#12[(app (letrec {E#1} in S#3) S#2)];E#15} in S#7) S#6)]
    ,
     A#9[(letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15} in (app S#7 S#6))]
  )

where

   Delta1 = {T#11,T#10,A#8,T#4,A#9}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (letrec {X#13=T#12;E#15} in S#7) S#6)],
           T#10  |->  (app (letrec {X#13=T#12;E#15} in S#7) S#6),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#7),
           E#5   |->  {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  A#9[(app (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15} in S#7) S#6)]
    -lapp1->                      A#9[(app (letrec {X#13=T#12[(app (letrec {E#1} in S#3) S#2)];E#15} in S#7) S#6)]
    ................................................................................
                                  A#9[(app (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (app (letrec {E#1} in S#3) S#2) S#6)]
    ,
     A#9[(letrec {E#1} in (app (app S#3 S#2) S#6))]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(letrec {E#1} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app [.] S#6)],
           T#10  |->  (app [.] S#6),
           T#11  |->  [.],
           S#7   |->  (app S#3 S#2),
           E#5   |->  {E#1}}

and instantiated rules:

                                  A#9[(app (letrec {E#1} in (app S#3 S#2)) S#6)]
    -lapp1->                      A#9[(app (app (letrec {E#1} in S#3) S#2) S#6)]
    ................................................................................
                                  A#9[(app (letrec {E#1} in (app S#3 S#2)) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#1} in (app (app S#3 S#2) S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {E#5} in S#7) T#11[(app (letrec {E#1} in S#3) S#2)])]
    ,
     A#9[(letrec {E#5} in (app S#7 T#11[(letrec {E#1} in (app S#3 S#2))]))]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#11[(letrec {E#1} in (app S#3 S#2))],(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (letrec {E#5} in S#7) T#11)],
           T#10  |->  (app (letrec {E#5} in S#7) T#11),
           S#6   |->  T#11[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in S#7) T#11[(letrec {E#1} in (app S#3 S#2))])]
    -lapp1->                      A#9[(app (letrec {E#5} in S#7) T#11[(app (letrec {E#1} in S#3) S#2)])]
    ................................................................................
                                  A#9[(app (letrec {E#5} in S#7) T#11[(letrec {E#1} in (app S#3 S#2))])]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app S#7 T#11[(letrec {E#1} in (app S#3 S#2))]))]
    

================================================================================
Critical Pair:

  (
     A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(app (letrec {E#1} in S#3) S#2)])]
    ,
     A#9[(app A#10[(letrec {E#5} in (app S#7 S#6))] T#11[(letrec {E#1} in (app S#3 S#2))])]
  )

where

   Delta1 = {A#8,T#4}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#4  |->  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11)],
           A#8  |->  A#9[(app A#10 T#11[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(letrec {E#1} in (app S#3 S#2))])]
    -lapp1->                      A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(app (letrec {E#1} in S#3) S#2)])]
    ................................................................................
                                  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(letrec {E#1} in (app S#3 S#2))])]
    -SR,lapp1->                   A#9[(app A#10[(letrec {E#5} in (app S#7 S#6))] T#11[(letrec {E#1} in (app S#3 S#2))])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#5} in T#10[(app (letrec {E#1} in S#3) S#2)]) S#6)
    ,
     (letrec {E#5} in (app T#10[(letrec {E#1} in (app S#3 S#2))] S#6))
  )

where

   Delta1 = {T#9,T#4}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8  |->  [.],
           T#4  |->  (app (letrec {E#5} in T#10) S#6),
           T#9  |->  (letrec {E#5} in T#10),
           S#7  |->  T#10[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (app (letrec {E#5} in T#10[(letrec {E#1} in (app S#3 S#2))]) S#6)
    -lapp1->                      (app (letrec {E#5} in T#10[(app (letrec {E#1} in S#3) S#2)]) S#6)
    ................................................................................
                                  (app (letrec {E#5} in T#10[(letrec {E#1} in (app S#3 S#2))]) S#6)
    -SR,lapp1->                   (letrec {E#5} in (app T#10[(letrec {E#1} in (app S#3 S#2))] S#6))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#11=T#10[(app (letrec {E#1} in S#3) S#2)];E#13} in S#7) S#6)
    ,
     (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13} in (app S#7 S#6))
  )

where

   Delta1 = {T#9,T#4}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  [.],
           T#4   |->  (app (letrec {X#11=T#10;E#13} in S#7) S#6),
           T#9   |->  (letrec {X#11=T#10;E#13} in S#7),
           E#5   |->  {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (app (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13} in S#7) S#6)
    -lapp1->                      (app (letrec {X#11=T#10[(app (letrec {E#1} in S#3) S#2)];E#13} in S#7) S#6)
    ................................................................................
                                  (app (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13} in S#7) S#6)
    -SR,lapp1->                   (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13} in (app S#7 S#6))
    

================================================================================
Critical Pair:

  (
     (app (app (letrec {E#1} in S#3) S#2) S#6)
    ,
     (letrec {E#1} in (app (app S#3 S#2) S#6))
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(letrec {E#1} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8  |->  [.],
           T#4  |->  (app [.] S#6),
           T#9  |->  [.],
           S#7  |->  (app S#3 S#2),
           E#5  |->  {E#1}}

and instantiated rules:

                                  (app (letrec {E#1} in (app S#3 S#2)) S#6)
    -lapp1->                      (app (app (letrec {E#1} in S#3) S#2) S#6)
    ................................................................................
                                  (app (letrec {E#1} in (app S#3 S#2)) S#6)
    -SR,lapp1->                   (letrec {E#1} in (app (app S#3 S#2) S#6))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#5} in S#7) T#9[(app (letrec {E#1} in S#3) S#2)])
    ,
     (letrec {E#5} in (app S#7 T#9[(letrec {E#1} in (app S#3 S#2))]))
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#9[(letrec {E#1} in (app S#3 S#2))],(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8  |->  [.],
           T#4  |->  (app (letrec {E#5} in S#7) T#9),
           S#6  |->  T#9[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (app (letrec {E#5} in S#7) T#9[(letrec {E#1} in (app S#3 S#2))])
    -lapp1->                      (app (letrec {E#5} in S#7) T#9[(app (letrec {E#1} in S#3) S#2)])
    ................................................................................
                                  (app (letrec {E#5} in S#7) T#9[(letrec {E#1} in (app S#3 S#2))])
    -SR,lapp1->                   (letrec {E#5} in (app S#7 T#9[(letrec {E#1} in (app S#3 S#2))]))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {E#6} in T#14[(app (letrec {E#1} in S#3) S#2)]) S#7)]
     )
    ,
     (letrec
        E#5
     in
        A#11[(letrec {E#6} in (app T#14[(letrec {E#1} in (app S#3 S#2))] S#7))]
     )
  )

where

   Delta1 = {T#13,T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14) S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {E#6} in T#14) S#7)],
           T#12  |->  (app (letrec {E#6} in T#14) S#7),
           T#13  |->  (letrec {E#6} in T#14),
           S#8   |->  T#14[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(letrec {E#1} in (app S#3 S#2))]) S#7)])
    -lapp1->                      (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(app (letrec {E#1} in S#3) S#2)]) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(letrec {E#1} in (app S#3 S#2))]) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[(letrec {E#1} in (app S#3 S#2))] S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {X#15=T#14[(app (letrec {E#1} in S#3) S#2)];E#17} in S#8) S#7)]
     )
    ,
     (letrec
        E#5
     in
        A#11[(letrec {X#15=T#14[(letrec {E#1} in (app S#3 S#2))];E#17} in (app S#8 S#7))]
     )
  )

where

   Delta1 = {T#13,T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {X#15=T#14[(letrec {E#1} in (app S#3 S#2))];E#17} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)],
           T#12  |->  (app (letrec {X#15=T#14;E#17} in S#8) S#7),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#8),
           E#6   |->  {X#15=T#14[(letrec {E#1} in (app S#3 S#2))];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[(letrec {E#1} in (app S#3 S#2))];E#17} in S#8) S#7)])
    -lapp1->                      (letrec {E#5} in A#11[(app (letrec {X#15=T#14[(app (letrec {E#1} in S#3) S#2)];E#17} in S#8) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[(letrec {E#1} in (app S#3 S#2))];E#17} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {X#15=T#14[(letrec {E#1} in (app S#3 S#2))];E#17} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in A#11[(app (app (letrec {E#1} in S#3) S#2) S#7)])
    ,
     (letrec {E#5} in A#11[(letrec {E#1} in (app (app S#3 S#2) S#7))])
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#1} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app [.] S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app [.] S#7)],
           T#12  |->  (app [.] S#7),
           T#13  |->  [.],
           S#8   |->  (app S#3 S#2),
           E#6   |->  {E#1}}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#1} in (app S#3 S#2)) S#7)])
    -lapp1->                      (letrec {E#5} in A#11[(app (app (letrec {E#1} in S#3) S#2) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#1} in (app S#3 S#2)) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#1} in (app (app S#3 S#2) S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {E#6} in S#8) T#13[(app (letrec {E#1} in S#3) S#2)])]
     )
    ,
     (letrec
        E#5
     in
        A#11[(letrec {E#6} in (app S#8 T#13[(letrec {E#1} in (app S#3 S#2))]))]
     )
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#13[(letrec {E#1} in (app S#3 S#2))],(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {E#6} in S#8) T#13)],
           T#12  |->  (app (letrec {E#6} in S#8) T#13),
           S#7   |->  T#13[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(letrec {E#1} in (app S#3 S#2))])])
    -lapp1->                      (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(app (letrec {E#1} in S#3) S#2)])])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(letrec {E#1} in (app S#3 S#2))])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 T#13[(letrec {E#1} in (app S#3 S#2))]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(app (letrec {E#1} in S#3) S#2)])]
     )
    ,
     (letrec
        E#5
     in
        A#11[(app A#12[(letrec {E#6} in (app S#8 S#7))] T#13[(letrec {E#1} in (app S#3 S#2))])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)]),
           T#10  |->  A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(letrec {E#1} in (app S#3 S#2))])])
    -lapp1->                      (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(app (letrec {E#1} in S#3) S#2)])])
    ................................................................................
                                  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(letrec {E#1} in (app S#3 S#2))])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(app A#12[(letrec {E#6} in (app S#8 S#7))] T#13[(letrec {E#1} in (app S#3 S#2))])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (app (letrec {E#6} in T#12[(app (letrec {E#1} in S#3) S#2)]) S#7)
     )
    ,
     (letrec
        E#5
     in
        (letrec {E#6} in (app T#12[(letrec {E#1} in (app S#3 S#2))] S#7))
     )
  )

where

   Delta1 = {T#11,T#10,T#4}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app (letrec {E#6} in T#12) S#7)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {E#6} in T#12) S#7),
           T#11  |->  (letrec {E#6} in T#12),
           S#8   |->  T#12[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in T#12[(letrec {E#1} in (app S#3 S#2))]) S#7))
    -lapp1->                      (letrec {E#5} in (app (letrec {E#6} in T#12[(app (letrec {E#1} in S#3) S#2)]) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in T#12[(letrec {E#1} in (app S#3 S#2))]) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app T#12[(letrec {E#1} in (app S#3 S#2))] S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (app (letrec {X#13=T#12[(app (letrec {E#1} in S#3) S#2)];E#15} in S#8) S#7)
     )
    ,
     (letrec
        E#5
     in
        (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15} in (app S#8 S#7))
     )
  )

where

   Delta1 = {T#11,T#10,T#4}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app (letrec {X#13=T#12;E#15} in S#8) S#7)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {X#13=T#12;E#15} in S#8) S#7),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#8),
           E#6   |->  {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15} in S#8) S#7))
    -lapp1->                      (letrec {E#5} in (app (letrec {X#13=T#12[(app (letrec {E#1} in S#3) S#2)];E#15} in S#8) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15} in S#8) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15} in (app S#8 S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (app (app (letrec {E#1} in S#3) S#2) S#7))
    ,
     (letrec {E#5} in (letrec {E#1} in (app (app S#3 S#2) S#7)))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#1} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app [.] S#7)),
           A#9   |->  [.],
           T#10  |->  (app [.] S#7),
           T#11  |->  [.],
           S#8   |->  (app S#3 S#2),
           E#6   |->  {E#1}}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#1} in (app S#3 S#2)) S#7))
    -lapp1->                      (letrec {E#5} in (app (app (letrec {E#1} in S#3) S#2) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#1} in (app S#3 S#2)) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#1} in (app (app S#3 S#2) S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (app (letrec {E#6} in S#8) T#11[(app (letrec {E#1} in S#3) S#2)])
     )
    ,
     (letrec
        E#5
     in
        (letrec {E#6} in (app S#8 T#11[(letrec {E#1} in (app S#3 S#2))]))
     )
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#11[(letrec {E#1} in (app S#3 S#2))],(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {E#6} in S#8) T#11),
           S#7   |->  T#11[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(letrec {E#1} in (app S#3 S#2))]))
    -lapp1->                      (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(app (letrec {E#1} in S#3) S#2)]))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(letrec {E#1} in (app S#3 S#2))]))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app S#8 T#11[(letrec {E#1} in (app S#3 S#2))])))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(app (letrec {E#1} in S#3) S#2)]
       ;E#13
     in
        A#9[(app (letrec {E#6} in S#8) S#7)]
     )
    ,
     (letrec
        X#11= T#10[(letrec {E#1} in (app S#3 S#2))]
       ;E#13
     in
        A#9[(letrec {E#6} in (app S#8 S#7))]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;E#13} in A#9[(app (letrec {E#6} in S#8) S#7)]),
           E#5   |->  {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -lapp1->                      (letrec {X#11=T#10[(app (letrec {E#1} in S#3) S#2)];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {X#11=T#10[(letrec {E#1} in (app S#3 S#2))];E#13} in A#9[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#5} in A#10[(app (letrec {E#6} in S#8) S#7)]) S#2)
    ,
     (letrec {E#5} in (app A#10[(letrec {E#6} in (app S#8 S#7))] S#2))
  )

where

   Delta1 = {A#9}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#5} in [.])),
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4  |->  [.],
           E#1  |->  {E#5},
           A#9  |->  (app A#10 S#2),
           S#3  |->  A#10[(app (letrec {E#6} in S#8) S#7)]}

and instantiated rules:

                                  (letrec {E#5} in (app A#10[(app (letrec {E#6} in S#8) S#7)] S#2))
    -lapp1->                      (app (letrec {E#5} in A#10[(app (letrec {E#6} in S#8) S#7)]) S#2)
    ................................................................................
                                  (letrec {E#5} in (app A#10[(app (letrec {E#6} in S#8) S#7)] S#2))
    -SR,lapp2->                   (letrec {E#5} in (app A#10[(letrec {E#6} in (app S#8 S#7))] S#2))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#5} in (letrec {E#6} in S#8)) S#2)
    ,
     (letrec {E#5} in (letrec {E#6} in (app S#8 S#2)))
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#5,E#6}
   Delta3 = {(S#2,(letrec {E#5} in [.])),
             (S#2,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#5,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4  |->  [.],
           E#1  |->  {E#5},
           A#9  |->  [.],
           S#7  |->  S#2,
           S#3  |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in S#8) S#2))
    -lapp1->                      (app (letrec {E#5} in (letrec {E#6} in S#8)) S#2)
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in S#8) S#2))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app S#8 S#2)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        A#13[(app A#14[(var X#5)] T#15[(app (letrec {E#1} in S#3) S#2)])]
     )
    ,
     (letrec
        E#6
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in (app S#3 S#2))])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {E#1} in (app S#3 S#2))])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {E#1} in (app S#3 S#2))])])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#5)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in (app S#3 S#2))])])
    -lapp1->                      (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(app (letrec {E#1} in S#3) S#2)])])
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in (app S#3 S#2))])])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in (app S#3 S#2))])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(app (letrec {E#1} in S#3) S#2)]
       ;E#15
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {E#1} in (app S#3 S#2))]
       ;E#15
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           E#6   |->  {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15},
           E#14  |->  {E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#13=T#12[(app (letrec {E#1} in S#3) S#2)];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#13=T#12[(letrec {E#1} in (app S#3 S#2))];E#15;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {E#7} in T#19[(app (letrec {E#1} in S#3) S#2)]) S#8)]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app T#19[(letrec {E#1} in (app S#3 S#2))] S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (letrec {E#7} in T#19) S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {E#7} in T#19) S#8)],
           T#17         |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[(letrec {E#1} in (app S#3 S#2))]) S#8)];E#6} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#5=A#16[(app (letrec {E#7} in T#19[(app (letrec {E#1} in S#3) S#2)]) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[(letrec {E#1} in (app S#3 S#2))]) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app T#19[(letrec {E#1} in (app S#3 S#2))] S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {X#20=T#19[(app (letrec {E#1} in S#3) S#2)];E#22} in S#9) S#8)]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {X#20=T#19[(letrec {E#1} in (app S#3 S#2))];E#22} in (app S#9 S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {X#20=T#19[(letrec {E#1} in (app S#3 S#2))];E#22} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)],
           T#17         |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[(letrec {E#1} in (app S#3 S#2))];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[(letrec {E#1} in (app S#3 S#2))];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#5=A#16[(app (letrec {X#20=T#19[(app (letrec {E#1} in S#3) S#2)];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[(letrec {E#1} in (app S#3 S#2))];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {X#20=T#19[(letrec {E#1} in (app S#3 S#2))];E#22} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (app (letrec {E#1} in S#3) S#2) S#8)]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#1} in (app (app S#3 S#2) S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {E#1} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app [.] S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app [.] S#8)],
           T#17         |->  (app [.] S#8),
           T#18         |->  [.],
           S#9          |->  (app S#3 S#2),
           E#7          |->  {E#1}}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#1} in (app S#3 S#2)) S#8)];E#6} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#5=A#16[(app (app (letrec {E#1} in S#3) S#2) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#1} in (app S#3 S#2)) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#1} in (app (app S#3 S#2) S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {E#7} in S#9) T#18[(app (letrec {E#1} in S#3) S#2)])]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app S#9 T#18[(letrec {E#1} in (app S#3 S#2))]))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#18[(letrec {E#1} in (app S#3 S#2))],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {E#7} in S#9) T#18)],
           T#17         |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[(letrec {E#1} in (app S#3 S#2))])];E#6} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[(app (letrec {E#1} in S#3) S#2)])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[(letrec {E#1} in (app S#3 S#2))])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 T#18[(letrec {E#1} in (app S#3 S#2))]))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(app (letrec {E#1} in S#3) S#2)])]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(app A#17[(letrec {E#7} in (app S#9 S#8))] T#18[(letrec {E#1} in (app S#3 S#2))])]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[(letrec {E#1} in (app S#3 S#2))])]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(letrec {E#1} in (app S#3 S#2))])];E#6} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(app (letrec {E#1} in S#3) S#2)])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(letrec {E#1} in (app S#3 S#2))])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(app A#17[(letrec {E#7} in (app S#9 S#8))] T#18[(letrec {E#1} in (app S#3 S#2))])];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {E#7} in T#17[(app (letrec {E#1} in S#3) S#2)]) S#8)
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {E#7} in (app T#17[(letrec {E#1} in (app S#3 S#2))] S#8))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#16,T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (letrec {E#7} in T#17) S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in T#17) S#8),
           T#16         |->  (letrec {E#7} in T#17),
           S#9          |->  T#17[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in T#17[(letrec {E#1} in (app S#3 S#2))]) S#8);E#6} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#5=(app (letrec {E#7} in T#17[(app (letrec {E#1} in S#3) S#2)]) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in T#17[(letrec {E#1} in (app S#3 S#2))]) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app T#17[(letrec {E#1} in (app S#3 S#2))] S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {X#18=T#17[(app (letrec {E#1} in S#3) S#2)];E#20} in S#9) S#8)
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {X#18=T#17[(letrec {E#1} in (app S#3 S#2))];E#20} in (app S#9 S#8))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#16,T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {X#18=T#17[(letrec {E#1} in (app S#3 S#2))];E#20} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (letrec {X#18=T#17;E#20} in S#9) S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {X#18=T#17;E#20} in S#9) S#8),
           T#16         |->  (letrec {X#18=T#17;E#20} in S#9),
           E#7          |->  {X#18=T#17[(letrec {E#1} in (app S#3 S#2))];E#20},
           E#19         |->  {E#20}}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {X#18=T#17[(letrec {E#1} in (app S#3 S#2))];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#5=(app (letrec {X#18=T#17[(app (letrec {E#1} in S#3) S#2)];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {X#18=T#17[(letrec {E#1} in (app S#3 S#2))];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {X#18=T#17[(letrec {E#1} in (app S#3 S#2))];E#20} in (app S#9 S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(app (app (letrec {E#1} in S#3) S#2) S#8);E#6} in A#10[(var X#5)])
    ,
     (letrec {X#5=(letrec {E#1} in (app (app S#3 S#2) S#8));E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {E#1} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app [.] S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#16         |->  [.],
           S#9          |->  (app S#3 S#2),
           E#7          |->  {E#1}}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#1} in (app S#3 S#2)) S#8);E#6} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#5=(app (app (letrec {E#1} in S#3) S#2) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#1} in (app S#3 S#2)) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#1} in (app (app S#3 S#2) S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {E#7} in S#9) T#16[(app (letrec {E#1} in S#3) S#2)])
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {E#7} in (app S#9 T#16[(letrec {E#1} in (app S#3 S#2))]))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#16[(letrec {E#1} in (app S#3 S#2))],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (letrec {E#7} in S#9) T#16);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in S#9) T#16),
           S#8          |->  T#16[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in S#9) T#16[(letrec {E#1} in (app S#3 S#2))]);E#6} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#5=(app (letrec {E#7} in S#9) T#16[(app (letrec {E#1} in S#3) S#2)]);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in S#9) T#16[(letrec {E#1} in (app S#3 S#2))]);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app S#9 T#16[(letrec {E#1} in (app S#3 S#2))]));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(app (letrec {E#1} in S#3) S#2)])]
       ;E#6
       ;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])]
       ;E#6
       ;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(app (letrec {E#1} in S#3) S#2)])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#6;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(app (letrec {E#1} in S#3) S#2)])]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(app (letrec {E#1} in S#3) S#2)])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in (app S#3 S#2))])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {E#7} in T#21[(app (letrec {E#1} in S#3) S#2)]) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app T#21[(letrec {E#1} in (app S#3 S#2))] S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (letrec {E#7} in T#21) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {E#7} in T#21) S#8)],
           T#19         |->  (app (letrec {E#7} in T#21) S#8),
           T#20         |->  (letrec {E#7} in T#21),
           S#9          |->  T#21[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[(letrec {E#1} in (app S#3 S#2))]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#16=A#18[(app (letrec {E#7} in T#21[(app (letrec {E#1} in S#3) S#2)]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[(letrec {E#1} in (app S#3 S#2))]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app T#21[(letrec {E#1} in (app S#3 S#2))] S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {X#22=T#21[(app (letrec {E#1} in S#3) S#2)];E#24} in S#9) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#22=T#21[(letrec {E#1} in (app S#3 S#2))];E#24} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {X#22=T#21[(letrec {E#1} in (app S#3 S#2))];E#24} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)],
           T#19         |->  (app (letrec {X#22=T#21;E#24} in S#9) S#8),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#9),
           E#7          |->  {X#22=T#21[(letrec {E#1} in (app S#3 S#2))];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[(letrec {E#1} in (app S#3 S#2))];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#16=A#18[(app (letrec {X#22=T#21[(app (letrec {E#1} in S#3) S#2)];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[(letrec {E#1} in (app S#3 S#2))];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {X#22=T#21[(letrec {E#1} in (app S#3 S#2))];E#24} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (app (letrec {E#1} in S#3) S#2) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#1} in (app (app S#3 S#2) S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {E#1} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app [.] S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app [.] S#8)],
           T#19         |->  (app [.] S#8),
           T#20         |->  [.],
           S#9          |->  (app S#3 S#2),
           E#7          |->  {E#1}}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#1} in (app S#3 S#2)) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#16=A#18[(app (app (letrec {E#1} in S#3) S#2) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#1} in (app S#3 S#2)) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#1} in (app (app S#3 S#2) S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {E#7} in S#9) T#20[(app (letrec {E#1} in S#3) S#2)])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 T#20[(letrec {E#1} in (app S#3 S#2))]))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#20[(letrec {E#1} in (app S#3 S#2))],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {E#7} in S#9) T#20)],
           T#19         |->  (app (letrec {E#7} in S#9) T#20),
           S#8          |->  T#20[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[(letrec {E#1} in (app S#3 S#2))])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[(app (letrec {E#1} in S#3) S#2)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[(letrec {E#1} in (app S#3 S#2))])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 T#20[(letrec {E#1} in (app S#3 S#2))]))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(app (letrec {E#1} in S#3) S#2)])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[(letrec {E#1} in (app S#3 S#2))])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[(letrec {E#1} in (app S#3 S#2))])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1} in (app S#3 S#2))])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(app (letrec {E#1} in S#3) S#2)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(letrec {E#1} in (app S#3 S#2))])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[(letrec {E#1} in (app S#3 S#2))])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {E#7} in T#19[(app (letrec {E#1} in S#3) S#2)]) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app T#19[(letrec {E#1} in (app S#3 S#2))] S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (letrec {E#7} in T#19) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in T#19[(letrec {E#1} in (app S#3 S#2))]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#16=(app (letrec {E#7} in T#19[(app (letrec {E#1} in S#3) S#2)]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in T#19[(letrec {E#1} in (app S#3 S#2))]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app T#19[(letrec {E#1} in (app S#3 S#2))] S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {X#20=T#19[(app (letrec {E#1} in S#3) S#2)];E#22} in S#9) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#20=T#19[(letrec {E#1} in (app S#3 S#2))];E#22} in (app S#9 S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {X#20=T#19[(letrec {E#1} in (app S#3 S#2))];E#22} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (letrec {X#20=T#19;E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[(letrec {E#1} in (app S#3 S#2))];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {X#20=T#19[(letrec {E#1} in (app S#3 S#2))];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#16=(app (letrec {X#20=T#19[(app (letrec {E#1} in S#3) S#2)];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {X#20=T#19[(letrec {E#1} in (app S#3 S#2))];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {X#20=T#19[(letrec {E#1} in (app S#3 S#2))];E#22} in (app S#9 S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (app (letrec {E#1} in S#3) S#2) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#1} in (app (app S#3 S#2) S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#8,(letrec {E#1} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app [.] S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#18         |->  [.],
           S#9          |->  (app S#3 S#2),
           E#7          |->  {E#1}}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#1} in (app S#3 S#2)) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#16=(app (app (letrec {E#1} in S#3) S#2) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#1} in (app S#3 S#2)) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#1} in (app (app S#3 S#2) S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {E#7} in S#9) T#18[(app (letrec {E#1} in S#3) S#2)])
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app S#9 T#18[(letrec {E#1} in (app S#3 S#2))]))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#18[(letrec {E#1} in (app S#3 S#2))],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (letrec {E#7} in S#9) T#18);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[(letrec {E#1} in (app S#3 S#2))]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in S#9) T#18[(letrec {E#1} in (app S#3 S#2))]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -lapp1->                      (letrec {X#16=(app (letrec {E#7} in S#9) T#18[(app (letrec {E#1} in S#3) S#2)]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in S#9) T#18[(letrec {E#1} in (app S#3 S#2))]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app S#9 T#18[(letrec {E#1} in (app S#3 S#2))]));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#12[(var X#5)]) S#2)
    ,
     (letrec
        E#6
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        (app A#12[(var X#5)] S#2)
     )
  )

where

   Delta1 = {A#10}
   Delta2 = {E#1,E#7}
   Delta3 = {(S#2,(letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),(app A#12[[.]] S#2)),
             ((var X#5),(app A#12[[.]] S#2))}
   Delta4=  {}

from overlapping -lapp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in (app S#3 S#2))]
    -lapp1->                      T#4[(app (letrec {E#1} in S#3) S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in (app S#3 S#2))]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#7}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#1   |->  {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]},
           A#10  |->  (app A#12 S#2),
           S#3   |->  A#12[(var X#5)]}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in (app A#12[(var X#5)] S#2))
    -lapp1->                      (app (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#12[(var X#5)]) S#2)
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in (app A#12[(var X#5)] S#2))
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in (app A#12[(var X#5)] S#2))
    

================================================================================
Critical Pair:

  (
     A#10[(app (\ X#6.S#8) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
    ,
     A#10[(letrec {X#6=T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#8)]
  )

where

   Delta1 = {T#11,A#9,T#4,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(\ X#6.[.])),
             (T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {X#6=[.]} in S#8)),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  A#9[(app (\ X#6.S#8) S#7)]
    -SR,lbeta1->                  A#9[(letrec {X#6=S#7} in S#8)]
    and constraints: (S#7,(\ X#6.[.])), (S#7,(letrec {X#6=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        A#9[(app (\ X#6.S#8) S#7)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#7,(\ X#6.[.])),(S#7,(letrec {X#6=[.]} in S#8)),((var X#1),C#5[[.]])}


and found solution:

    Sol = {A#9   |->  A#10,
           T#4   |->  A#10[(app (\ X#6.S#8) T#12)],
           T#11  |->  (app (\ X#6.S#8) T#12),
           S#7   |->  T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  A#10[(app (\ X#6.S#8) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
    -cpx-in1->                    A#10[(app (\ X#6.S#8) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
    ................................................................................
                                  A#10[(app (\ X#6.S#8) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
    -SR,lbeta1->                  A#10[(letrec {X#6=T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#8)]
    

================================================================================
Critical Pair:

  (
     A#10[(app A#11[(app (\ X#6.S#8) S#7)] T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
    ,
     A#10[(app A#11[(letrec {X#6=S#7} in S#8)] T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
  )

where

   Delta1 = {A#9,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#7,(\ X#6.[.])),
             (S#7,(letrec {X#6=[.]} in S#8)),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  A#9[(app (\ X#6.S#8) S#7)]
    -SR,lbeta1->                  A#9[(letrec {X#6=S#7} in S#8)]
    and constraints: (S#7,(\ X#6.[.])), (S#7,(letrec {X#6=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        A#9[(app (\ X#6.S#8) S#7)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#7,(\ X#6.[.])),(S#7,(letrec {X#6=[.]} in S#8)),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4  |->  A#10[(app A#11[(app (\ X#6.S#8) S#7)] T#12)],
           A#9  |->  A#10[(app A#11 T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  A#10[(app A#11[(app (\ X#6.S#8) S#7)] T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
    -cpx-in1->                    A#10[(app A#11[(app (\ X#6.S#8) S#7)] T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
    ................................................................................
                                  A#10[(app A#11[(app (\ X#6.S#8) S#7)] T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
    -SR,lbeta1->                  A#10[(app A#11[(letrec {X#6=S#7} in S#8)] T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
    

================================================================================
Critical Pair:

  (
     (app (\ X#6.S#8) T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])
    ,
     (letrec {X#6=T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#8)
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(\ X#6.[.])),
             (T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {X#6=[.]} in S#8)),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  A#9[(app (\ X#6.S#8) S#7)]
    -SR,lbeta1->                  A#9[(letrec {X#6=S#7} in S#8)]
    and constraints: (S#7,(\ X#6.[.])), (S#7,(letrec {X#6=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        A#9[(app (\ X#6.S#8) S#7)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#7,(\ X#6.[.])),(S#7,(letrec {X#6=[.]} in S#8)),((var X#1),C#5[[.]])}


and found solution:

    Sol = {A#9  |->  [.],
           T#4  |->  (app (\ X#6.S#8) T#10),
           S#7  |->  T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (app (\ X#6.S#8) T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])
    -cpx-in1->                    (app (\ X#6.S#8) T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])
    ................................................................................
                                  (app (\ X#6.S#8) T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])
    -SR,lbeta1->                  (letrec {X#6=T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#8)
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#12[(app (\ X#6.S#9) T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
     )
    ,
     (letrec
        E#7
     in
        A#12[(letrec {X#6=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#9)]
     )
  )

where

   Delta1 = {T#13,A#10,T#11,T#4,A#12}
   Delta2 = {E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(\ X#6.[.])),
             (T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {X#6=[.]} in S#9)),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#7} in A#12[(app (\ X#6.S#9) T#14)]),
           A#10  |->  A#12,
           T#11  |->  A#12[(app (\ X#6.S#9) T#14)],
           T#13  |->  (app (\ X#6.S#9) T#14),
           S#8   |->  T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {E#7} in A#12[(app (\ X#6.S#9) T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -cpx-in1->                    (letrec {E#7} in A#12[(app (\ X#6.S#9) T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])])
    ................................................................................
                                  (letrec {E#7} in A#12[(app (\ X#6.S#9) T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -SR,lbeta2->                  (letrec {E#7} in A#12[(letrec {X#6=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#12[(app A#13[(app (\ X#6.S#9) S#8)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
     )
    ,
     (letrec
        E#7
     in
        A#12[(app A#13[(letrec {X#6=S#8} in S#9)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
     )
  )

where

   Delta1 = {A#10,T#11,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#7} in A#12[(app A#13[(app (\ X#6.S#9) S#8)] T#14)]),
           T#11  |->  A#12[(app A#13[(app (\ X#6.S#9) S#8)] T#14)],
           A#10  |->  A#12[(app A#13 T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {E#7} in A#12[(app A#13[(app (\ X#6.S#9) S#8)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -cpx-in1->                    (letrec {E#7} in A#12[(app A#13[(app (\ X#6.S#9) S#8)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])])
    ................................................................................
                                  (letrec {E#7} in A#12[(app A#13[(app (\ X#6.S#9) S#8)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -SR,lbeta2->                  (letrec {E#7} in A#12[(app A#13[(letrec {X#6=S#8} in S#9)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (app (\ X#6.S#9) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])
     )
    ,
     (letrec
        E#7
     in
        (letrec {X#6=T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#9)
     )
  )

where

   Delta1 = {T#11,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(\ X#6.[.])),
             (T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {X#6=[.]} in S#9)),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#7} in (app (\ X#6.S#9) T#12)),
           A#10  |->  [.],
           T#11  |->  (app (\ X#6.S#9) T#12),
           S#8   |->  T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {E#7} in (app (\ X#6.S#9) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]))
    -cpx-in1->                    (letrec {E#7} in (app (\ X#6.S#9) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]))
    ................................................................................
                                  (letrec {E#7} in (app (\ X#6.S#9) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]))
    -SR,lbeta2->                  (letrec {E#7} in (letrec {X#6=T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#9))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#12= T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
       ;E#14
     in
        A#10[(app (\ X#6.S#9) S#8)]
     )
    ,
     (letrec
        X#12= T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;E#14
     in
        A#10[(letrec {X#6=S#8} in S#9)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#12=T#11;E#14} in A#10[(app (\ X#6.S#9) S#8)]),
           E#7   |->  {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14},
           E#13  |->  {E#14}}

and instantiated rules:

                                  (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14} in A#10[(app (\ X#6.S#9) S#8)])
    -cpx-in1->                    (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#14} in A#10[(app (\ X#6.S#9) S#8)])
    ................................................................................
                                  (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14} in A#10[(letrec {X#6=S#8} in S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#2);E#11} in A#12[(app (\ X#6.C#15[(var X#1)]) S#8)])
    ,
     (letrec {X#1=(var X#2);E#11} in A#12[(letrec {X#6=S#8} in C#15[(var X#2)])])
  )

where

   Delta1 = {C#14,C#13,A#10,C#5,A#12}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#12[(app (\ X#6.C#15) S#8)]),
             ((var X#2),A#12[(app (\ X#6.C#15) S#8)]),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in C#15[(var X#2)])),
             ((var X#1),A#12[(app (\ X#6.C#15[[.]]) S#8)])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#7   |->  {X#1=(var X#2);E#11},
           E#3   |->  {E#11},
           A#10  |->  A#12,
           C#5   |->  A#12[(app (\ X#6.C#15) S#8)],
           C#13  |->  (app (\ X#6.C#15) S#8),
           C#14  |->  (\ X#6.C#15),
           S#9   |->  C#15[(var X#2)]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#11} in A#12[(app (\ X#6.C#15[(var X#2)]) S#8)])
    -cpx-in1->                    (letrec {X#1=(var X#2);E#11} in A#12[(app (\ X#6.C#15[(var X#1)]) S#8)])
    ................................................................................
                                  (letrec {X#1=(var X#2);E#11} in A#12[(app (\ X#6.C#15[(var X#2)]) S#8)])
    -SR,lbeta2->                  (letrec {X#1=(var X#2);E#11} in A#12[(letrec {X#6=S#8} in C#15[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#2);E#11} in A#12[(app (\ X#6.S#9) C#14[(var X#1)])])
    ,
     (letrec {X#1=(var X#2);E#11} in A#12[(letrec {X#6=C#14[(var X#2)]} in S#9)])
  )

where

   Delta1 = {C#13,A#10,C#5,A#12}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#12[(app (\ X#6.S#9) C#14)]),
             ((var X#2),A#12[(app (\ X#6.S#9) C#14)]),
             (C#14[(var X#2)],(\ X#6.[.])),
             (C#14[(var X#2)],(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#12[(app (\ X#6.S#9) C#14[[.]])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#7   |->  {X#1=(var X#2);E#11},
           E#3   |->  {E#11},
           A#10  |->  A#12,
           C#5   |->  A#12[(app (\ X#6.S#9) C#14)],
           C#13  |->  (app (\ X#6.S#9) C#14),
           S#8   |->  C#14[(var X#2)]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#11} in A#12[(app (\ X#6.S#9) C#14[(var X#2)])])
    -cpx-in1->                    (letrec {X#1=(var X#2);E#11} in A#12[(app (\ X#6.S#9) C#14[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(var X#2);E#11} in A#12[(app (\ X#6.S#9) C#14[(var X#2)])])
    -SR,lbeta2->                  (letrec {X#1=(var X#2);E#11} in A#12[(letrec {X#6=C#14[(var X#2)]} in S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;E#11
     in
        A#12[(app A#13[(app (\ X#6.S#9) S#8)] C#14[(var X#1)])]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;E#11
     in
        A#12[(app A#13[(letrec {X#6=S#8} in S#9)] C#14[(var X#2)])]
     )
  )

where

   Delta1 = {A#10,C#5}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#12[(app A#13[(app (\ X#6.S#9) S#8)] C#14)]),
             ((var X#2),A#12[(app A#13[(app (\ X#6.S#9) S#8)] C#14)]),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#12[(app A#13[(app (\ X#6.S#9) S#8)] C#14[[.]])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#7   |->  {X#1=(var X#2);E#11},
           E#3   |->  {E#11},
           C#5   |->  A#12[(app A#13[(app (\ X#6.S#9) S#8)] C#14)],
           A#10  |->  A#12[(app A#13 C#14[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#11} in A#12[(app A#13[(app (\ X#6.S#9) S#8)] C#14[(var X#2)])])
    -cpx-in1->                    (letrec {X#1=(var X#2);E#11} in A#12[(app A#13[(app (\ X#6.S#9) S#8)] C#14[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(var X#2);E#11} in A#12[(app A#13[(app (\ X#6.S#9) S#8)] C#14[(var X#2)])])
    -SR,lbeta2->                  (letrec {X#1=(var X#2);E#11} in A#12[(app A#13[(letrec {X#6=S#8} in S#9)] C#14[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#2);E#11} in (app (\ X#6.C#13[(var X#1)]) S#8))
    ,
     (letrec {X#1=(var X#2);E#11} in (letrec {X#6=S#8} in C#13[(var X#2)]))
  )

where

   Delta1 = {C#12,C#5}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (\ X#6.C#13) S#8)),
             ((var X#2),(app (\ X#6.C#13) S#8)),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in C#13[(var X#2)])),
             ((var X#1),(app (\ X#6.C#13[[.]]) S#8))}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#7   |->  {X#1=(var X#2);E#11},
           E#3   |->  {E#11},
           A#10  |->  [.],
           C#5   |->  (app (\ X#6.C#13) S#8),
           C#12  |->  (\ X#6.C#13),
           S#9   |->  C#13[(var X#2)]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#11} in (app (\ X#6.C#13[(var X#2)]) S#8))
    -cpx-in1->                    (letrec {X#1=(var X#2);E#11} in (app (\ X#6.C#13[(var X#1)]) S#8))
    ................................................................................
                                  (letrec {X#1=(var X#2);E#11} in (app (\ X#6.C#13[(var X#2)]) S#8))
    -SR,lbeta2->                  (letrec {X#1=(var X#2);E#11} in (letrec {X#6=S#8} in C#13[(var X#2)]))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#2);E#11} in (app (\ X#6.S#9) C#12[(var X#1)]))
    ,
     (letrec {X#1=(var X#2);E#11} in (letrec {X#6=C#12[(var X#2)]} in S#9))
  )

where

   Delta1 = {C#5}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (\ X#6.S#9) C#12)),
             ((var X#2),(app (\ X#6.S#9) C#12)),
             (C#12[(var X#2)],(\ X#6.[.])),
             (C#12[(var X#2)],(letrec {X#6=[.]} in S#9)),
             ((var X#1),(app (\ X#6.S#9) C#12[[.]]))}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#7   |->  {X#1=(var X#2);E#11},
           E#3   |->  {E#11},
           A#10  |->  [.],
           C#5   |->  (app (\ X#6.S#9) C#12),
           S#8   |->  C#12[(var X#2)]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#11} in (app (\ X#6.S#9) C#12[(var X#2)]))
    -cpx-in1->                    (letrec {X#1=(var X#2);E#11} in (app (\ X#6.S#9) C#12[(var X#1)]))
    ................................................................................
                                  (letrec {X#1=(var X#2);E#11} in (app (\ X#6.S#9) C#12[(var X#2)]))
    -SR,lbeta2->                  (letrec {X#1=(var X#2);E#11} in (letrec {X#6=C#12[(var X#2)]} in S#9))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
       ;EE#12[X#6,(app (\ X#7.S#10) S#9)]
     in
        A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
     )
    ,
     (letrec
        E#8
       ;EE#12[X#6,(letrec {X#7=S#9} in S#10)]
     in
        A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
     )
  )

where

   Delta1 = {A#11,T#13,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#14[(app A#15[[.]] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]),
             ((var X#6),A#14[(app A#15[[.]] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#6)] T#16)],
           A#11  |->  A#14[(app A#15 T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -cpx-in1->                    (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])])
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
       ;E#16
       ;EE#12[X#6,(app (\ X#7.S#10) S#9)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;E#16
       ;EE#12[X#6,(letrec {X#7=S#9} in S#10)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#14=T#13;E#16;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)]),
           E#8   |->  {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16},
           E#15  |->  {E#16;EE#12[X#6,(app (\ X#7.S#10) S#9)]}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#16;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#17[(app (\ X#7.S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#8
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#17[(letrec {X#7=T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#10)]
       ;E#8
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#18,A#16,T#13,T#4,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(\ X#7.[.])),
             (T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {X#7=[.]} in S#10)),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#17[(app (\ X#7.S#10) T#19)];E#8} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#6,
           E#15         |->  {E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[(app (\ X#7.S#10) T#19)],
           T#18         |->  (app (\ X#7.S#10) T#19),
           S#9          |->  T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#6=A#17[(app (\ X#7.S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#6=A#17[(app (\ X#7.S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#8} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#17[(app (\ X#7.S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#6=A#17[(letrec {X#7=T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#10)];E#8} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#17[(app A#18[(app (\ X#7.S#10) S#9)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#8
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#17[(app A#18[(letrec {X#7=S#9} in S#10)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#8
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#17[(app A#18[(app (\ X#7.S#10) S#9)] T#19)];E#8} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]},
           X#14         |->  X#6,
           E#15         |->  {E#8},
           T#13         |->  A#17[(app A#18[(app (\ X#7.S#10) S#9)] T#19)],
           A#16         |->  A#17[(app A#18 T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=A#17[(app A#18[(app (\ X#7.S#10) S#9)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#6=A#17[(app A#18[(app (\ X#7.S#10) S#9)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#8} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#17[(app A#18[(app (\ X#7.S#10) S#9)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#6=A#17[(app A#18[(letrec {X#7=S#9} in S#10)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (app (\ X#7.S#10) T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])
       ;E#8
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= (letrec {X#7=T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#10)
       ;E#8
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(\ X#7.[.])),
             (T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {X#7=[.]} in S#10)),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(app (\ X#7.S#10) T#17);E#8} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#6,
           E#15         |->  {E#8},
           A#16         |->  [.],
           T#13         |->  (app (\ X#7.S#10) T#17),
           S#9          |->  T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#6=(app (\ X#7.S#10) T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]);E#8} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#6=(app (\ X#7.S#10) T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]);E#8} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(app (\ X#7.S#10) T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]);E#8} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#6=(letrec {X#7=T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#10);E#8} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#8
       ;EE#18[X#17,(app (\ X#7.S#10) S#9)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#8
       ;EE#18[X#17,(letrec {X#7=S#9} in S#10)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#19[(app A#20[(var X#17)] T#21)];E#8;EE#18[X#17,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];EE#18[X#17,[.2]]},
           X#14         |->  X#6,
           E#15         |->  {E#8;EE#18[X#17,(app (\ X#7.S#10) S#9)]},
           T#13         |->  A#19[(app A#20[(var X#17)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;EE#18[X#17,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#8;EE#18[X#17,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;EE#18[X#17,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;EE#18[X#17,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#8
       ;EE#19[X#6,(var X#17)]
       ;EE#20[X#18,(app (\ X#7.S#10) S#9)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#8
       ;EE#19[X#6,(var X#17)]
       ;EE#20[X#18,(letrec {X#7=S#9} in S#10)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23)];E#8;EE#19[X#6,(var X#17)];EE#20[X#18,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {E#8;EE#19[X#6,(var X#17)];EE#20[X#18,(app (\ X#7.S#10) S#9)]},
           T#13         |->  A#21[(app A#22[(var X#18)] T#23)],
           A#16         |->  A#21[(app A#22 T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;EE#19[X#6,(var X#17)];EE#20[X#18,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#8;EE#19[X#6,(var X#17)];EE#20[X#18,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;EE#19[X#6,(var X#17)];EE#20[X#18,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;EE#19[X#6,(var X#17)];EE#20[X#18,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app (\ X#7.S#10) T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#8
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#19[(letrec {X#7=T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#10)]
       ;E#8
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#20,A#16,T#13,T#4,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(\ X#7.[.])),
             (T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {X#7=[.]} in S#10)),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app (\ X#7.S#10) T#21)];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#8;EE#18[X#6,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[(app (\ X#7.S#10) T#21)],
           T#20         |->  (app (\ X#7.S#10) T#21),
           S#9          |->  T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app (\ X#7.S#10) T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#17=A#19[(app (\ X#7.S#10) T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#19[(app (\ X#7.S#10) T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#17=A#19[(letrec {X#7=T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#10)];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[(app (\ X#7.S#10) S#9)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#8
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(letrec {X#7=S#9} in S#10)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#8
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app A#20[(app (\ X#7.S#10) S#9)] T#21)];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#8;EE#18[X#6,(var X#17)]},
           T#13         |->  A#19[(app A#20[(app (\ X#7.S#10) S#9)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(app (\ X#7.S#10) S#9)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#17=A#19[(app A#20[(app (\ X#7.S#10) S#9)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(app (\ X#7.S#10) S#9)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#17=A#19[(app A#20[(letrec {X#7=S#9} in S#10)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (app (\ X#7.S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])
       ;E#8
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= (letrec {X#7=T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#10)
       ;E#8
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(\ X#7.[.])),
             (T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {X#7=[.]} in S#10)),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=(app (\ X#7.S#10) T#19);E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#8;EE#18[X#6,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  (app (\ X#7.S#10) T#19),
           S#9          |->  T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#17=(app (\ X#7.S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]);E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#17=(app (\ X#7.S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]);E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=(app (\ X#7.S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]);E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#17=(letrec {X#7=T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]} in S#10);E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#6)
       ;E#13
       ;EE#12[X#6,(app (\ X#7.S#10) S#9)]
     in
        A#14[(var X#1)]
     )
    ,
     (letrec
        X#1= (var X#6)
       ;E#13
       ;EE#12[X#6,(letrec {X#7=S#9} in S#10)]
     in
        A#14[(var X#6)]
     )
  )

where

   Delta1 = {A#11,C#5,A#14}
   Delta2 = {}
   Delta3 = {((var X#1),A#14[[.]]),
             ((var X#6),A#14[[.]]),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),A#14[[.]]),
             ((var X#6),A#14[[.]]),
             ((var X#6),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#8   |->  {X#1=(var X#6);E#13},
           E#3   |->  {E#13;EE#12[X#6,(app (\ X#7.S#10) S#9)]},
           A#11  |->  A#14,
           C#5   |->  A#14[[.]],
           C#15  |->  [.],
           X#2   |->  X#6}

and instantiated rules:

                                  (letrec {X#1=(var X#6);E#13;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#14[(var X#6)])
    -cpx-in1->                    (letrec {X#1=(var X#6);E#13;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#14[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#6);E#13;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#14[(var X#6)])
    -SR,lbeta3->                  (letrec {X#1=(var X#6);E#13;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#14[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;E#13
       ;EE#12[X#2,(app (\ X#7.S#10) S#9)]
     in
        A#14[(var X#1)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;E#13
       ;EE#12[X#2,(letrec {X#7=S#9} in S#10)]
     in
        A#14[(var X#2)]
     )
  )

where

   Delta1 = {A#11,C#5,A#14}
   Delta2 = {}
   Delta3 = {((var X#1),A#14),
             ((var X#2),A#14),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),A#14[[.]]),
             ((var X#2),A#14[[.]]),
             ((var X#2),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#8   |->  {X#1=(var X#2);E#13},
           E#3   |->  {E#13;EE#12[X#2,(app (\ X#7.S#10) S#9)]},
           A#11  |->  A#14[[.]],
           C#5   |->  A#14,
           A#15  |->  [.],
           X#6   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#13;EE#12[X#2,(app (\ X#7.S#10) S#9)]} in A#14[(var X#2)])
    -cpx-in1->                    (letrec {X#1=(var X#2);E#13;EE#12[X#2,(app (\ X#7.S#10) S#9)]} in A#14[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#2);E#13;EE#12[X#2,(app (\ X#7.S#10) S#9)]} in A#14[(var X#2)])
    -SR,lbeta3->                  (letrec {X#1=(var X#2);E#13;EE#12[X#2,(letrec {X#7=S#9} in S#10)]} in A#14[(var X#2)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;E#13
       ;EE#12[X#6,(app (\ X#7.S#10) S#9)]
     in
        A#14[(app A#15[(var X#6)] C#16[(var X#1)])]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;E#13
       ;EE#12[X#6,(letrec {X#7=S#9} in S#10)]
     in
        A#14[(app A#15[(var X#6)] C#16[(var X#2)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {}
   Delta3 = {((var X#1),A#14[(app A#15[(var X#6)] C#16)]),
             ((var X#2),A#14[(app A#15[(var X#6)] C#16)]),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),A#14[(app A#15[(var X#6)] C#16[[.]])]),
             ((var X#6),A#14[(app A#15[[.]] C#16[(var X#2)])]),
             ((var X#6),A#14[(app A#15[[.]] C#16[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#8   |->  {X#1=(var X#2);E#13},
           E#3   |->  {E#13;EE#12[X#6,(app (\ X#7.S#10) S#9)]},
           C#5   |->  A#14[(app A#15[(var X#6)] C#16)],
           A#11  |->  A#14[(app A#15 C#16[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#13;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#14[(app A#15[(var X#6)] C#16[(var X#2)])])
    -cpx-in1->                    (letrec {X#1=(var X#2);E#13;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#14[(app A#15[(var X#6)] C#16[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(var X#2);E#13;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#14[(app A#15[(var X#6)] C#16[(var X#2)])])
    -SR,lbeta3->                  (letrec {X#1=(var X#2);E#13;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#14[(app A#15[(var X#6)] C#16[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#2);E#13;EE#12[X#2,(app (\ X#7.S#10) S#9)]} in (var X#1))
    ,
     (letrec {X#1=(var X#2);E#13;EE#12[X#2,(letrec {X#7=S#9} in S#10)]} in (var X#2))
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#8   |->  {X#1=(var X#2);E#13},
           E#3   |->  {E#13;EE#12[X#2,(app (\ X#7.S#10) S#9)]},
           C#5   |->  [.],
           A#11  |->  [.],
           X#6   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#13;EE#12[X#2,(app (\ X#7.S#10) S#9)]} in (var X#2))
    -cpx-in1->                    (letrec {X#1=(var X#2);E#13;EE#12[X#2,(app (\ X#7.S#10) S#9)]} in (var X#1))
    ................................................................................
                                  (letrec {X#1=(var X#2);E#13;EE#12[X#2,(app (\ X#7.S#10) S#9)]} in (var X#2))
    -SR,lbeta3->                  (letrec {X#1=(var X#2);E#13;EE#12[X#2,(letrec {X#7=S#9} in S#10)]} in (var X#2))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (var X#2)
       ;E#8
       ;EE#15[X#2,(app (\ X#7.S#10) S#9)]
     in
        A#16[(app A#17[(var X#6)] C#18[(var X#6)])]
     )
    ,
     (letrec
        X#6= (var X#2)
       ;E#8
       ;EE#15[X#2,(letrec {X#7=S#9} in S#10)]
     in
        A#16[(app A#17[(var X#6)] C#18[(var X#2)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {}
   Delta3 = {((var X#6),A#16[(app A#17[(var X#6)] C#18)]),
             ((var X#2),A#16[(app A#17[(var X#6)] C#18)]),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#6),A#16[(app A#17[(var X#6)] C#18[[.]])]),
             ((var X#6),A#16[(app A#17[[.]] C#18[(var X#2)])]),
             ((var X#6),A#16[(app A#17[[.]] C#18[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           EE#12[.1,.2] |-> {[.1]=(var X#2);EE#15[X#2,[.2]]},
           X#1          |->  X#6,
           E#3          |->  {E#8;EE#15[X#2,(app (\ X#7.S#10) S#9)]},
           A#13         |->  [.],
           X#14         |->  X#2,
           C#5          |->  A#16[(app A#17[(var X#6)] C#18)],
           A#11         |->  A#16[(app A#17 C#18[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#6=(var X#2);E#8;EE#15[X#2,(app (\ X#7.S#10) S#9)]} in A#16[(app A#17[(var X#6)] C#18[(var X#2)])])
    -cpx-in1->                    (letrec {X#6=(var X#2);E#8;EE#15[X#2,(app (\ X#7.S#10) S#9)]} in A#16[(app A#17[(var X#6)] C#18[(var X#6)])])
    ................................................................................
                                  (letrec {X#6=(var X#2);E#8;EE#15[X#2,(app (\ X#7.S#10) S#9)]} in A#16[(app A#17[(var X#6)] C#18[(var X#2)])])
    -SR,lbeta3->                  (letrec {X#6=(var X#2);E#8;EE#15[X#2,(letrec {X#7=S#9} in S#10)]} in A#16[(app A#17[(var X#6)] C#18[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= (var X#2)
       ;E#8
       ;EE#16[X#6,(var X#14)]
       ;EE#17[X#2,(app (\ X#7.S#10) S#9)]
     in
        A#18[(app A#19[(var X#6)] C#20[(var X#14)])]
     )
    ,
     (letrec
        X#14= (var X#2)
       ;E#8
       ;EE#16[X#6,(var X#14)]
       ;EE#17[X#2,(letrec {X#7=S#9} in S#10)]
     in
        A#18[(app A#19[(var X#6)] C#20[(var X#2)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {}
   Delta3 = {((var X#14),A#18[(app A#19[(var X#6)] C#20)]),
             ((var X#2),A#18[(app A#19[(var X#6)] C#20)]),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#14),A#18[(app A#19[(var X#6)] C#20[[.]])]),
             ((var X#6),A#18[(app A#19[[.]] C#20[(var X#2)])]),
             ((var X#6),A#18[(app A#19[[.]] C#20[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           EE#12[.1,.2] |-> {X#14=(var X#2);EE#16[[.1],(var X#14)];EE#17[X#2,[.2]]},
           X#1          |->  X#14,
           E#3          |->  {E#8;EE#16[X#6,(var X#14)];EE#17[X#2,(app (\ X#7.S#10) S#9)]},
           A#13         |->  [.],
           X#15         |->  X#2,
           C#5          |->  A#18[(app A#19[(var X#6)] C#20)],
           A#11         |->  A#18[(app A#19 C#20[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#14=(var X#2);E#8;EE#16[X#6,(var X#14)];EE#17[X#2,(app (\ X#7.S#10) S#9)]} in A#18[(app A#19[(var X#6)] C#20[(var X#2)])])
    -cpx-in1->                    (letrec {X#14=(var X#2);E#8;EE#16[X#6,(var X#14)];EE#17[X#2,(app (\ X#7.S#10) S#9)]} in A#18[(app A#19[(var X#6)] C#20[(var X#14)])])
    ................................................................................
                                  (letrec {X#14=(var X#2);E#8;EE#16[X#6,(var X#14)];EE#17[X#2,(app (\ X#7.S#10) S#9)]} in A#18[(app A#19[(var X#6)] C#20[(var X#2)])])
    -SR,lbeta3->                  (letrec {X#14=(var X#2);E#8;EE#16[X#6,(var X#14)];EE#17[X#2,(letrec {X#7=S#9} in S#10)]} in A#18[(app A#19[(var X#6)] C#20[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#9)
       ;E#8
     in
        A#12[(app A#13[(var X#6)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#9)
       ;E#8
     in
        A#12[(app A#13[(\ X#7.S#9)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
     )
  )

where

   Delta1 = {A#10,T#11,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#12[(app A#13[[.]] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(\ X#7.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(\ X#7.S#9);E#8} in A#12[(app A#13[(var X#6)] T#14)]),
           T#11  |->  A#12[(app A#13[(var X#6)] T#14)],
           A#10  |->  A#12[(app A#13 T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#12[(app A#13[(var X#6)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#9);E#8} in A#12[(app A#13[(var X#6)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#12[(app A#13[(var X#6)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#12[(app A#13[(\ X#7.S#9)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#12= T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
       ;X#6= (\ X#7.S#9)
       ;E#14
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#12= T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;X#6= (\ X#7.S#9)
       ;E#14
     in
        A#10[(\ X#7.S#9)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(\ X#7.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#12=T#11;X#6=(\ X#7.S#9);E#14} in A#10[(var X#6)]),
           E#8   |->  {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14},
           E#13  |->  {X#6=(\ X#7.S#9);E#14}}

and instantiated rules:

                                  (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(\ X#7.S#9);E#14} in A#10[(var X#6)])
    -cpx-in1->                    (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];X#6=(\ X#7.S#9);E#14} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(\ X#7.S#9);E#14} in A#10[(var X#6)])
    -SR,cp-in1->                  (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(\ X#7.S#9);E#14} in A#10[(\ X#7.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#6);X#6=(\ X#7.S#9);E#11} in A#12[(var X#1)])
    ,
     (letrec {X#1=(var X#6);X#6=(\ X#7.S#9);E#11} in A#12[(\ X#7.S#9)])
  )

where

   Delta1 = {A#10,C#5,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),A#12[[.]]),
             ((var X#6),A#12[[.]]),
             ((var X#1),A#12[[.]]),
             ((var X#6),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(\ X#7.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#8   |->  {X#1=(var X#6);E#11},
           E#3   |->  {X#6=(\ X#7.S#9);E#11},
           A#10  |->  A#12,
           C#5   |->  A#12[[.]],
           C#13  |->  [.],
           X#2   |->  X#6}

and instantiated rules:

                                  (letrec {X#1=(var X#6);X#6=(\ X#7.S#9);E#11} in A#12[(var X#6)])
    -cpx-in1->                    (letrec {X#1=(var X#6);X#6=(\ X#7.S#9);E#11} in A#12[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#6);X#6=(\ X#7.S#9);E#11} in A#12[(var X#6)])
    -SR,cp-in1->                  (letrec {X#1=(var X#6);X#6=(\ X#7.S#9);E#11} in A#12[(\ X#7.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#2);X#2=(\ X#7.S#9);E#11} in A#12[(var X#1)])
    ,
     (letrec {X#1=(var X#2);X#2=(\ X#7.S#9);E#11} in A#12[(\ X#7.S#9)])
  )

where

   Delta1 = {A#10,C#5,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),A#12),
             ((var X#2),A#12),
             ((var X#1),A#12[[.]]),
             ((var X#2),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(\ X#7.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#8   |->  {X#1=(var X#2);E#11},
           E#3   |->  {X#2=(\ X#7.S#9);E#11},
           A#10  |->  A#12[[.]],
           C#5   |->  A#12,
           A#13  |->  [.],
           X#6   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#2=(\ X#7.S#9);E#11} in A#12[(var X#2)])
    -cpx-in1->                    (letrec {X#1=(var X#2);X#2=(\ X#7.S#9);E#11} in A#12[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#2=(\ X#7.S#9);E#11} in A#12[(var X#2)])
    -SR,cp-in1->                  (letrec {X#1=(var X#2);X#2=(\ X#7.S#9);E#11} in A#12[(\ X#7.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#9)
       ;E#11
     in
        A#12[(app A#13[(var X#6)] C#14[(var X#1)])]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#9)
       ;E#11
     in
        A#12[(app A#13[(\ X#7.S#9)] C#14[(var X#2)])]
     )
  )

where

   Delta1 = {A#10,C#5}
   Delta2 = {}
   Delta3 = {((var X#1),A#12[(app A#13[(var X#6)] C#14)]),
             ((var X#2),A#12[(app A#13[(var X#6)] C#14)]),
             ((var X#1),A#12[(app A#13[(var X#6)] C#14[[.]])]),
             ((var X#6),A#12[(app A#13[[.]] C#14[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(\ X#7.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#8   |->  {X#1=(var X#2);E#11},
           E#3   |->  {X#6=(\ X#7.S#9);E#11},
           C#5   |->  A#12[(app A#13[(var X#6)] C#14)],
           A#10  |->  A#12[(app A#13 C#14[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#9);E#11} in A#12[(app A#13[(var X#6)] C#14[(var X#2)])])
    -cpx-in1->                    (letrec {X#1=(var X#2);X#6=(\ X#7.S#9);E#11} in A#12[(app A#13[(var X#6)] C#14[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#9);E#11} in A#12[(app A#13[(var X#6)] C#14[(var X#2)])])
    -SR,cp-in1->                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#9);E#11} in A#12[(app A#13[(\ X#7.S#9)] C#14[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#2);X#2=(\ X#7.S#9);E#11} in (var X#1))
    ,
     (letrec {X#1=(var X#2);X#2=(\ X#7.S#9);E#11} in (\ X#7.S#9))
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(\ X#7.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#8   |->  {X#1=(var X#2);E#11},
           E#3   |->  {X#2=(\ X#7.S#9);E#11},
           C#5   |->  [.],
           A#10  |->  [.],
           X#6   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#2=(\ X#7.S#9);E#11} in (var X#2))
    -cpx-in1->                    (letrec {X#1=(var X#2);X#2=(\ X#7.S#9);E#11} in (var X#1))
    ................................................................................
                                  (letrec {X#1=(var X#2);X#2=(\ X#7.S#9);E#11} in (var X#2))
    -SR,cp-in1->                  (letrec {X#1=(var X#2);X#2=(\ X#7.S#9);E#11} in (\ X#7.S#9))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#10)
       ;E#9
       ;VV#12|X#8,(var X#6)|
     in
        A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;E#9
       ;VV#12|X#8,(var X#6)|
     in
        A#14[(app A#15[(\ X#7.S#10)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
     )
  )

where

   Delta1 = {A#11,T#13,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#14[(app A#15[[.]] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#14[(app A#15[(var X#8)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#8)] T#16)],
           A#11  |->  A#14[(app A#15 T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#14[(app A#15[(\ X#7.S#10)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
       ;X#6= (\ X#7.S#10)
       ;E#16
       ;VV#12|X#8,(var X#6)|
     in
        A#11[(var X#8)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;X#6= (\ X#7.S#10)
       ;E#16
       ;VV#12|X#8,(var X#6)|
     in
        A#11[(\ X#7.S#10)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#11[[.]]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4   |->  (letrec {X#14=T#13;X#6=(\ X#7.S#10);E#16;VV#12|X#8,(var X#6)|} in A#11[(var X#8)]),
           E#9   |->  {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16},
           E#15  |->  {X#6=(\ X#7.S#10);E#16;VV#12|X#8,(var X#6)|}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(\ X#7.S#10);E#16;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -cpx-in1->                    (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];X#6=(\ X#7.S#10);E#16;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(\ X#7.S#10);E#16;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(\ X#7.S#10);E#16;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#8)
       ;X#6= (\ X#7.S#10)
       ;E#13
       ;VV#12|X#8,(var X#6)|
     in
        A#14[(var X#1)]
     )
    ,
     (letrec
        X#1= (var X#8)
       ;X#6= (\ X#7.S#10)
       ;E#13
       ;VV#12|X#8,(var X#6)|
     in
        A#14[(\ X#7.S#10)]
     )
  )

where

   Delta1 = {A#11,C#5,A#14}
   Delta2 = {}
   Delta3 = {((var X#1),A#14[[.]]),
             ((var X#8),A#14[[.]]),
             ((var X#1),A#14[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#14[[.]]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4   |->  [.],
           E#9   |->  {X#1=(var X#8);E#13},
           E#3   |->  {X#6=(\ X#7.S#10);E#13;VV#12|X#8,(var X#6)|},
           A#11  |->  A#14,
           C#5   |->  A#14[[.]],
           C#15  |->  [.],
           X#2   |->  X#8}

and instantiated rules:

                                  (letrec {X#1=(var X#8);X#6=(\ X#7.S#10);E#13;VV#12|X#8,(var X#6)|} in A#14[(var X#8)])
    -cpx-in1->                    (letrec {X#1=(var X#8);X#6=(\ X#7.S#10);E#13;VV#12|X#8,(var X#6)|} in A#14[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#8);X#6=(\ X#7.S#10);E#13;VV#12|X#8,(var X#6)|} in A#14[(var X#8)])
    -SR,cp-in2->                  (letrec {X#1=(var X#8);X#6=(\ X#7.S#10);E#13;VV#12|X#8,(var X#6)|} in A#14[(\ X#7.S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#10)
       ;E#13
       ;VV#12|X#2,(var X#6)|
     in
        A#14[(var X#1)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#10)
       ;E#13
       ;VV#12|X#2,(var X#6)|
     in
        A#14[(\ X#7.S#10)]
     )
  )

where

   Delta1 = {A#11,C#5,A#14}
   Delta2 = {}
   Delta3 = {((var X#1),A#14),
             ((var X#2),A#14),
             ((var X#1),A#14[[.]]),
             ((var X#6),[.]),
             ((var X#2),A#14[[.]]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4   |->  [.],
           E#9   |->  {X#1=(var X#2);E#13},
           E#3   |->  {X#6=(\ X#7.S#10);E#13;VV#12|X#2,(var X#6)|},
           A#11  |->  A#14[[.]],
           C#5   |->  A#14,
           A#15  |->  [.],
           X#8   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#13;VV#12|X#2,(var X#6)|} in A#14[(var X#2)])
    -cpx-in1->                    (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#13;VV#12|X#2,(var X#6)|} in A#14[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#13;VV#12|X#2,(var X#6)|} in A#14[(var X#2)])
    -SR,cp-in2->                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#13;VV#12|X#2,(var X#6)|} in A#14[(\ X#7.S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#10)
       ;E#13
       ;VV#12|X#8,(var X#6)|
     in
        A#14[(app A#15[(var X#8)] C#16[(var X#1)])]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#10)
       ;E#13
       ;VV#12|X#8,(var X#6)|
     in
        A#14[(app A#15[(\ X#7.S#10)] C#16[(var X#2)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {}
   Delta3 = {((var X#1),A#14[(app A#15[(var X#8)] C#16)]),
             ((var X#2),A#14[(app A#15[(var X#8)] C#16)]),
             ((var X#1),A#14[(app A#15[(var X#8)] C#16[[.]])]),
             ((var X#6),[.]),
             ((var X#8),A#14[(app A#15[[.]] C#16[(var X#2)])]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4   |->  [.],
           E#9   |->  {X#1=(var X#2);E#13},
           E#3   |->  {X#6=(\ X#7.S#10);E#13;VV#12|X#8,(var X#6)|},
           C#5   |->  A#14[(app A#15[(var X#8)] C#16)],
           A#11  |->  A#14[(app A#15 C#16[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#13;VV#12|X#8,(var X#6)|} in A#14[(app A#15[(var X#8)] C#16[(var X#2)])])
    -cpx-in1->                    (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#13;VV#12|X#8,(var X#6)|} in A#14[(app A#15[(var X#8)] C#16[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#13;VV#12|X#8,(var X#6)|} in A#14[(app A#15[(var X#8)] C#16[(var X#2)])])
    -SR,cp-in2->                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#13;VV#12|X#8,(var X#6)|} in A#14[(app A#15[(\ X#7.S#10)] C#16[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#13;VV#12|X#2,(var X#6)|} in (var X#1))
    ,
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#10)
       ;E#13
       ;VV#12|X#2,(var X#6)|
     in
        (\ X#7.S#10)
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#1),[.]),
             ((var X#6),[.]),
             ((var X#2),[.]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4   |->  [.],
           E#9   |->  {X#1=(var X#2);E#13},
           E#3   |->  {X#6=(\ X#7.S#10);E#13;VV#12|X#2,(var X#6)|},
           C#5   |->  [.],
           A#11  |->  [.],
           X#8   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#13;VV#12|X#2,(var X#6)|} in (var X#2))
    -cpx-in1->                    (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#13;VV#12|X#2,(var X#6)|} in (var X#1))
    ................................................................................
                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#13;VV#12|X#2,(var X#6)|} in (var X#2))
    -SR,cp-in2->                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#13;VV#12|X#2,(var X#6)|} in (\ X#7.S#10))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= (var X#6)
       ;E#9
     in
        A#14[(app A#15[(var X#8)] C#16[(var X#8)])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= (var X#6)
       ;E#9
     in
        A#14[(app A#15[(\ X#7.S#10)] C#16[(var X#6)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {}
   Delta3 = {((var X#8),A#14[(app A#15[(var X#8)] C#16)]),
             ((var X#6),A#14[(app A#15[(var X#8)] C#16)]),
             ((var X#8),A#14[(app A#15[(var X#8)] C#16[[.]])]),
             ((var X#6),[.]),
             ((var X#8),A#14[(app A#15[[.]] C#16[(var X#6)])]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4          |->  [.],
           VV#12|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#8,
           X#2          |->  X#6,
           E#3          |->  {X#6=(\ X#7.S#10);E#9},
           C#5          |->  A#14[(app A#15[(var X#8)] C#16)],
           A#11         |->  A#14[(app A#15 C#16[(var X#6)])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);X#8=(var X#6);E#9} in A#14[(app A#15[(var X#8)] C#16[(var X#6)])])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#10);X#8=(var X#6);E#9} in A#14[(app A#15[(var X#8)] C#16[(var X#8)])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);X#8=(var X#6);E#9} in A#14[(app A#15[(var X#8)] C#16[(var X#6)])])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);X#8=(var X#6);E#9} in A#14[(app A#15[(\ X#7.S#10)] C#16[(var X#6)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= (var X#14)
       ;E#9
       ;VV#15|X#14,(var X#6)|
     in
        A#16[(app A#17[(var X#8)] C#18[(var X#8)])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= (var X#14)
       ;E#9
       ;VV#15|X#14,(var X#6)|
     in
        A#16[(app A#17[(\ X#7.S#10)] C#18[(var X#14)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {}
   Delta3 = {((var X#8),A#16[(app A#17[(var X#8)] C#18)]),
             ((var X#14),A#16[(app A#17[(var X#8)] C#18)]),
             ((var X#8),A#16[(app A#17[(var X#8)] C#18[[.]])]),
             ((var X#6),[.]),
             ((var X#8),A#16[(app A#17[[.]] C#18[(var X#14)])]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4          |->  [.],
           VV#12|.1,.2| |-> {[.1]=(var X#14);VV#15|X#14,[.2]|},
           X#1          |->  X#8,
           X#2          |->  X#14,
           E#3          |->  {X#6=(\ X#7.S#10);E#9;VV#15|X#14,(var X#6)|},
           C#5          |->  A#16[(app A#17[(var X#8)] C#18)],
           A#11         |->  A#16[(app A#17 C#18[(var X#14)])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);X#8=(var X#14);E#9;VV#15|X#14,(var X#6)|} in A#16[(app A#17[(var X#8)] C#18[(var X#14)])])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#10);X#8=(var X#14);E#9;VV#15|X#14,(var X#6)|} in A#16[(app A#17[(var X#8)] C#18[(var X#8)])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);X#8=(var X#14);E#9;VV#15|X#14,(var X#6)|} in A#16[(app A#17[(var X#8)] C#18[(var X#14)])])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);X#8=(var X#14);E#9;VV#15|X#14,(var X#6)|} in A#16[(app A#17[(\ X#7.S#10)] C#18[(var X#14)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= (var X#15)
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;VV#16|X#8,(var X#14)|
       ;VV#17|X#15,(var X#6)|
     in
        A#18[(app A#19[(var X#8)] C#20[(var X#14)])]
     )
    ,
     (letrec
        X#14= (var X#15)
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;VV#16|X#8,(var X#14)|
       ;VV#17|X#15,(var X#6)|
     in
        A#18[(app A#19[(\ X#7.S#10)] C#20[(var X#15)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {}
   Delta3 = {((var X#14),A#18[(app A#19[(var X#8)] C#20)]),
             ((var X#15),A#18[(app A#19[(var X#8)] C#20)]),
             ((var X#14),A#18[(app A#19[(var X#8)] C#20[[.]])]),
             ((var X#6),[.]),
             ((var X#8),A#18[(app A#19[[.]] C#20[(var X#15)])]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4          |->  [.],
           VV#12|.1,.2| |-> {X#14=(var X#15);VV#16|[.1],(var X#14)|;VV#17|X#15,[.2]|},
           X#1          |->  X#14,
           X#2          |->  X#15,
           E#3          |->  {X#6=(\ X#7.S#10);E#9;VV#16|X#8,(var X#14)|;VV#17|X#15,(var X#6)|},
           C#5          |->  A#18[(app A#19[(var X#8)] C#20)],
           A#11         |->  A#18[(app A#19 C#20[(var X#15)])]}

and instantiated rules:

                                  (letrec {X#14=(var X#15);X#6=(\ X#7.S#10);E#9;VV#16|X#8,(var X#14)|;VV#17|X#15,(var X#6)|} in A#18[(app A#19[(var X#8)] C#20[(var X#15)])])
    -cpx-in1->                    (letrec {X#14=(var X#15);X#6=(\ X#7.S#10);E#9;VV#16|X#8,(var X#14)|;VV#17|X#15,(var X#6)|} in A#18[(app A#19[(var X#8)] C#20[(var X#14)])])
    ................................................................................
                                  (letrec {X#14=(var X#15);X#6=(\ X#7.S#10);E#9;VV#16|X#8,(var X#14)|;VV#17|X#15,(var X#6)|} in A#18[(app A#19[(var X#8)] C#20[(var X#15)])])
    -SR,cp-in2->                  (letrec {X#14=(var X#15);X#6=(\ X#7.S#10);E#9;VV#16|X#8,(var X#14)|;VV#17|X#15,(var X#6)|} in A#18[(app A#19[(\ X#7.S#10)] C#20[(var X#15)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= (var X#6)
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;VV#15|X#8,(var X#14)|
     in
        A#16[(app A#17[(var X#8)] C#18[(var X#14)])]
     )
    ,
     (letrec
        X#14= (var X#6)
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;VV#15|X#8,(var X#14)|
     in
        A#16[(app A#17[(\ X#7.S#10)] C#18[(var X#6)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {}
   Delta3 = {((var X#14),A#16[(app A#17[(var X#8)] C#18)]),
             ((var X#6),A#16[(app A#17[(var X#8)] C#18)]),
             ((var X#14),A#16[(app A#17[(var X#8)] C#18[[.]])]),
             ((var X#6),[.]),
             ((var X#8),A#16[(app A#17[[.]] C#18[(var X#6)])]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4          |->  [.],
           VV#12|.1,.2| |-> {X#14=[.2];VV#15|[.1],(var X#14)|},
           X#1          |->  X#14,
           X#2          |->  X#6,
           E#3          |->  {X#6=(\ X#7.S#10);E#9;VV#15|X#8,(var X#14)|},
           C#5          |->  A#16[(app A#17[(var X#8)] C#18)],
           A#11         |->  A#16[(app A#17 C#18[(var X#6)])]}

and instantiated rules:

                                  (letrec {X#14=(var X#6);X#6=(\ X#7.S#10);E#9;VV#15|X#8,(var X#14)|} in A#16[(app A#17[(var X#8)] C#18[(var X#6)])])
    -cpx-in1->                    (letrec {X#14=(var X#6);X#6=(\ X#7.S#10);E#9;VV#15|X#8,(var X#14)|} in A#16[(app A#17[(var X#8)] C#18[(var X#14)])])
    ................................................................................
                                  (letrec {X#14=(var X#6);X#6=(\ X#7.S#10);E#9;VV#15|X#8,(var X#14)|} in A#16[(app A#17[(var X#8)] C#18[(var X#6)])])
    -SR,cp-in2->                  (letrec {X#14=(var X#6);X#6=(\ X#7.S#10);E#9;VV#15|X#8,(var X#14)|} in A#16[(app A#17[(\ X#7.S#10)] C#18[(var X#6)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#10)
       ;E#9
       ;EE#13[X#8,A#11[(var X#6)]]
     in
        A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;E#9
       ;EE#13[X#8,A#11[(\ X#7.S#10)]]
     in
        A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
     )
  )

where

   Delta1 = {A#12,T#14,T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#15[(app A#16[[.]] T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]),
             ((var X#8),A#15[(app A#16[[.]] T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#15[(app A#16[(var X#8)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#8)] T#17)],
           A#12  |->  A#15[(app A#16 T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
       ;X#6= (\ X#7.S#10)
       ;E#17
       ;EE#13[X#8,A#11[(var X#6)]]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;X#6= (\ X#7.S#10)
       ;E#17
       ;EE#13[X#8,A#11[(\ X#7.S#10)]]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#15=T#14;X#6=(\ X#7.S#10);E#17;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)]),
           E#9   |->  {X#15=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#17},
           E#16  |->  {X#6=(\ X#7.S#10);E#17;EE#13[X#8,A#11[(var X#6)]]}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(\ X#7.S#10);E#17;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -cpx-in1->                    (letrec {X#15=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];X#6=(\ X#7.S#10);E#17;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(\ X#7.S#10);E#17;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#15=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(\ X#7.S#10);E#17;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#18[A#20[(app A#21[(var X#6)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]]
       ;E#9
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#18[A#20[(app A#21[(\ X#7.S#10)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]]
       ;E#9
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#19,A#17,T#14,T#4,A#11,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#20[(app A#21[[.]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#10);X#8=A#18[A#20[(app A#21[(var X#6)] T#22)]];E#9} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#8,
           E#16         |->  {X#6=(\ X#7.S#10);E#9},
           A#17         |->  A#18,
           T#14         |->  A#18[A#20[(app A#21[(var X#6)] T#22)]],
           T#19         |->  A#20[(app A#21[(var X#6)] T#22)],
           A#11         |->  A#20[(app A#21 T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);X#8=A#18[A#20[(app A#21[(var X#6)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]];E#9} in A#12[(var X#8)])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#10);X#8=A#18[A#20[(app A#21[(var X#6)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]];E#9} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);X#8=A#18[A#20[(app A#21[(var X#6)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]];E#9} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);X#8=A#18[A#20[(app A#21[(\ X#7.S#10)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]];E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#18[(app A#19[A#11[(var X#6)]] T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#9
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#18[(app A#19[A#11[(\ X#7.S#10)]] T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#9
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[A#11[(var X#6)]] T#20)];E#9} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]},
           X#15         |->  X#8,
           E#16         |->  {X#6=(\ X#7.S#10);E#9},
           T#14         |->  A#18[(app A#19[A#11[(var X#6)]] T#20)],
           A#17         |->  A#18[(app A#19 T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[A#11[(var X#6)]] T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9} in A#12[(var X#8)])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[A#11[(var X#6)]] T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#9} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[A#11[(var X#6)]] T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[A#11[(\ X#7.S#10)]] T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#18[(app A#19[(var X#6)] T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#9
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#18[(app A#19[(\ X#7.S#10)] T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#9
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#14,T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#18[(app A#19[[.]] T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[(var X#6)] T#20)];E#9} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#8,
           E#16         |->  {X#6=(\ X#7.S#10);E#9},
           A#17         |->  [.],
           T#14         |->  A#18[(app A#19[(var X#6)] T#20)],
           A#11         |->  A#18[(app A#19 T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[(var X#6)] T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9} in A#12[(var X#8)])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[(var X#6)] T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#9} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[(var X#6)] T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[(\ X#7.S#10)] T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#9
       ;EE#19[X#18,A#11[(var X#6)]]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#9
       ;EE#19[X#18,A#11[(\ X#7.S#10)]]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#10);X#8=A#20[(app A#21[(var X#18)] T#22)];E#9;EE#19[X#18,A#11[(var X#6)]]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];EE#19[X#18,[.2]]},
           X#15         |->  X#8,
           E#16         |->  {X#6=(\ X#7.S#10);E#9;EE#19[X#18,A#11[(var X#6)]]},
           T#14         |->  A#20[(app A#21[(var X#18)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9;EE#19[X#18,A#11[(var X#6)]]} in A#12[(var X#8)])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#10);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#9;EE#19[X#18,A#11[(var X#6)]]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9;EE#19[X#18,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9;EE#19[X#18,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#20[X#8,(var X#18)]
       ;EE#21[X#19,A#11[(var X#6)]]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#20[X#8,(var X#18)]
       ;EE#21[X#19,A#11[(\ X#7.S#10)]]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24)];X#6=(\ X#7.S#10);E#9;EE#20[X#8,(var X#18)];EE#21[X#19,A#11[(var X#6)]]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#15         |->  X#18,
           E#16         |->  {X#6=(\ X#7.S#10);E#9;EE#20[X#8,(var X#18)];EE#21[X#19,A#11[(var X#6)]]},
           T#14         |->  A#22[(app A#23[(var X#19)] T#24)],
           A#17         |->  A#22[(app A#23 T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#10);E#9;EE#20[X#8,(var X#18)];EE#21[X#19,A#11[(var X#6)]]} in A#12[(var X#8)])
    -cpx-in1->                    (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];X#6=(\ X#7.S#10);E#9;EE#20[X#8,(var X#18)];EE#21[X#19,A#11[(var X#6)]]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#10);E#9;EE#20[X#8,(var X#18)];EE#21[X#19,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#10);E#9;EE#20[X#8,(var X#18)];EE#21[X#19,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[A#22[(app A#23[(var X#6)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= A#20[A#22[(app A#23[(\ X#7.S#10)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#21,A#17,T#14,T#4,A#11,A#20}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#22[(app A#23[[.]] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#18=A#20[A#22[(app A#23[(var X#6)] T#24)]];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[A#22[(app A#23[(var X#6)] T#24)]],
           T#21         |->  A#22[(app A#23[(var X#6)] T#24)],
           A#11         |->  A#22[(app A#23 T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#18=A#20[A#22[(app A#23[(var X#6)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -cpx-in1->                    (letrec {X#18=A#20[A#22[(app A#23[(var X#6)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#18=A#20[A#22[(app A#23[(var X#6)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#18=A#20[A#22[(app A#23[(\ X#7.S#10)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[A#11[(var X#6)]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[A#11[(\ X#7.S#10)]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#18=A#20[(app A#21[A#11[(var X#6)]] T#22)];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]},
           T#14         |->  A#20[(app A#21[A#11[(var X#6)]] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[A#11[(var X#6)]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -cpx-in1->                    (letrec {X#18=A#20[(app A#21[A#11[(var X#6)]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[A#11[(var X#6)]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#18=A#20[(app A#21[A#11[(\ X#7.S#10)]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(var X#6)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(\ X#7.S#10)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#14,T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#20[(app A#21[[.]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#18=A#20[(app A#21[(var X#6)] T#22)];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  A#20[(app A#21[(var X#6)] T#22)],
           A#11         |->  A#20[(app A#21 T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(var X#6)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -cpx-in1->                    (letrec {X#18=A#20[(app A#21[(var X#6)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(var X#6)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#18=A#20[(app A#21[(\ X#7.S#10)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#8)
       ;X#6= (\ X#7.S#10)
       ;E#14
       ;EE#13[X#8,A#11[(var X#6)]]
     in
        A#15[(var X#1)]
     )
    ,
     (letrec
        X#1= (var X#8)
       ;X#6= (\ X#7.S#10)
       ;E#14
       ;EE#13[X#8,A#11[(\ X#7.S#10)]]
     in
        A#15[(var X#8)]
     )
  )

where

   Delta1 = {A#12,C#5,A#11,A#15}
   Delta2 = {}
   Delta3 = {((var X#1),A#15[[.]]),
             ((var X#8),A#15[[.]]),
             ((var X#1),A#15[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#15[[.]]),
             ((var X#8),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#9   |->  {X#1=(var X#8);E#14},
           E#3   |->  {X#6=(\ X#7.S#10);E#14;EE#13[X#8,A#11[(var X#6)]]},
           A#12  |->  A#15,
           C#5   |->  A#15[[.]],
           C#16  |->  [.],
           X#2   |->  X#8}

and instantiated rules:

                                  (letrec {X#1=(var X#8);X#6=(\ X#7.S#10);E#14;EE#13[X#8,A#11[(var X#6)]]} in A#15[(var X#8)])
    -cpx-in1->                    (letrec {X#1=(var X#8);X#6=(\ X#7.S#10);E#14;EE#13[X#8,A#11[(var X#6)]]} in A#15[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#8);X#6=(\ X#7.S#10);E#14;EE#13[X#8,A#11[(var X#6)]]} in A#15[(var X#8)])
    -SR,cp-e1->                   (letrec {X#1=(var X#8);X#6=(\ X#7.S#10);E#14;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#15[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#10)
       ;E#14
       ;EE#13[X#2,A#11[(var X#6)]]
     in
        A#15[(var X#1)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#10)
       ;E#14
       ;EE#13[X#2,A#11[(\ X#7.S#10)]]
     in
        A#15[(var X#2)]
     )
  )

where

   Delta1 = {A#12,C#5,A#11,A#15}
   Delta2 = {}
   Delta3 = {((var X#1),A#15),
             ((var X#2),A#15),
             ((var X#1),A#15[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#2),A#15[[.]]),
             ((var X#2),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#9   |->  {X#1=(var X#2);E#14},
           E#3   |->  {X#6=(\ X#7.S#10);E#14;EE#13[X#2,A#11[(var X#6)]]},
           A#12  |->  A#15[[.]],
           C#5   |->  A#15,
           A#16  |->  [.],
           X#8   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#14;EE#13[X#2,A#11[(var X#6)]]} in A#15[(var X#2)])
    -cpx-in1->                    (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#14;EE#13[X#2,A#11[(var X#6)]]} in A#15[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#14;EE#13[X#2,A#11[(var X#6)]]} in A#15[(var X#2)])
    -SR,cp-e1->                   (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#14;EE#13[X#2,A#11[(\ X#7.S#10)]]} in A#15[(var X#2)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#10)
       ;E#14
       ;EE#13[X#8,A#11[(var X#6)]]
     in
        A#15[(app A#16[(var X#8)] C#17[(var X#1)])]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#10)
       ;E#14
       ;EE#13[X#8,A#11[(\ X#7.S#10)]]
     in
        A#15[(app A#16[(var X#8)] C#17[(var X#2)])]
     )
  )

where

   Delta1 = {A#12,C#5,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),A#15[(app A#16[(var X#8)] C#17)]),
             ((var X#2),A#15[(app A#16[(var X#8)] C#17)]),
             ((var X#1),A#15[(app A#16[(var X#8)] C#17[[.]])]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#15[(app A#16[[.]] C#17[(var X#2)])]),
             ((var X#8),A#15[(app A#16[[.]] C#17[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#9   |->  {X#1=(var X#2);E#14},
           E#3   |->  {X#6=(\ X#7.S#10);E#14;EE#13[X#8,A#11[(var X#6)]]},
           C#5   |->  A#15[(app A#16[(var X#8)] C#17)],
           A#12  |->  A#15[(app A#16 C#17[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#14;EE#13[X#8,A#11[(var X#6)]]} in A#15[(app A#16[(var X#8)] C#17[(var X#2)])])
    -cpx-in1->                    (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#14;EE#13[X#8,A#11[(var X#6)]]} in A#15[(app A#16[(var X#8)] C#17[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#14;EE#13[X#8,A#11[(var X#6)]]} in A#15[(app A#16[(var X#8)] C#17[(var X#2)])])
    -SR,cp-e1->                   (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#14;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#15[(app A#16[(var X#8)] C#17[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#10)
       ;E#14
       ;EE#13[X#2,A#11[(var X#6)]]
     in
        (var X#1)
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#10)
       ;E#14
       ;EE#13[X#2,A#11[(\ X#7.S#10)]]
     in
        (var X#2)
     )
  )

where

   Delta1 = {A#11}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#1),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#2),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#9   |->  {X#1=(var X#2);E#14},
           E#3   |->  {X#6=(\ X#7.S#10);E#14;EE#13[X#2,A#11[(var X#6)]]},
           C#5   |->  [.],
           A#12  |->  [.],
           X#8   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#14;EE#13[X#2,A#11[(var X#6)]]} in (var X#2))
    -cpx-in1->                    (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#14;EE#13[X#2,A#11[(var X#6)]]} in (var X#1))
    ................................................................................
                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#14;EE#13[X#2,A#11[(var X#6)]]} in (var X#2))
    -SR,cp-e1->                   (letrec {X#1=(var X#2);X#6=(\ X#7.S#10);E#14;EE#13[X#2,A#11[(\ X#7.S#10)]]} in (var X#2))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= (var X#2)
       ;E#9
       ;EE#16[X#2,A#11[(var X#6)]]
     in
        A#17[(app A#18[(var X#8)] C#19[(var X#8)])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= (var X#2)
       ;E#9
       ;EE#16[X#2,A#11[(\ X#7.S#10)]]
     in
        A#17[(app A#18[(var X#8)] C#19[(var X#2)])]
     )
  )

where

   Delta1 = {A#12,C#5,A#11}
   Delta2 = {}
   Delta3 = {((var X#8),A#17[(app A#18[(var X#8)] C#19)]),
             ((var X#2),A#17[(app A#18[(var X#8)] C#19)]),
             ((var X#8),A#17[(app A#18[(var X#8)] C#19[[.]])]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#17[(app A#18[[.]] C#19[(var X#2)])]),
             ((var X#8),A#17[(app A#18[[.]] C#19[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           EE#13[.1,.2] |-> {[.1]=(var X#2);EE#16[X#2,[.2]]},
           X#1          |->  X#8,
           E#3          |->  {X#6=(\ X#7.S#10);E#9;EE#16[X#2,A#11[(var X#6)]]},
           A#14         |->  [.],
           X#15         |->  X#2,
           C#5          |->  A#17[(app A#18[(var X#8)] C#19)],
           A#12         |->  A#17[(app A#18 C#19[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);X#8=(var X#2);E#9;EE#16[X#2,A#11[(var X#6)]]} in A#17[(app A#18[(var X#8)] C#19[(var X#2)])])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#10);X#8=(var X#2);E#9;EE#16[X#2,A#11[(var X#6)]]} in A#17[(app A#18[(var X#8)] C#19[(var X#8)])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);X#8=(var X#2);E#9;EE#16[X#2,A#11[(var X#6)]]} in A#17[(app A#18[(var X#8)] C#19[(var X#2)])])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);X#8=(var X#2);E#9;EE#16[X#2,A#11[(\ X#7.S#10)]]} in A#17[(app A#18[(var X#8)] C#19[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#2)
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#17[X#8,(var X#15)]
       ;EE#18[X#2,A#11[(var X#6)]]
     in
        A#19[(app A#20[(var X#8)] C#21[(var X#15)])]
     )
    ,
     (letrec
        X#15= (var X#2)
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#17[X#8,(var X#15)]
       ;EE#18[X#2,A#11[(\ X#7.S#10)]]
     in
        A#19[(app A#20[(var X#8)] C#21[(var X#2)])]
     )
  )

where

   Delta1 = {A#12,C#5,A#11}
   Delta2 = {}
   Delta3 = {((var X#15),A#19[(app A#20[(var X#8)] C#21)]),
             ((var X#2),A#19[(app A#20[(var X#8)] C#21)]),
             ((var X#15),A#19[(app A#20[(var X#8)] C#21[[.]])]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#19[(app A#20[[.]] C#21[(var X#2)])]),
             ((var X#8),A#19[(app A#20[[.]] C#21[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           EE#13[.1,.2] |-> {X#15=(var X#2);EE#17[[.1],(var X#15)];EE#18[X#2,[.2]]},
           X#1          |->  X#15,
           E#3          |->  {X#6=(\ X#7.S#10);E#9;EE#17[X#8,(var X#15)];EE#18[X#2,A#11[(var X#6)]]},
           A#14         |->  [.],
           X#16         |->  X#2,
           C#5          |->  A#19[(app A#20[(var X#8)] C#21)],
           A#12         |->  A#19[(app A#20 C#21[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#15=(var X#2);X#6=(\ X#7.S#10);E#9;EE#17[X#8,(var X#15)];EE#18[X#2,A#11[(var X#6)]]} in A#19[(app A#20[(var X#8)] C#21[(var X#2)])])
    -cpx-in1->                    (letrec {X#15=(var X#2);X#6=(\ X#7.S#10);E#9;EE#17[X#8,(var X#15)];EE#18[X#2,A#11[(var X#6)]]} in A#19[(app A#20[(var X#8)] C#21[(var X#15)])])
    ................................................................................
                                  (letrec {X#15=(var X#2);X#6=(\ X#7.S#10);E#9;EE#17[X#8,(var X#15)];EE#18[X#2,A#11[(var X#6)]]} in A#19[(app A#20[(var X#8)] C#21[(var X#2)])])
    -SR,cp-e1->                   (letrec {X#15=(var X#2);X#6=(\ X#7.S#10);E#9;EE#17[X#8,(var X#15)];EE#18[X#2,A#11[(\ X#7.S#10)]]} in A#19[(app A#20[(var X#8)] C#21[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#17[(app A#18[(var X#8)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#17[(app A#18[(var X#8)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
     )
  )

where

   Delta1 = {A#13,T#16,T#4,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#17[(app A#18[[.]] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#17[(app A#18[[.]] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(app A#18[(var X#8)] T#19)]),
           T#16  |->  A#17[(app A#18[(var X#8)] T#19)],
           A#13  |->  A#17[(app A#18 T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(app A#18[(var X#8)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(app A#18[(var X#8)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(app A#18[(var X#8)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#17[(app A#18[(var X#8)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
       ;X#6= (\ X#7.S#11)
       ;E#19
       ;EE#14[X#8,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;X#6= (\ X#7.S#11)
       ;E#19
       ;EE#14[X#8,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#4,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#17=T#16;X#6=(\ X#7.S#11);E#19;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           E#10  |->  {X#17=T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#19},
           E#18  |->  {X#6=(\ X#7.S#11);E#19;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|}}

and instantiated rules:

                                  (letrec {X#17=T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(\ X#7.S#11);E#19;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -cpx-in1->                    (letrec {X#17=T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];X#6=(\ X#7.S#11);E#19;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(\ X#7.S#11);E#19;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#17=T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(\ X#7.S#11);E#19;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#20[A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]]
       ;E#10
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#20[A#22[(app A#23[(\ X#7.S#11)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]]
       ;E#10
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#21,A#19,T#16,T#4,A#12,A#20}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#22[(app A#23[[.]] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#11);X#8=A#20[A#22[(app A#23[(var X#9)] T#24)]];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#20[[.2]]},
           X#17         |->  X#8,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;VV#15|X#9,(var X#6)|},
           A#19         |->  A#20,
           T#16         |->  A#20[A#22[(app A#23[(var X#9)] T#24)]],
           T#21         |->  A#22[(app A#23[(var X#9)] T#24)],
           A#12         |->  A#22[(app A#23 T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);X#8=A#20[A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#11);X#8=A#20[A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);X#8=A#20[A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);X#8=A#20[A#22[(app A#23[(\ X#7.S#11)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#20[(app A#21[A#12[(var X#9)]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#10
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#20[(app A#21[A#12[(\ X#7.S#11)]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#10
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#19,T#16,T#4,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[A#12[(var X#9)]] T#22)];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#20[(app A#21[[.2]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]},
           X#17         |->  X#8,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;VV#15|X#9,(var X#6)|},
           T#16         |->  A#20[(app A#21[A#12[(var X#9)]] T#22)],
           A#19         |->  A#20[(app A#21 T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[A#12[(var X#9)]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[A#12[(var X#9)]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[A#12[(var X#9)]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[A#12[(\ X#7.S#11)]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#20[(app A#21[(var X#9)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#10
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#20[(app A#21[(\ X#7.S#11)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#10
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#16,T#4,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#20[(app A#21[[.]] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[(var X#9)] T#22)];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#17         |->  X#8,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;VV#15|X#9,(var X#6)|},
           A#19         |->  [.],
           T#16         |->  A#20[(app A#21[(var X#9)] T#22)],
           A#12         |->  A#20[(app A#21 T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[(var X#9)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[(var X#9)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[(var X#9)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[(\ X#7.S#11)] T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#10
       ;EE#21[X#20,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#10
       ;EE#21[X#20,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#19,T#16,T#4,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#11);X#8=A#22[(app A#23[(var X#20)] T#24)];E#10;EE#21[X#20,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];EE#21[X#20,[.2]]},
           X#17         |->  X#8,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;EE#21[X#20,A#12[(var X#9)]];VV#15|X#9,(var X#6)|},
           T#16         |->  A#22[(app A#23[(var X#20)] T#24)],
           A#19         |->  A#22[(app A#23 T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);X#8=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#10;EE#21[X#20,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#11);X#8=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#10;EE#21[X#20,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);X#8=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#10;EE#21[X#20,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);X#8=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#10;EE#21[X#20,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#22[X#8,(var X#20)]
       ;EE#23[X#21,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#20= A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#22[X#8,(var X#20)]
       ;EE#23[X#21,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#19,T#16,T#4,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26)];X#6=(\ X#7.S#11);E#10;EE#22[X#8,(var X#20)];EE#23[X#21,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];EE#22[[.1],(var X#20)];EE#23[X#21,[.2]]},
           X#17         |->  X#20,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;EE#22[X#8,(var X#20)];EE#23[X#21,A#12[(var X#9)]];VV#15|X#9,(var X#6)|},
           T#16         |->  A#24[(app A#25[(var X#21)] T#26)],
           A#19         |->  A#24[(app A#25 T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#11);E#10;EE#22[X#8,(var X#20)];EE#23[X#21,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -cpx-in1->                    (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];X#6=(\ X#7.S#11);E#10;EE#22[X#8,(var X#20)];EE#23[X#21,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#11);E#10;EE#22[X#8,(var X#20)];EE#23[X#21,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#11);E#10;EE#22[X#8,(var X#20)];EE#23[X#21,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[A#24[(app A#25[(var X#9)] T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#21[X#8,(var X#20)]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#20= A#22[A#24[(app A#25[(\ X#7.S#11)] T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#21[X#8,(var X#20)]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#23,A#19,T#16,T#4,A#12,A#22}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#24[(app A#25[[.]] T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#20=A#22[A#24[(app A#25[(var X#9)] T#26)]];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#20=A#22[[.2]];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|},
           A#19         |->  A#22,
           T#16         |->  A#22[A#24[(app A#25[(var X#9)] T#26)]],
           T#23         |->  A#24[(app A#25[(var X#9)] T#26)],
           A#12         |->  A#24[(app A#25 T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#20=A#22[A#24[(app A#25[(var X#9)] T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -cpx-in1->                    (letrec {X#20=A#22[A#24[(app A#25[(var X#9)] T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#20=A#22[A#24[(app A#25[(var X#9)] T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#20=A#22[A#24[(app A#25[(\ X#7.S#11)] T#26[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app A#23[A#12[(var X#9)]] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#21[X#8,(var X#20)]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#20= A#22[(app A#23[A#12[(\ X#7.S#11)]] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#21[X#8,(var X#20)]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#19,T#16,T#4,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#20=A#22[(app A#23[A#12[(var X#9)]] T#24)];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#20=A#22[(app A#23[[.2]] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|},
           T#16         |->  A#22[(app A#23[A#12[(var X#9)]] T#24)],
           A#19         |->  A#22[(app A#23 T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app A#23[A#12[(var X#9)]] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -cpx-in1->                    (letrec {X#20=A#22[(app A#23[A#12[(var X#9)]] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#20=A#22[(app A#23[A#12[(var X#9)]] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#20=A#22[(app A#23[A#12[(\ X#7.S#11)]] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#21[X#8,(var X#20)]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#20= A#22[(app A#23[(\ X#7.S#11)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#21[X#8,(var X#20)]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#16,T#4,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#22[(app A#23[[.]] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#20=A#22[(app A#23[(var X#9)] T#24)];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|},
           A#19         |->  [.],
           T#16         |->  A#22[(app A#23[(var X#9)] T#24)],
           A#12         |->  A#22[(app A#23 T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -cpx-in1->                    (letrec {X#20=A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#20=A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#20=A#22[(app A#23[(\ X#7.S#11)] T#24[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#8)
       ;X#6= (\ X#7.S#11)
       ;E#16
       ;EE#14[X#8,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#17[(var X#1)]
     )
    ,
     (letrec
        X#1= (var X#8)
       ;X#6= (\ X#7.S#11)
       ;E#16
       ;EE#14[X#8,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#17[(var X#8)]
     )
  )

where

   Delta1 = {A#13,C#5,A#12,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),A#17[[.]]),
             ((var X#8),A#17[[.]]),
             ((var X#1),A#17[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#17[[.]]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#17[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#10  |->  {X#1=(var X#8);E#16},
           E#3   |->  {X#6=(\ X#7.S#11);E#16;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|},
           A#13  |->  A#17,
           C#5   |->  A#17[[.]],
           C#18  |->  [.],
           X#2   |->  X#8}

and instantiated rules:

                                  (letrec {X#1=(var X#8);X#6=(\ X#7.S#11);E#16;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(var X#8)])
    -cpx-in1->                    (letrec {X#1=(var X#8);X#6=(\ X#7.S#11);E#16;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#8);X#6=(\ X#7.S#11);E#16;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(var X#8)])
    -SR,cp-e2->                   (letrec {X#1=(var X#8);X#6=(\ X#7.S#11);E#16;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#17[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#11)
       ;E#16
       ;EE#14[X#2,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#17[(var X#1)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#11)
       ;E#16
       ;EE#14[X#2,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#17[(var X#2)]
     )
  )

where

   Delta1 = {A#13,C#5,A#12,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),A#17),
             ((var X#2),A#17),
             ((var X#1),A#17[[.]]),
             ((var X#6),[.]),
             ((var X#2),A#17[[.]]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#2),A#17[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#10  |->  {X#1=(var X#2);E#16},
           E#3   |->  {X#6=(\ X#7.S#11);E#16;EE#14[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|},
           A#13  |->  A#17[[.]],
           C#5   |->  A#17,
           A#18  |->  [.],
           X#8   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#11);E#16;EE#14[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(var X#2)])
    -cpx-in1->                    (letrec {X#1=(var X#2);X#6=(\ X#7.S#11);E#16;EE#14[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#11);E#16;EE#14[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(var X#2)])
    -SR,cp-e2->                   (letrec {X#1=(var X#2);X#6=(\ X#7.S#11);E#16;EE#14[X#2,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#17[(var X#2)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#11)
       ;E#16
       ;EE#14[X#8,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#17[(app A#18[(var X#8)] C#19[(var X#1)])]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#11)
       ;E#16
       ;EE#14[X#8,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#17[(app A#18[(var X#8)] C#19[(var X#2)])]
     )
  )

where

   Delta1 = {A#13,C#5,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),A#17[(app A#18[(var X#8)] C#19)]),
             ((var X#2),A#17[(app A#18[(var X#8)] C#19)]),
             ((var X#1),A#17[(app A#18[(var X#8)] C#19[[.]])]),
             ((var X#6),[.]),
             ((var X#8),A#17[(app A#18[[.]] C#19[(var X#2)])]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#17[(app A#18[[.]] C#19[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#10  |->  {X#1=(var X#2);E#16},
           E#3   |->  {X#6=(\ X#7.S#11);E#16;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|},
           C#5   |->  A#17[(app A#18[(var X#8)] C#19)],
           A#13  |->  A#17[(app A#18 C#19[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#11);E#16;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(app A#18[(var X#8)] C#19[(var X#2)])])
    -cpx-in1->                    (letrec {X#1=(var X#2);X#6=(\ X#7.S#11);E#16;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(app A#18[(var X#8)] C#19[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#11);E#16;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(app A#18[(var X#8)] C#19[(var X#2)])])
    -SR,cp-e2->                   (letrec {X#1=(var X#2);X#6=(\ X#7.S#11);E#16;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#17[(app A#18[(var X#8)] C#19[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#11)
       ;E#16
       ;EE#14[X#2,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        (var X#1)
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#6= (\ X#7.S#11)
       ;E#16
       ;EE#14[X#2,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        (var X#2)
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#1),[.]),
             ((var X#6),[.]),
             ((var X#2),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#10  |->  {X#1=(var X#2);E#16},
           E#3   |->  {X#6=(\ X#7.S#11);E#16;EE#14[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|},
           C#5   |->  [.],
           A#13  |->  [.],
           X#8   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#11);E#16;EE#14[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in (var X#2))
    -cpx-in1->                    (letrec {X#1=(var X#2);X#6=(\ X#7.S#11);E#16;EE#14[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in (var X#1))
    ................................................................................
                                  (letrec {X#1=(var X#2);X#6=(\ X#7.S#11);E#16;EE#14[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in (var X#2))
    -SR,cp-e2->                   (letrec {X#1=(var X#2);X#6=(\ X#7.S#11);E#16;EE#14[X#2,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in (var X#2))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#11)
       ;X#9= (var X#6)
       ;E#10
       ;EE#14[X#8,A#12[(var X#9)]]
     in
        A#17[(app A#18[(var X#8)] C#19[(var X#9)])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;X#9= (var X#6)
       ;E#10
       ;EE#14[X#8,A#12[(\ X#7.S#11)]]
     in
        A#17[(app A#18[(var X#8)] C#19[(var X#6)])]
     )
  )

where

   Delta1 = {A#13,C#5,A#12}
   Delta2 = {}
   Delta3 = {((var X#9),A#17[(app A#18[(var X#8)] C#19)]),
             ((var X#6),A#17[(app A#18[(var X#8)] C#19)]),
             ((var X#9),A#17[(app A#18[(var X#8)] C#19[[.]])]),
             ((var X#6),[.]),
             ((var X#8),A#17[(app A#18[[.]] C#19[(var X#6)])]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#17[(app A#18[[.]] C#19[(var X#6)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           VV#15|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#9,
           X#2          |->  X#6,
           E#3          |->  {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]]},
           C#5          |->  A#17[(app A#18[(var X#8)] C#19)],
           A#13         |->  A#17[(app A#18 C#19[(var X#6)])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);X#9=(var X#6);E#10;EE#14[X#8,A#12[(var X#9)]]} in A#17[(app A#18[(var X#8)] C#19[(var X#6)])])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#11);X#9=(var X#6);E#10;EE#14[X#8,A#12[(var X#9)]]} in A#17[(app A#18[(var X#8)] C#19[(var X#9)])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);X#9=(var X#6);E#10;EE#14[X#8,A#12[(var X#9)]]} in A#17[(app A#18[(var X#8)] C#19[(var X#6)])])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);X#9=(var X#6);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]]} in A#17[(app A#18[(var X#8)] C#19[(var X#6)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#11)
       ;X#9= (var X#17)
       ;E#10
       ;EE#14[X#8,A#12[(var X#9)]]
       ;VV#18|X#17,(var X#6)|
     in
        A#19[(app A#20[(var X#8)] C#21[(var X#9)])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;X#9= (var X#17)
       ;E#10
       ;EE#14[X#8,A#12[(\ X#7.S#11)]]
       ;VV#18|X#17,(var X#6)|
     in
        A#19[(app A#20[(var X#8)] C#21[(var X#17)])]
     )
  )

where

   Delta1 = {A#13,C#5,A#12}
   Delta2 = {}
   Delta3 = {((var X#9),A#19[(app A#20[(var X#8)] C#21)]),
             ((var X#17),A#19[(app A#20[(var X#8)] C#21)]),
             ((var X#9),A#19[(app A#20[(var X#8)] C#21[[.]])]),
             ((var X#6),[.]),
             ((var X#8),A#19[(app A#20[[.]] C#21[(var X#17)])]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#19[(app A#20[[.]] C#21[(var X#17)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           VV#15|.1,.2| |-> {[.1]=(var X#17);VV#18|X#17,[.2]|},
           X#1          |->  X#9,
           X#2          |->  X#17,
           E#3          |->  {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#18|X#17,(var X#6)|},
           C#5          |->  A#19[(app A#20[(var X#8)] C#21)],
           A#13         |->  A#19[(app A#20 C#21[(var X#17)])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);X#9=(var X#17);E#10;EE#14[X#8,A#12[(var X#9)]];VV#18|X#17,(var X#6)|} in A#19[(app A#20[(var X#8)] C#21[(var X#17)])])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#11);X#9=(var X#17);E#10;EE#14[X#8,A#12[(var X#9)]];VV#18|X#17,(var X#6)|} in A#19[(app A#20[(var X#8)] C#21[(var X#9)])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);X#9=(var X#17);E#10;EE#14[X#8,A#12[(var X#9)]];VV#18|X#17,(var X#6)|} in A#19[(app A#20[(var X#8)] C#21[(var X#17)])])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);X#9=(var X#17);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#18|X#17,(var X#6)|} in A#19[(app A#20[(var X#8)] C#21[(var X#17)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#18)
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(var X#9)]]
       ;VV#19|X#9,(var X#17)|
       ;VV#20|X#18,(var X#6)|
     in
        A#21[(app A#22[(var X#8)] C#23[(var X#17)])]
     )
    ,
     (letrec
        X#17= (var X#18)
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(\ X#7.S#11)]]
       ;VV#19|X#9,(var X#17)|
       ;VV#20|X#18,(var X#6)|
     in
        A#21[(app A#22[(var X#8)] C#23[(var X#18)])]
     )
  )

where

   Delta1 = {A#13,C#5,A#12}
   Delta2 = {}
   Delta3 = {((var X#17),A#21[(app A#22[(var X#8)] C#23)]),
             ((var X#18),A#21[(app A#22[(var X#8)] C#23)]),
             ((var X#17),A#21[(app A#22[(var X#8)] C#23[[.]])]),
             ((var X#6),[.]),
             ((var X#8),A#21[(app A#22[[.]] C#23[(var X#18)])]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#21[(app A#22[[.]] C#23[(var X#18)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           VV#15|.1,.2| |-> {X#17=(var X#18);VV#19|[.1],(var X#17)|;VV#20|X#18,[.2]|},
           X#1          |->  X#17,
           X#2          |->  X#18,
           E#3          |->  {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#19|X#9,(var X#17)|;VV#20|X#18,(var X#6)|},
           C#5          |->  A#21[(app A#22[(var X#8)] C#23)],
           A#13         |->  A#21[(app A#22 C#23[(var X#18)])]}

and instantiated rules:

                                  (letrec {X#17=(var X#18);X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#19|X#9,(var X#17)|;VV#20|X#18,(var X#6)|} in A#21[(app A#22[(var X#8)] C#23[(var X#18)])])
    -cpx-in1->                    (letrec {X#17=(var X#18);X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#19|X#9,(var X#17)|;VV#20|X#18,(var X#6)|} in A#21[(app A#22[(var X#8)] C#23[(var X#17)])])
    ................................................................................
                                  (letrec {X#17=(var X#18);X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#19|X#9,(var X#17)|;VV#20|X#18,(var X#6)|} in A#21[(app A#22[(var X#8)] C#23[(var X#18)])])
    -SR,cp-e2->                   (letrec {X#17=(var X#18);X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#19|X#9,(var X#17)|;VV#20|X#18,(var X#6)|} in A#21[(app A#22[(var X#8)] C#23[(var X#18)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#6)
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(var X#9)]]
       ;VV#18|X#9,(var X#17)|
     in
        A#19[(app A#20[(var X#8)] C#21[(var X#17)])]
     )
    ,
     (letrec
        X#17= (var X#6)
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(\ X#7.S#11)]]
       ;VV#18|X#9,(var X#17)|
     in
        A#19[(app A#20[(var X#8)] C#21[(var X#6)])]
     )
  )

where

   Delta1 = {A#13,C#5,A#12}
   Delta2 = {}
   Delta3 = {((var X#17),A#19[(app A#20[(var X#8)] C#21)]),
             ((var X#6),A#19[(app A#20[(var X#8)] C#21)]),
             ((var X#17),A#19[(app A#20[(var X#8)] C#21[[.]])]),
             ((var X#6),[.]),
             ((var X#8),A#19[(app A#20[[.]] C#21[(var X#6)])]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#19[(app A#20[[.]] C#21[(var X#6)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           VV#15|.1,.2| |-> {X#17=[.2];VV#18|[.1],(var X#17)|},
           X#1          |->  X#17,
           X#2          |->  X#6,
           E#3          |->  {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#18|X#9,(var X#17)|},
           C#5          |->  A#19[(app A#20[(var X#8)] C#21)],
           A#13         |->  A#19[(app A#20 C#21[(var X#6)])]}

and instantiated rules:

                                  (letrec {X#17=(var X#6);X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#18|X#9,(var X#17)|} in A#19[(app A#20[(var X#8)] C#21[(var X#6)])])
    -cpx-in1->                    (letrec {X#17=(var X#6);X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#18|X#9,(var X#17)|} in A#19[(app A#20[(var X#8)] C#21[(var X#17)])])
    ................................................................................
                                  (letrec {X#17=(var X#6);X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#18|X#9,(var X#17)|} in A#19[(app A#20[(var X#8)] C#21[(var X#6)])])
    -SR,cp-e2->                   (letrec {X#17=(var X#6);X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#18|X#9,(var X#17)|} in A#19[(app A#20[(var X#8)] C#21[(var X#6)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= (var X#2)
       ;E#10
       ;EE#18[X#2,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#19[(app A#20[(var X#8)] C#21[(var X#8)])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= (var X#2)
       ;E#10
       ;EE#18[X#2,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#19[(app A#20[(var X#8)] C#21[(var X#2)])]
     )
  )

where

   Delta1 = {A#13,C#5,A#12}
   Delta2 = {}
   Delta3 = {((var X#8),A#19[(app A#20[(var X#8)] C#21)]),
             ((var X#2),A#19[(app A#20[(var X#8)] C#21)]),
             ((var X#8),A#19[(app A#20[(var X#8)] C#21[[.]])]),
             ((var X#6),[.]),
             ((var X#8),A#19[(app A#20[[.]] C#21[(var X#2)])]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#19[(app A#20[[.]] C#21[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           EE#14[.1,.2] |-> {[.1]=(var X#2);EE#18[X#2,[.2]]},
           X#1          |->  X#8,
           E#3          |->  {X#6=(\ X#7.S#11);E#10;EE#18[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|},
           A#16         |->  [.],
           X#17         |->  X#2,
           C#5          |->  A#19[(app A#20[(var X#8)] C#21)],
           A#13         |->  A#19[(app A#20 C#21[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);X#8=(var X#2);E#10;EE#18[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#19[(app A#20[(var X#8)] C#21[(var X#2)])])
    -cpx-in1->                    (letrec {X#6=(\ X#7.S#11);X#8=(var X#2);E#10;EE#18[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#19[(app A#20[(var X#8)] C#21[(var X#8)])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);X#8=(var X#2);E#10;EE#18[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#19[(app A#20[(var X#8)] C#21[(var X#2)])])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);X#8=(var X#2);E#10;EE#18[X#2,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#19[(app A#20[(var X#8)] C#21[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#2)
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#2,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#21[(app A#22[(var X#8)] C#23[(var X#17)])]
     )
    ,
     (letrec
        X#17= (var X#2)
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#2,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#21[(app A#22[(var X#8)] C#23[(var X#2)])]
     )
  )

where

   Delta1 = {A#13,C#5,A#12}
   Delta2 = {}
   Delta3 = {((var X#17),A#21[(app A#22[(var X#8)] C#23)]),
             ((var X#2),A#21[(app A#22[(var X#8)] C#23)]),
             ((var X#17),A#21[(app A#22[(var X#8)] C#23[[.]])]),
             ((var X#6),[.]),
             ((var X#8),A#21[(app A#22[[.]] C#23[(var X#2)])]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#21[(app A#22[[.]] C#23[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#1),C#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           EE#14[.1,.2] |-> {X#17=(var X#2);EE#19[[.1],(var X#17)];EE#20[X#2,[.2]]},
           X#1          |->  X#17,
           E#3          |->  {X#6=(\ X#7.S#11);E#10;EE#19[X#8,(var X#17)];EE#20[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|},
           A#16         |->  [.],
           X#18         |->  X#2,
           C#5          |->  A#21[(app A#22[(var X#8)] C#23)],
           A#13         |->  A#21[(app A#22 C#23[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#17=(var X#2);X#6=(\ X#7.S#11);E#10;EE#19[X#8,(var X#17)];EE#20[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#21[(app A#22[(var X#8)] C#23[(var X#2)])])
    -cpx-in1->                    (letrec {X#17=(var X#2);X#6=(\ X#7.S#11);E#10;EE#19[X#8,(var X#17)];EE#20[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#21[(app A#22[(var X#8)] C#23[(var X#17)])])
    ................................................................................
                                  (letrec {X#17=(var X#2);X#6=(\ X#7.S#11);E#10;EE#19[X#8,(var X#17)];EE#20[X#2,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#21[(app A#22[(var X#8)] C#23[(var X#2)])])
    -SR,cp-e2->                   (letrec {X#17=(var X#2);X#6=(\ X#7.S#11);E#10;EE#19[X#8,(var X#17)];EE#20[X#2,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#21[(app A#22[(var X#8)] C#23[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        (letrec {E#7} in T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])
     )
    ,
     (letrec {E#6;E#7} in T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])
  )

where

   Delta1 = {T#9,T#4}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             [{E#6},(letrec {E#7} in [.])],
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {E#6;E#7} in S#8)
    and constraints: E#6/= {}, E#7/= {}, ({E#6},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in (letrec {E#7} in S#8))}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),[{E#6},(letrec {E#7} in [.])],((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4  |->  (letrec {E#6} in (letrec {E#7} in T#10)),
           T#9  |->  (letrec {E#7} in T#10),
           S#8  |->  T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {E#6} in (letrec {E#7} in T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]))
    -cpx-in1->                    (letrec {E#6} in (letrec {E#7} in T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]))
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]))
    -SR,llet-in1->                (letrec {E#6;E#7} in T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        (letrec {X#11=T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#13} in S#8)
     )
    ,
     (letrec
        X#11= T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;E#13
       ;E#6
     in
        S#8
     )
  )

where

   Delta1 = {T#9,T#4}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             [{E#6},(letrec {X#11=T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#13} in [.])],
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {E#6;E#7} in S#8)
    and constraints: E#6/= {}, E#7/= {}, ({E#6},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in (letrec {E#7} in S#8))}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),[{E#6},(letrec {E#7} in [.])],((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in (letrec {X#11=T#10;E#13} in S#8)),
           T#9   |->  (letrec {X#11=T#10;E#13} in S#8),
           E#7   |->  {X#11=T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {E#6} in (letrec {X#11=T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#13} in S#8))
    -cpx-in1->                    (letrec {E#6} in (letrec {X#11=T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#13} in S#8))
    ................................................................................
                                  (letrec {E#6} in (letrec {X#11=T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#13} in S#8))
    -SR,llet-in1->                (letrec {X#11=T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#13;E#6} in S#8)
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]))
    ,
     (letrec {X#1=(var X#2);E#3;E#6} in C#5[(var X#2)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             [{E#6},(letrec {X#1=(var X#2);E#3} in [.])],
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {E#6;E#7} in S#8)
    and constraints: E#6/= {}, E#7/= {}, ({E#6},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in (letrec {E#7} in S#8))}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),[{E#6},(letrec {E#7} in [.])],((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4  |->  (letrec {E#6} in [.]),
           T#9  |->  [.],
           S#8  |->  C#5[(var X#2)],
           E#7  |->  {X#1=(var X#2);E#3}}

and instantiated rules:

                                  (letrec {E#6} in (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]))
    -cpx-in1->                    (letrec {E#6} in (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]))
    ................................................................................
                                  (letrec {E#6} in (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]))
    -SR,llet-in1->                (letrec {X#1=(var X#2);E#3;E#6} in C#5[(var X#2)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= T#9[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
       ;E#12
     in
        (letrec {E#7} in S#8)
     )
    ,
     (letrec
        X#10= T#9[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;E#12
       ;E#7
     in
        S#8
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             [{X#10=T#9[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#12},(letrec {E#7} in [.])],
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {E#6;E#7} in S#8)
    and constraints: E#6/= {}, E#7/= {}, ({E#6},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in (letrec {E#7} in S#8))}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),[{E#6},(letrec {E#7} in [.])],((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#10=T#9;E#12} in (letrec {E#7} in S#8)),
           E#6   |->  {X#10=T#9[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#12},
           E#11  |->  {E#12}}

and instantiated rules:

                                  (letrec {X#10=T#9[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#12} in (letrec {E#7} in S#8))
    -cpx-in1->                    (letrec {X#10=T#9[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#12} in (letrec {E#7} in S#8))
    ................................................................................
                                  (letrec {X#10=T#9[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#12} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {X#10=T#9[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#12;E#7} in S#8)
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#2);E#9} in (letrec {E#7} in C#10[(var X#1)]))
    ,
     (letrec {X#1=(var X#2);E#7;E#9} in C#10[(var X#2)])
  )

where

   Delta1 = {C#5}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),(letrec {E#7} in C#10)),
             ((var X#2),(letrec {E#7} in C#10)),
             [{X#1=(var X#2);E#9},(letrec {E#7} in [.])],
             ((var X#1),(letrec {E#7} in C#10[[.]]))}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {E#6;E#7} in S#8)
    and constraints: E#6/= {}, E#7/= {}, ({E#6},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in (letrec {E#7} in S#8))}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),[{E#6},(letrec {E#7} in [.])],((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           E#6  |->  {X#1=(var X#2);E#9},
           E#3  |->  {E#9},
           C#5  |->  (letrec {E#7} in C#10),
           S#8  |->  C#10[(var X#2)]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#9} in (letrec {E#7} in C#10[(var X#2)]))
    -cpx-in1->                    (letrec {X#1=(var X#2);E#9} in (letrec {E#7} in C#10[(var X#1)]))
    ................................................................................
                                  (letrec {X#1=(var X#2);E#9} in (letrec {E#7} in C#10[(var X#2)]))
    -SR,llet-in1->                (letrec {X#1=(var X#2);E#7;E#9} in C#10[(var X#2)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#2);E#9} in (letrec {X#11=C#10[(var X#1)];E#13} in S#8))
    ,
     (letrec {X#1=(var X#2);X#11=C#10[(var X#2)];E#13;E#9} in S#8)
  )

where

   Delta1 = {C#5}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),(letrec {X#11=C#10;E#13} in S#8)),
             ((var X#2),(letrec {X#11=C#10;E#13} in S#8)),
             [{X#1=(var X#2);E#9},(letrec {X#11=C#10[(var X#2)];E#13} in [.])],
             ((var X#1),(letrec {X#11=C#10[[.]];E#13} in S#8))}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {E#6;E#7} in S#8)
    and constraints: E#6/= {}, E#7/= {}, ({E#6},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in (letrec {E#7} in S#8))}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),[{E#6},(letrec {E#7} in [.])],((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#6   |->  {X#1=(var X#2);E#9},
           E#3   |->  {E#9},
           C#5   |->  (letrec {X#11=C#10;E#13} in S#8),
           E#7   |->  {X#11=C#10[(var X#2)];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#9} in (letrec {X#11=C#10[(var X#2)];E#13} in S#8))
    -cpx-in1->                    (letrec {X#1=(var X#2);E#9} in (letrec {X#11=C#10[(var X#1)];E#13} in S#8))
    ................................................................................
                                  (letrec {X#1=(var X#2);E#9} in (letrec {X#11=C#10[(var X#2)];E#13} in S#8))
    -SR,llet-in1->                (letrec {X#1=(var X#2);X#11=C#10[(var X#2)];E#13;E#9} in S#8)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {E#7} in S#9)
       ;E#8
     in
        A#12[(app A#13[(var X#6)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
     )
    ,
     (letrec
        X#6= S#9
       ;E#7
       ;E#8
     in
        A#12[(app A#13[(var X#6)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
     )
  )

where

   Delta1 = {A#10,T#11,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (A#12[(app A#13[(var X#6)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])],(letrec {E#7} in [.])),
             [{E#8},(letrec {E#7} in [.])],
             ((var X#1),C#5[[.]]),
             ((var X#6),A#12[(app A#13[[.]] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]),
             ((var X#6),A#12[(app A#13[[.]] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),C#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#12[(app A#13[(var X#6)] T#14)]),
           T#11  |->  A#12[(app A#13[(var X#6)] T#14)],
           A#10  |->  A#12[(app A#13 T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#12[(app A#13[(var X#6)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -cpx-in1->                    (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#12[(app A#13[(var X#6)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])])
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#12[(app A#13[(var X#6)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#12[(app A#13[(var X#6)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {E#7} in T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#6= T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;E#7
       ;E#8
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#11,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8},(letrec {E#7} in [.])],
             ((var X#1),C#5[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),C#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(letrec {E#7} in T#14);E#8} in A#10[(var X#6)]),
           X#12  |->  X#6,
           E#13  |->  {E#8},
           T#11  |->  (letrec {E#7} in T#14),
           S#9   |->  T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#7} in T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]);E#8} in A#10[(var X#6)])
    -cpx-in1->                    (letrec {X#6=(letrec {E#7} in T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]);E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {X#15=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#17} in S#9)
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;X#6= S#9
       ;E#17
       ;E#8
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#11,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (A#10[(var X#6)],(letrec {X#15=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#17} in [.])),
             [{E#8},(letrec {X#15=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#17} in [.])],
             ((var X#1),C#5[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),C#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(letrec {X#15=T#14;E#17} in S#9);E#8} in A#10[(var X#6)]),
           X#12  |->  X#6,
           E#13  |->  {E#8},
           T#11  |->  (letrec {X#15=T#14;E#17} in S#9),
           E#7   |->  {X#15=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {X#6=(letrec {X#15=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#17} in S#9);E#8} in A#10[(var X#6)])
    -cpx-in1->                    (letrec {X#6=(letrec {X#15=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#17} in S#9);E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(letrec {X#15=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#17} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#15=T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=S#9;E#17;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#1=(var X#2);X#6=C#5[(var X#2)];E#3;E#8} in A#10[(var X#6)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (A#10[(var X#6)],(letrec {X#1=(var X#2);E#3} in [.])),
             [{E#8},(letrec {X#1=(var X#2);E#3} in [.])],
             ((var X#1),C#5[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),C#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=[.];E#8} in A#10[(var X#6)]),
           X#12  |->  X#6,
           E#13  |->  {E#8},
           T#11  |->  [.],
           S#9   |->  C#5[(var X#2)],
           E#7   |->  {X#1=(var X#2);E#3}}

and instantiated rules:

                                  (letrec {X#6=(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]);E#8} in A#10[(var X#6)])
    -cpx-in1->                    (letrec {X#6=(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]);E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#1=(var X#2);X#6=C#5[(var X#2)];E#3;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#12= T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
       ;X#6= (letrec {E#7} in S#9)
       ;E#14
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#12= T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;X#6= S#9
       ;E#14
       ;E#7
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14},(letrec {E#7} in [.])],
             ((var X#1),C#5[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),C#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#12=T#11;X#6=(letrec {E#7} in S#9);E#14} in A#10[(var X#6)]),
           E#8   |->  {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14},
           E#13  |->  {X#6=(letrec {E#7} in S#9);E#14}}

and instantiated rules:

                                  (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(letrec {E#7} in S#9);E#14} in A#10[(var X#6)])
    -cpx-in1->                    (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];X#6=(letrec {E#7} in S#9);E#14} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(letrec {E#7} in S#9);E#14} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=S#9;E#14;E#7} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#6);X#6=(letrec {E#7} in S#9);E#11} in A#12[(var X#1)])
    ,
     (letrec {X#1=(var X#6);X#6=S#9;E#11;E#7} in A#12[(var X#6)])
  )

where

   Delta1 = {A#10,C#5,A#12}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#12[[.]]),
             ((var X#6),A#12[[.]]),
             (A#12[(var X#6)],(letrec {E#7} in [.])),
             [{X#1=(var X#6);E#11},(letrec {E#7} in [.])],
             ((var X#1),A#12[[.]]),
             ((var X#6),A#12[[.]]),
             ((var X#6),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),C#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#8   |->  {X#1=(var X#6);E#11},
           E#3   |->  {X#6=(letrec {E#7} in S#9);E#11},
           A#10  |->  A#12,
           C#5   |->  A#12[[.]],
           C#13  |->  [.],
           X#2   |->  X#6}

and instantiated rules:

                                  (letrec {X#1=(var X#6);X#6=(letrec {E#7} in S#9);E#11} in A#12[(var X#6)])
    -cpx-in1->                    (letrec {X#1=(var X#6);X#6=(letrec {E#7} in S#9);E#11} in A#12[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#6);X#6=(letrec {E#7} in S#9);E#11} in A#12[(var X#6)])
    -SR,llet-e1->                 (letrec {X#1=(var X#6);X#6=S#9;E#11;E#7} in A#12[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#2);X#2=(letrec {E#7} in S#9);E#11} in A#12[(var X#1)])
    ,
     (letrec {X#1=(var X#2);X#2=S#9;E#11;E#7} in A#12[(var X#2)])
  )

where

   Delta1 = {A#10,C#5,A#12}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#12),
             ((var X#2),A#12),
             (A#12[(var X#2)],(letrec {E#7} in [.])),
             [{X#1=(var X#2);E#11},(letrec {E#7} in [.])],
             ((var X#1),A#12[[.]]),
             ((var X#2),A#12[[.]]),
             ((var X#2),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),C#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#8   |->  {X#1=(var X#2);E#11},
           E#3   |->  {X#2=(letrec {E#7} in S#9);E#11},
           A#10  |->  A#12[[.]],
           C#5   |->  A#12,
           A#13  |->  [.],
           X#6   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#2=(letrec {E#7} in S#9);E#11} in A#12[(var X#2)])
    -cpx-in1->                    (letrec {X#1=(var X#2);X#2=(letrec {E#7} in S#9);E#11} in A#12[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#2=(letrec {E#7} in S#9);E#11} in A#12[(var X#2)])
    -SR,llet-e1->                 (letrec {X#1=(var X#2);X#2=S#9;E#11;E#7} in A#12[(var X#2)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;X#6= (letrec {E#7} in S#9)
       ;E#11
     in
        A#12[(app A#13[(var X#6)] C#14[(var X#1)])]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#6= S#9
       ;E#11
       ;E#7
     in
        A#12[(app A#13[(var X#6)] C#14[(var X#2)])]
     )
  )

where

   Delta1 = {A#10,C#5}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#12[(app A#13[(var X#6)] C#14)]),
             ((var X#2),A#12[(app A#13[(var X#6)] C#14)]),
             (A#12[(app A#13[(var X#6)] C#14[(var X#2)])],(letrec {E#7} in [.])),
             [{X#1=(var X#2);E#11},(letrec {E#7} in [.])],
             ((var X#1),A#12[(app A#13[(var X#6)] C#14[[.]])]),
             ((var X#6),A#12[(app A#13[[.]] C#14[(var X#2)])]),
             ((var X#6),A#12[(app A#13[[.]] C#14[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),C#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#8   |->  {X#1=(var X#2);E#11},
           E#3   |->  {X#6=(letrec {E#7} in S#9);E#11},
           C#5   |->  A#12[(app A#13[(var X#6)] C#14)],
           A#10  |->  A#12[(app A#13 C#14[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#6=(letrec {E#7} in S#9);E#11} in A#12[(app A#13[(var X#6)] C#14[(var X#2)])])
    -cpx-in1->                    (letrec {X#1=(var X#2);X#6=(letrec {E#7} in S#9);E#11} in A#12[(app A#13[(var X#6)] C#14[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#6=(letrec {E#7} in S#9);E#11} in A#12[(app A#13[(var X#6)] C#14[(var X#2)])])
    -SR,llet-e1->                 (letrec {X#1=(var X#2);X#6=S#9;E#11;E#7} in A#12[(app A#13[(var X#6)] C#14[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#2);X#2=(letrec {E#7} in S#9);E#11} in (var X#1))
    ,
     (letrec {X#1=(var X#2);X#2=S#9;E#11;E#7} in (var X#2))
  )

where

   Delta1 = {}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#2),(letrec {E#7} in [.])),
             [{X#1=(var X#2);E#11},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),C#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#8   |->  {X#1=(var X#2);E#11},
           E#3   |->  {X#2=(letrec {E#7} in S#9);E#11},
           C#5   |->  [.],
           A#10  |->  [.],
           X#6   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#2=(letrec {E#7} in S#9);E#11} in (var X#2))
    -cpx-in1->                    (letrec {X#1=(var X#2);X#2=(letrec {E#7} in S#9);E#11} in (var X#1))
    ................................................................................
                                  (letrec {X#1=(var X#2);X#2=(letrec {E#7} in S#9);E#11} in (var X#2))
    -SR,llet-e1->                 (letrec {X#1=(var X#2);X#2=S#9;E#11;E#7} in (var X#2))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {E#8} in S#10)
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#14[(app A#15[(var X#7)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
     )
    ,
     (letrec
        X#6= S#10
       ;E#8
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#14[(app A#15[(var X#7)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
     )
  )

where

   Delta1 = {A#11,T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),
             (A#14[(app A#15[(var X#7)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])],(letrec {E#8} in [.])),
             [{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#14[(app A#15[[.]] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]),
             ((var X#6),[.]),
             ((var X#7),A#14[(app A#15[[.]] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#14[(app A#15[(var X#7)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#7)] T#16)],
           A#11  |->  A#14[(app A#15 T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#14[(app A#15[(var X#7)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -cpx-in1->                    (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#14[(app A#15[(var X#7)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])])
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#14[(app A#15[(var X#7)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#14[(app A#15[(var X#7)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {E#8} in T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#6= T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;E#8
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(letrec {E#8} in T#16);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)]),
           X#14  |->  X#6,
           E#15  |->  {E#9;EE#12[X#7,(var X#6)]},
           T#13  |->  (letrec {E#8} in T#16),
           S#10  |->  T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#8} in T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -cpx-in1->                    (letrec {X#6=(letrec {E#8} in T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec
                X#17= T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
               ;E#19
             in
                S#10
             )
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;X#6= S#10
       ;E#19
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#6),(letrec {X#17=T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#19;E#9;EE#12[X#7,(var X#6)]} in [.])),
             (A#11[(var X#7)],(letrec {X#17=T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#19} in [.])),
             [{E#9;EE#12[X#7,(var X#6)]},(letrec {X#17=T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#19} in [.])],
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(letrec {X#17=T#16;E#19} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)]),
           X#14  |->  X#6,
           E#15  |->  {E#9;EE#12[X#7,(var X#6)]},
           T#13  |->  (letrec {X#17=T#16;E#19} in S#10),
           E#8   |->  {X#17=T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#19},
           E#18  |->  {E#19}}

and instantiated rules:

                                  (letrec {X#6=(letrec {X#17=T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#19} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -cpx-in1->                    (letrec {X#6=(letrec {X#17=T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#19} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#6=(letrec {X#17=T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#19} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#17=T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=S#10;E#19;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#6= C#5[(var X#2)]
       ;E#3
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#6),(letrec {X#1=(var X#2);E#3;E#9;EE#12[X#7,(var X#6)]} in [.])),
             (A#11[(var X#7)],(letrec {X#1=(var X#2);E#3} in [.])),
             [{E#9;EE#12[X#7,(var X#6)]},(letrec {X#1=(var X#2);E#3} in [.])],
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=[.];E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)]),
           X#14  |->  X#6,
           E#15  |->  {E#9;EE#12[X#7,(var X#6)]},
           T#13  |->  [.],
           S#10  |->  C#5[(var X#2)],
           E#8   |->  {X#1=(var X#2);E#3}}

and instantiated rules:

                                  (letrec {X#6=(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -cpx-in1->                    (letrec {X#6=(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#6=(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#1=(var X#2);X#6=C#5[(var X#2)];E#3;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
       ;X#6= (letrec {E#8} in S#10)
       ;E#16
       ;EE#12[X#7,(var X#6)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;X#6= S#10
       ;E#16
       ;E#8
       ;EE#12[X#7,(var X#6)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#6),(letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16;E#8;EE#12[X#7,(var X#6)]} in [.])),
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#14=T#13;X#6=(letrec {E#8} in S#10);E#16;EE#12[X#7,(var X#6)]} in A#11[(var X#7)]),
           E#9   |->  {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16},
           E#15  |->  {X#6=(letrec {E#8} in S#10);E#16;EE#12[X#7,(var X#6)]}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(letrec {E#8} in S#10);E#16;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -cpx-in1->                    (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];X#6=(letrec {E#8} in S#10);E#16;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=(letrec {E#8} in S#10);E#16;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];X#6=S#10;E#16;E#8;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {E#8} in S#10)
       ;X#7= A#17[(app A#18[(var X#6)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#9
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#6= S#10
       ;X#7= A#17[(app A#18[(var X#6)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#8
       ;E#9
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#6),(letrec {X#7=A#17[(app A#18[(var X#6)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;E#9} in [.])),
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#7=A#17[(app A#18[(var X#6)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9},(letrec {E#8} in [.])],
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(letrec {E#8} in S#10);X#7=A#17[(app A#18[(var X#6)] T#19)];E#9} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]},
           X#14         |->  X#7,
           E#15         |->  {X#6=(letrec {E#8} in S#10);E#9},
           T#13         |->  A#17[(app A#18[(var X#6)] T#19)],
           A#16         |->  A#17[(app A#18 T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#8} in S#10);X#7=A#17[(app A#18[(var X#6)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9} in A#11[(var X#7)])
    -cpx-in1->                    (letrec {X#6=(letrec {E#8} in S#10);X#7=A#17[(app A#18[(var X#6)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#9} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);X#7=A#17[(app A#18[(var X#6)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;X#7=A#17[(app A#18[(var X#6)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;E#9} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {E#8} in S#10)
       ;X#7= A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#9
       ;EE#18[X#17,(var X#6)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#6= S#10
       ;X#7= A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#8
       ;E#9
       ;EE#18[X#17,(var X#6)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#6),(letrec {X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;E#9;EE#18[X#17,(var X#6)]} in [.])),
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9;EE#18[X#17,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(letrec {E#8} in S#10);X#7=A#19[(app A#20[(var X#17)] T#21)];E#9;EE#18[X#17,(var X#6)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#6=(letrec {E#8} in S#10);E#9;EE#18[X#17,(var X#6)]},
           T#13         |->  A#19[(app A#20[(var X#17)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#8} in S#10);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9;EE#18[X#17,(var X#6)]} in A#11[(var X#7)])
    -cpx-in1->                    (letrec {X#6=(letrec {E#8} in S#10);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#9;EE#18[X#17,(var X#6)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9;EE#18[X#17,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;E#9;EE#18[X#17,(var X#6)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;X#6= (letrec {E#8} in S#10)
       ;E#9
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,(var X#6)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;X#6= S#10
       ;E#8
       ;E#9
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,(var X#6)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#6),(letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]} in [.])),
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23)];X#6=(letrec {E#8} in S#10);E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#6=(letrec {E#8} in S#10);E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]},
           T#13         |->  A#21[(app A#22[(var X#18)] T#23)],
           A#16         |->  A#21[(app A#22 T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(letrec {E#8} in S#10);E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]} in A#11[(var X#7)])
    -cpx-in1->                    (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];X#6=(letrec {E#8} in S#10);E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(letrec {E#8} in S#10);E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=S#10;E#8;E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[(var X#6)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;X#6= (letrec {E#8} in S#10)
       ;E#9
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(var X#6)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;X#6= S#10
       ;E#8
       ;E#9
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             ((var X#6),(letrec {X#17=A#19[(app A#20[(var X#6)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#8;E#9;EE#18[X#7,(var X#17)]} in [.])),
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#17=A#19[(app A#20[(var X#6)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#9;EE#18[X#7,(var X#17)]},(letrec {E#8} in [.])],
             ((var X#1),C#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app A#20[(var X#6)] T#21)];X#6=(letrec {E#8} in S#10);E#9;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#6=(letrec {E#8} in S#10);E#9;EE#18[X#7,(var X#17)]},
           T#13         |->  A#19[(app A#20[(var X#6)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(var X#6)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(letrec {E#8} in S#10);E#9;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -cpx-in1->                    (letrec {X#17=A#19[(app A#20[(var X#6)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];X#6=(letrec {E#8} in S#10);E#9;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(var X#6)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=(letrec {E#8} in S#10);E#9;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#17=A#19[(app A#20[(var X#6)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];X#6=S#10;E#8;E#9;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#7)
       ;X#6= (letrec {E#8} in S#10)
       ;E#13
       ;EE#12[X#7,(var X#6)]
     in
        A#14[(var X#1)]
     )
    ,
     (letrec
        X#1= (var X#7)
       ;X#6= S#10
       ;E#13
       ;E#8
       ;EE#12[X#7,(var X#6)]
     in
        A#14[(var X#7)]
     )
  )

where

   Delta1 = {A#11,C#5,A#14}
   Delta2 = {E#8}
   Delta3 = {((var X#1),A#14[[.]]),
             ((var X#7),A#14[[.]]),
             ((var X#6),(letrec {X#1=(var X#7);E#13;E#8;EE#12[X#7,(var X#6)]} in [.])),
             (A#14[(var X#7)],(letrec {E#8} in [.])),
             [{X#1=(var X#7);E#13;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),A#14[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#14[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#9   |->  {X#1=(var X#7);E#13},
           E#3   |->  {X#6=(letrec {E#8} in S#10);E#13;EE#12[X#7,(var X#6)]},
           A#11  |->  A#14,
           C#5   |->  A#14[[.]],
           C#15  |->  [.],
           X#2   |->  X#7}

and instantiated rules:

                                  (letrec {X#1=(var X#7);X#6=(letrec {E#8} in S#10);E#13;EE#12[X#7,(var X#6)]} in A#14[(var X#7)])
    -cpx-in1->                    (letrec {X#1=(var X#7);X#6=(letrec {E#8} in S#10);E#13;EE#12[X#7,(var X#6)]} in A#14[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#7);X#6=(letrec {E#8} in S#10);E#13;EE#12[X#7,(var X#6)]} in A#14[(var X#7)])
    -SR,llet-e2->                 (letrec {X#1=(var X#7);X#6=S#10;E#13;E#8;EE#12[X#7,(var X#6)]} in A#14[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;X#6= (letrec {E#8} in S#10)
       ;E#13
       ;EE#12[X#2,(var X#6)]
     in
        A#14[(var X#1)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#6= S#10
       ;E#13
       ;E#8
       ;EE#12[X#2,(var X#6)]
     in
        A#14[(var X#2)]
     )
  )

where

   Delta1 = {A#11,C#5,A#14}
   Delta2 = {E#8}
   Delta3 = {((var X#1),A#14),
             ((var X#2),A#14),
             ((var X#6),(letrec {X#1=(var X#2);E#13;E#8;EE#12[X#2,(var X#6)]} in [.])),
             (A#14[(var X#2)],(letrec {E#8} in [.])),
             [{X#1=(var X#2);E#13;EE#12[X#2,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),A#14[[.]]),
             ((var X#6),[.]),
             ((var X#2),A#14[[.]]),
             ((var X#6),[.]),
             ((var X#2),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#9   |->  {X#1=(var X#2);E#13},
           E#3   |->  {X#6=(letrec {E#8} in S#10);E#13;EE#12[X#2,(var X#6)]},
           A#11  |->  A#14[[.]],
           C#5   |->  A#14,
           A#15  |->  [.],
           X#7   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#6=(letrec {E#8} in S#10);E#13;EE#12[X#2,(var X#6)]} in A#14[(var X#2)])
    -cpx-in1->                    (letrec {X#1=(var X#2);X#6=(letrec {E#8} in S#10);E#13;EE#12[X#2,(var X#6)]} in A#14[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#6=(letrec {E#8} in S#10);E#13;EE#12[X#2,(var X#6)]} in A#14[(var X#2)])
    -SR,llet-e2->                 (letrec {X#1=(var X#2);X#6=S#10;E#13;E#8;EE#12[X#2,(var X#6)]} in A#14[(var X#2)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;X#6= (letrec {E#8} in S#10)
       ;E#13
       ;EE#12[X#7,(var X#6)]
     in
        A#14[(app A#15[(var X#7)] C#16[(var X#1)])]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#6= S#10
       ;E#13
       ;E#8
       ;EE#12[X#7,(var X#6)]
     in
        A#14[(app A#15[(var X#7)] C#16[(var X#2)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {E#8}
   Delta3 = {((var X#1),A#14[(app A#15[(var X#7)] C#16)]),
             ((var X#2),A#14[(app A#15[(var X#7)] C#16)]),
             ((var X#6),(letrec {X#1=(var X#2);E#13;E#8;EE#12[X#7,(var X#6)]} in [.])),
             (A#14[(app A#15[(var X#7)] C#16[(var X#2)])],(letrec {E#8} in [.])),
             [{X#1=(var X#2);E#13;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),A#14[(app A#15[(var X#7)] C#16[[.]])]),
             ((var X#6),[.]),
             ((var X#7),A#14[(app A#15[[.]] C#16[(var X#2)])]),
             ((var X#6),[.]),
             ((var X#7),A#14[(app A#15[[.]] C#16[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#9   |->  {X#1=(var X#2);E#13},
           E#3   |->  {X#6=(letrec {E#8} in S#10);E#13;EE#12[X#7,(var X#6)]},
           C#5   |->  A#14[(app A#15[(var X#7)] C#16)],
           A#11  |->  A#14[(app A#15 C#16[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#6=(letrec {E#8} in S#10);E#13;EE#12[X#7,(var X#6)]} in A#14[(app A#15[(var X#7)] C#16[(var X#2)])])
    -cpx-in1->                    (letrec {X#1=(var X#2);X#6=(letrec {E#8} in S#10);E#13;EE#12[X#7,(var X#6)]} in A#14[(app A#15[(var X#7)] C#16[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#6=(letrec {E#8} in S#10);E#13;EE#12[X#7,(var X#6)]} in A#14[(app A#15[(var X#7)] C#16[(var X#2)])])
    -SR,llet-e2->                 (letrec {X#1=(var X#2);X#6=S#10;E#13;E#8;EE#12[X#7,(var X#6)]} in A#14[(app A#15[(var X#7)] C#16[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;X#6= (letrec {E#8} in S#10)
       ;E#13
       ;EE#12[X#2,(var X#6)]
     in
        (var X#1)
     )
    ,
     (letrec {X#1=(var X#2);X#6=S#10;E#13;E#8;EE#12[X#2,(var X#6)]} in (var X#2))
  )

where

   Delta1 = {}
   Delta2 = {E#8}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#6),(letrec {X#1=(var X#2);E#13;E#8;EE#12[X#2,(var X#6)]} in [.])),
             ((var X#2),(letrec {E#8} in [.])),
             [{X#1=(var X#2);E#13;EE#12[X#2,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),[.]),
             ((var X#6),[.]),
             ((var X#2),[.]),
             ((var X#6),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#9   |->  {X#1=(var X#2);E#13},
           E#3   |->  {X#6=(letrec {E#8} in S#10);E#13;EE#12[X#2,(var X#6)]},
           C#5   |->  [.],
           A#11  |->  [.],
           X#7   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#6=(letrec {E#8} in S#10);E#13;EE#12[X#2,(var X#6)]} in (var X#2))
    -cpx-in1->                    (letrec {X#1=(var X#2);X#6=(letrec {E#8} in S#10);E#13;EE#12[X#2,(var X#6)]} in (var X#1))
    ................................................................................
                                  (letrec {X#1=(var X#2);X#6=(letrec {E#8} in S#10);E#13;EE#12[X#2,(var X#6)]} in (var X#2))
    -SR,llet-e2->                 (letrec {X#1=(var X#2);X#6=S#10;E#13;E#8;EE#12[X#2,(var X#6)]} in (var X#2))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (letrec {E#8} in S#10)
       ;X#7= (var X#2)
       ;E#9
     in
        A#14[(app A#15[(var X#7)] C#16[(var X#7)])]
     )
    ,
     (letrec
        X#2= S#10
       ;X#7= (var X#2)
       ;E#8
       ;E#9
     in
        A#14[(app A#15[(var X#7)] C#16[(var X#2)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {E#8}
   Delta3 = {((var X#7),A#14[(app A#15[(var X#7)] C#16)]),
             ((var X#2),A#14[(app A#15[(var X#7)] C#16)]),
             ((var X#2),(letrec {X#7=(var X#2);E#8;E#9} in [.])),
             (A#14[(app A#15[(var X#7)] C#16[(var X#2)])],(letrec {E#8} in [.])),
             [{X#7=(var X#2);E#9},(letrec {E#8} in [.])],
             ((var X#7),A#14[(app A#15[(var X#7)] C#16[[.]])]),
             ((var X#2),[.]),
             ((var X#7),A#14[(app A#15[[.]] C#16[(var X#2)])]),
             ((var X#2),[.]),
             ((var X#7),A#14[(app A#15[[.]] C#16[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#7,
           E#3          |->  {X#2=(letrec {E#8} in S#10);E#9},
           A#13         |->  [.],
           X#6          |->  X#2,
           C#5          |->  A#14[(app A#15[(var X#7)] C#16)],
           A#11         |->  A#14[(app A#15 C#16[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#2=(letrec {E#8} in S#10);X#7=(var X#2);E#9} in A#14[(app A#15[(var X#7)] C#16[(var X#2)])])
    -cpx-in1->                    (letrec {X#2=(letrec {E#8} in S#10);X#7=(var X#2);E#9} in A#14[(app A#15[(var X#7)] C#16[(var X#7)])])
    ................................................................................
                                  (letrec {X#2=(letrec {E#8} in S#10);X#7=(var X#2);E#9} in A#14[(app A#15[(var X#7)] C#16[(var X#2)])])
    -SR,llet-e2->                 (letrec {X#2=S#10;X#7=(var X#2);E#8;E#9} in A#14[(app A#15[(var X#7)] C#16[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {E#8} in S#10)
       ;X#7= (var X#2)
       ;E#9
       ;EE#15[X#2,(var X#6)]
     in
        A#16[(app A#17[(var X#7)] C#18[(var X#7)])]
     )
    ,
     (letrec
        X#6= S#10
       ;X#7= (var X#2)
       ;E#8
       ;E#9
       ;EE#15[X#2,(var X#6)]
     in
        A#16[(app A#17[(var X#7)] C#18[(var X#2)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {E#8}
   Delta3 = {((var X#7),A#16[(app A#17[(var X#7)] C#18)]),
             ((var X#2),A#16[(app A#17[(var X#7)] C#18)]),
             ((var X#6),(letrec {X#7=(var X#2);E#8;E#9;EE#15[X#2,(var X#6)]} in [.])),
             (A#16[(app A#17[(var X#7)] C#18[(var X#2)])],(letrec {E#8} in [.])),
             [{X#7=(var X#2);E#9;EE#15[X#2,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#7),A#16[(app A#17[(var X#7)] C#18[[.]])]),
             ((var X#6),[.]),
             ((var X#7),A#16[(app A#17[[.]] C#18[(var X#2)])]),
             ((var X#6),[.]),
             ((var X#7),A#16[(app A#17[[.]] C#18[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           EE#12[.1,.2] |-> {[.1]=(var X#2);EE#15[X#2,[.2]]},
           X#1          |->  X#7,
           E#3          |->  {X#6=(letrec {E#8} in S#10);E#9;EE#15[X#2,(var X#6)]},
           A#13         |->  [.],
           X#14         |->  X#2,
           C#5          |->  A#16[(app A#17[(var X#7)] C#18)],
           A#11         |->  A#16[(app A#17 C#18[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#8} in S#10);X#7=(var X#2);E#9;EE#15[X#2,(var X#6)]} in A#16[(app A#17[(var X#7)] C#18[(var X#2)])])
    -cpx-in1->                    (letrec {X#6=(letrec {E#8} in S#10);X#7=(var X#2);E#9;EE#15[X#2,(var X#6)]} in A#16[(app A#17[(var X#7)] C#18[(var X#7)])])
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);X#7=(var X#2);E#9;EE#15[X#2,(var X#6)]} in A#16[(app A#17[(var X#7)] C#18[(var X#2)])])
    -SR,llet-e2->                 (letrec {X#6=S#10;X#7=(var X#2);E#8;E#9;EE#15[X#2,(var X#6)]} in A#16[(app A#17[(var X#7)] C#18[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= (var X#2)
       ;X#6= (letrec {E#8} in S#10)
       ;E#9
       ;EE#16[X#7,(var X#14)]
       ;EE#17[X#2,(var X#6)]
     in
        A#18[(app A#19[(var X#7)] C#20[(var X#14)])]
     )
    ,
     (letrec
        X#14= (var X#2)
       ;X#6= S#10
       ;E#8
       ;E#9
       ;EE#16[X#7,(var X#14)]
       ;EE#17[X#2,(var X#6)]
     in
        A#18[(app A#19[(var X#7)] C#20[(var X#2)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {E#8}
   Delta3 = {((var X#14),A#18[(app A#19[(var X#7)] C#20)]),
             ((var X#2),A#18[(app A#19[(var X#7)] C#20)]),
             ((var X#6),(letrec {X#14=(var X#2);E#8;E#9;EE#16[X#7,(var X#14)];EE#17[X#2,(var X#6)]} in [.])),
             (A#18[(app A#19[(var X#7)] C#20[(var X#2)])],(letrec {E#8} in [.])),
             [{X#14=(var X#2);E#9;EE#16[X#7,(var X#14)];EE#17[X#2,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#14),A#18[(app A#19[(var X#7)] C#20[[.]])]),
             ((var X#6),[.]),
             ((var X#7),A#18[(app A#19[[.]] C#20[(var X#2)])]),
             ((var X#6),[.]),
             ((var X#7),A#18[(app A#19[[.]] C#20[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           EE#12[.1,.2] |-> {X#14=(var X#2);EE#16[[.1],(var X#14)];EE#17[X#2,[.2]]},
           X#1          |->  X#14,
           E#3          |->  {X#6=(letrec {E#8} in S#10);E#9;EE#16[X#7,(var X#14)];EE#17[X#2,(var X#6)]},
           A#13         |->  [.],
           X#15         |->  X#2,
           C#5          |->  A#18[(app A#19[(var X#7)] C#20)],
           A#11         |->  A#18[(app A#19 C#20[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#14=(var X#2);X#6=(letrec {E#8} in S#10);E#9;EE#16[X#7,(var X#14)];EE#17[X#2,(var X#6)]} in A#18[(app A#19[(var X#7)] C#20[(var X#2)])])
    -cpx-in1->                    (letrec {X#14=(var X#2);X#6=(letrec {E#8} in S#10);E#9;EE#16[X#7,(var X#14)];EE#17[X#2,(var X#6)]} in A#18[(app A#19[(var X#7)] C#20[(var X#14)])])
    ................................................................................
                                  (letrec {X#14=(var X#2);X#6=(letrec {E#8} in S#10);E#9;EE#16[X#7,(var X#14)];EE#17[X#2,(var X#6)]} in A#18[(app A#19[(var X#7)] C#20[(var X#2)])])
    -SR,llet-e2->                 (letrec {X#14=(var X#2);X#6=S#10;E#8;E#9;EE#16[X#7,(var X#14)];EE#17[X#2,(var X#6)]} in A#18[(app A#19[(var X#7)] C#20[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= (var X#2)
       ;X#2= (letrec {E#8} in S#10)
       ;E#9
       ;EE#15[X#7,(var X#14)]
     in
        A#16[(app A#17[(var X#7)] C#18[(var X#14)])]
     )
    ,
     (letrec
        X#14= (var X#2)
       ;X#2= S#10
       ;E#8
       ;E#9
       ;EE#15[X#7,(var X#14)]
     in
        A#16[(app A#17[(var X#7)] C#18[(var X#2)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {E#8}
   Delta3 = {((var X#14),A#16[(app A#17[(var X#7)] C#18)]),
             ((var X#2),A#16[(app A#17[(var X#7)] C#18)]),
             ((var X#2),(letrec {X#14=(var X#2);E#8;E#9;EE#15[X#7,(var X#14)]} in [.])),
             (A#16[(app A#17[(var X#7)] C#18[(var X#2)])],(letrec {E#8} in [.])),
             [{X#14=(var X#2);E#9;EE#15[X#7,(var X#14)]},(letrec {E#8} in [.])],
             ((var X#14),A#16[(app A#17[(var X#7)] C#18[[.]])]),
             ((var X#2),[.]),
             ((var X#7),A#16[(app A#17[[.]] C#18[(var X#2)])]),
             ((var X#2),[.]),
             ((var X#7),A#16[(app A#17[[.]] C#18[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),C#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           EE#12[.1,.2] |-> {X#14=[.2];EE#15[[.1],(var X#14)]},
           X#1          |->  X#14,
           E#3          |->  {X#2=(letrec {E#8} in S#10);E#9;EE#15[X#7,(var X#14)]},
           A#13         |->  [.],
           X#6          |->  X#2,
           C#5          |->  A#16[(app A#17[(var X#7)] C#18)],
           A#11         |->  A#16[(app A#17 C#18[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#14=(var X#2);X#2=(letrec {E#8} in S#10);E#9;EE#15[X#7,(var X#14)]} in A#16[(app A#17[(var X#7)] C#18[(var X#2)])])
    -cpx-in1->                    (letrec {X#14=(var X#2);X#2=(letrec {E#8} in S#10);E#9;EE#15[X#7,(var X#14)]} in A#16[(app A#17[(var X#7)] C#18[(var X#14)])])
    ................................................................................
                                  (letrec {X#14=(var X#2);X#2=(letrec {E#8} in S#10);E#9;EE#15[X#7,(var X#14)]} in A#16[(app A#17[(var X#7)] C#18[(var X#2)])])
    -SR,llet-e2->                 (letrec {X#14=(var X#2);X#2=S#10;E#8;E#9;EE#15[X#7,(var X#14)]} in A#16[(app A#17[(var X#7)] C#18[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     A#10[(app (letrec {E#6} in T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#7)]
    ,
     A#10[(letrec {E#6} in (app T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#7))]
  )

where

   Delta1 = {T#12,T#11,A#9,T#4,A#10}
   Delta2 = {E#6}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#7,(letrec {E#6} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {A#9   |->  A#10,
           T#4   |->  A#10[(app (letrec {E#6} in T#13) S#7)],
           T#11  |->  (app (letrec {E#6} in T#13) S#7),
           T#12  |->  (letrec {E#6} in T#13),
           S#8   |->  T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  A#10[(app (letrec {E#6} in T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#7)]
    -cpx-in1->                    A#10[(app (letrec {E#6} in T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#7)]
    ................................................................................
                                  A#10[(app (letrec {E#6} in T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#7)]
    -SR,lapp1->                   A#10[(letrec {E#6} in (app T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#7))]
    

================================================================================
Critical Pair:

  (
     A#10[(app (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#16} in S#8) S#7)]
    ,
     A#10[(letrec
              X#14= T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
             ;E#16
           in
              (app S#8 S#7)
           )]
  )

where

   Delta1 = {T#12,T#11,A#9,T#4,A#10}
   Delta2 = {E#6}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#7,(letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#7,(letrec {E#6} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {A#9   |->  A#10,
           T#4   |->  A#10[(app (letrec {X#14=T#13;E#16} in S#8) S#7)],
           T#11  |->  (app (letrec {X#14=T#13;E#16} in S#8) S#7),
           T#12  |->  (letrec {X#14=T#13;E#16} in S#8),
           E#6   |->  {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  A#10[(app (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16} in S#8) S#7)]
    -cpx-in1->                    A#10[(app (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#16} in S#8) S#7)]
    ................................................................................
                                  A#10[(app (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16} in S#8) S#7)]
    -SR,lapp1->                   A#10[(letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16} in (app S#8 S#7))]
    

================================================================================
Critical Pair:

  (
     A#10[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#7)]
    ,
     A#10[(letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#7))]
  )

where

   Delta1 = {T#11,A#9,T#4,A#10}
   Delta2 = {E#6}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#7,(letrec {X#1=(var X#2);E#3} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#7,(letrec {E#6} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {A#9   |->  A#10,
           T#4   |->  A#10[(app [.] S#7)],
           T#11  |->  (app [.] S#7),
           T#12  |->  [.],
           S#8   |->  C#5[(var X#2)],
           E#6   |->  {X#1=(var X#2);E#3}}

and instantiated rules:

                                  A#10[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#7)]
    -cpx-in1->                    A#10[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#7)]
    ................................................................................
                                  A#10[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#7)]
    -SR,lapp1->                   A#10[(letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#7))]
    

================================================================================
Critical Pair:

  (
     A#10[(app (letrec {E#6} in S#8) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
    ,
     A#10[(letrec {E#6} in (app S#8 T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]))]
  )

where

   Delta1 = {T#11,A#9,T#4,A#10}
   Delta2 = {E#6}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {E#6} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#7,(letrec {E#6} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {A#9   |->  A#10,
           T#4   |->  A#10[(app (letrec {E#6} in S#8) T#12)],
           T#11  |->  (app (letrec {E#6} in S#8) T#12),
           S#7   |->  T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  A#10[(app (letrec {E#6} in S#8) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
    -cpx-in1->                    A#10[(app (letrec {E#6} in S#8) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
    ................................................................................
                                  A#10[(app (letrec {E#6} in S#8) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
    -SR,lapp1->                   A#10[(letrec {E#6} in (app S#8 T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]))]
    

================================================================================
Critical Pair:

  (
     A#10[(app A#11[(app (letrec {E#6} in S#8) S#7)] T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
    ,
     A#10[(app A#11[(letrec {E#6} in (app S#8 S#7))] T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
  )

where

   Delta1 = {A#9,T#4}
   Delta2 = {E#6}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#7,(letrec {E#6} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4  |->  A#10[(app A#11[(app (letrec {E#6} in S#8) S#7)] T#12)],
           A#9  |->  A#10[(app A#11 T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  A#10[(app A#11[(app (letrec {E#6} in S#8) S#7)] T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
    -cpx-in1->                    A#10[(app A#11[(app (letrec {E#6} in S#8) S#7)] T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
    ................................................................................
                                  A#10[(app A#11[(app (letrec {E#6} in S#8) S#7)] T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
    -SR,lapp1->                   A#10[(app A#11[(letrec {E#6} in (app S#8 S#7))] T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#6} in T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#7)
    ,
     (letrec {E#6} in (app T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#7))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#6}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#7,(letrec {E#6} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {A#9   |->  [.],
           T#4   |->  (app (letrec {E#6} in T#11) S#7),
           T#10  |->  (letrec {E#6} in T#11),
           S#8   |->  T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (app (letrec {E#6} in T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#7)
    -cpx-in1->                    (app (letrec {E#6} in T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#7)
    ................................................................................
                                  (app (letrec {E#6} in T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#7)
    -SR,lapp1->                   (letrec {E#6} in (app T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#7))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#14} in S#8) S#7)
    ,
     (letrec
        X#12= T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;E#14
     in
        (app S#8 S#7)
     )
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#6}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#7,(letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#7,(letrec {E#6} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {A#9   |->  [.],
           T#4   |->  (app (letrec {X#12=T#11;E#14} in S#8) S#7),
           T#10  |->  (letrec {X#12=T#11;E#14} in S#8),
           E#6   |->  {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14},
           E#13  |->  {E#14}}

and instantiated rules:

                                  (app (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14} in S#8) S#7)
    -cpx-in1->                    (app (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#14} in S#8) S#7)
    ................................................................................
                                  (app (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14} in S#8) S#7)
    -SR,lapp1->                   (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14} in (app S#8 S#7))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#7)
    ,
     (letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#7))
  )

where

   Delta1 = {T#4}
   Delta2 = {E#6}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#7,(letrec {X#1=(var X#2);E#3} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#7,(letrec {E#6} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {A#9   |->  [.],
           T#4   |->  (app [.] S#7),
           T#10  |->  [.],
           S#8   |->  C#5[(var X#2)],
           E#6   |->  {X#1=(var X#2);E#3}}

and instantiated rules:

                                  (app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#7)
    -cpx-in1->                    (app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#7)
    ................................................................................
                                  (app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#7)
    -SR,lapp1->                   (letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#7))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#6} in S#8) T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])
    ,
     (letrec {E#6} in (app S#8 T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]))
  )

where

   Delta1 = {T#4}
   Delta2 = {E#6}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {E#6} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#7,(letrec {E#6} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {A#9  |->  [.],
           T#4  |->  (app (letrec {E#6} in S#8) T#10),
           S#7  |->  T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (app (letrec {E#6} in S#8) T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])
    -cpx-in1->                    (app (letrec {E#6} in S#8) T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])
    ................................................................................
                                  (app (letrec {E#6} in S#8) T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])
    -SR,lapp1->                   (letrec {E#6} in (app S#8 T#10[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#12[(app (letrec {E#7} in T#15[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#8)]
     )
    ,
     (letrec
        E#6
     in
        A#12[(letrec {E#7} in (app T#15[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#8))]
     )
  )

where

   Delta1 = {T#14,T#13,A#10,T#11,T#4,A#12}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#12[(app (letrec {E#7} in T#15) S#8)]),
           A#10  |->  A#12,
           T#11  |->  A#12[(app (letrec {E#7} in T#15) S#8)],
           T#13  |->  (app (letrec {E#7} in T#15) S#8),
           T#14  |->  (letrec {E#7} in T#15),
           S#9   |->  T#15[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {E#6} in A#12[(app (letrec {E#7} in T#15[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#8)])
    -cpx-in1->                    (letrec {E#6} in A#12[(app (letrec {E#7} in T#15[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#8)])
    ................................................................................
                                  (letrec {E#6} in A#12[(app (letrec {E#7} in T#15[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#12[(letrec {E#7} in (app T#15[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#8))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#12[(app (letrec {X#16=T#15[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#18} in S#9) S#8)]
     )
    ,
     (letrec
        E#6
     in
        A#12[(letrec
                 X#16= T#15[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
                ;E#18
              in
                 (app S#9 S#8)
              )]
     )
  )

where

   Delta1 = {T#14,T#13,A#10,T#11,T#4,A#12}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#8,(letrec {X#16=T#15[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#18} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#12[(app (letrec {X#16=T#15;E#18} in S#9) S#8)]),
           A#10  |->  A#12,
           T#11  |->  A#12[(app (letrec {X#16=T#15;E#18} in S#9) S#8)],
           T#13  |->  (app (letrec {X#16=T#15;E#18} in S#9) S#8),
           T#14  |->  (letrec {X#16=T#15;E#18} in S#9),
           E#7   |->  {X#16=T#15[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {E#6} in A#12[(app (letrec {X#16=T#15[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#18} in S#9) S#8)])
    -cpx-in1->                    (letrec {E#6} in A#12[(app (letrec {X#16=T#15[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#18} in S#9) S#8)])
    ................................................................................
                                  (letrec {E#6} in A#12[(app (letrec {X#16=T#15[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#18} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#12[(letrec {X#16=T#15[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#18} in (app S#9 S#8))])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in A#12[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#8)])
    ,
     (letrec {E#6} in A#12[(letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#8))])
  )

where

   Delta1 = {T#13,A#10,T#11,T#4,A#12}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#8,(letrec {X#1=(var X#2);E#3} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#12[(app [.] S#8)]),
           A#10  |->  A#12,
           T#11  |->  A#12[(app [.] S#8)],
           T#13  |->  (app [.] S#8),
           T#14  |->  [.],
           S#9   |->  C#5[(var X#2)],
           E#7   |->  {X#1=(var X#2);E#3}}

and instantiated rules:

                                  (letrec {E#6} in A#12[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#8)])
    -cpx-in1->                    (letrec {E#6} in A#12[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#8)])
    ................................................................................
                                  (letrec {E#6} in A#12[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#12[(letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#8))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#12[(app (letrec {E#7} in S#9) T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
     )
    ,
     (letrec
        E#6
     in
        A#12[(letrec {E#7} in (app S#9 T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]))]
     )
  )

where

   Delta1 = {T#13,A#10,T#11,T#4,A#12}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {E#7} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#12[(app (letrec {E#7} in S#9) T#14)]),
           A#10  |->  A#12,
           T#11  |->  A#12[(app (letrec {E#7} in S#9) T#14)],
           T#13  |->  (app (letrec {E#7} in S#9) T#14),
           S#8   |->  T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {E#6} in A#12[(app (letrec {E#7} in S#9) T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -cpx-in1->                    (letrec {E#6} in A#12[(app (letrec {E#7} in S#9) T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])])
    ................................................................................
                                  (letrec {E#6} in A#12[(app (letrec {E#7} in S#9) T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -SR,lapp2->                   (letrec {E#6} in A#12[(letrec {E#7} in (app S#9 T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
     )
    ,
     (letrec
        E#6
     in
        A#12[(app A#13[(letrec {E#7} in (app S#9 S#8))] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
     )
  )

where

   Delta1 = {A#10,T#11,T#4}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] T#14)]),
           T#11  |->  A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] T#14)],
           A#10  |->  A#12[(app A#13 T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {E#6} in A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -cpx-in1->                    (letrec {E#6} in A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])])
    ................................................................................
                                  (letrec {E#6} in A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -SR,lapp2->                   (letrec {E#6} in A#12[(app A#13[(letrec {E#7} in (app S#9 S#8))] T#14[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        (app (letrec {E#7} in T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#8)
     )
    ,
     (letrec
        E#6
     in
        (letrec {E#7} in (app T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#8))
     )
  )

where

   Delta1 = {T#12,T#11,T#4}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in (app (letrec {E#7} in T#13) S#8)),
           A#10  |->  [.],
           T#11  |->  (app (letrec {E#7} in T#13) S#8),
           T#12  |->  (letrec {E#7} in T#13),
           S#9   |->  T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {E#6} in (app (letrec {E#7} in T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#8))
    -cpx-in1->                    (letrec {E#6} in (app (letrec {E#7} in T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#8))
    ................................................................................
                                  (letrec {E#6} in (app (letrec {E#7} in T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#8))
    -SR,lapp2->                   (letrec {E#6} in (letrec {E#7} in (app T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#8)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        (app (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#16} in S#9) S#8)
     )
    ,
     (letrec
        E#6
     in
        (letrec
           X#14= T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
          ;E#16
        in
           (app S#9 S#8)
        )
     )
  )

where

   Delta1 = {T#12,T#11,T#4}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#8,(letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in (app (letrec {X#14=T#13;E#16} in S#9) S#8)),
           A#10  |->  [.],
           T#11  |->  (app (letrec {X#14=T#13;E#16} in S#9) S#8),
           T#12  |->  (letrec {X#14=T#13;E#16} in S#9),
           E#7   |->  {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {E#6} in (app (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16} in S#9) S#8))
    -cpx-in1->                    (letrec {E#6} in (app (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#16} in S#9) S#8))
    ................................................................................
                                  (letrec {E#6} in (app (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16} in S#9) S#8))
    -SR,lapp2->                   (letrec {E#6} in (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16} in (app S#9 S#8)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#8))
    ,
     (letrec {E#6} in (letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#8)))
  )

where

   Delta1 = {T#11,T#4}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#8,(letrec {X#1=(var X#2);E#3} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in (app [.] S#8)),
           A#10  |->  [.],
           T#11  |->  (app [.] S#8),
           T#12  |->  [.],
           S#9   |->  C#5[(var X#2)],
           E#7   |->  {X#1=(var X#2);E#3}}

and instantiated rules:

                                  (letrec {E#6} in (app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#8))
    -cpx-in1->                    (letrec {E#6} in (app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#8))
    ................................................................................
                                  (letrec {E#6} in (app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#8))
    -SR,lapp2->                   (letrec {E#6} in (letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#8)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        (app (letrec {E#7} in S#9) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])
     )
    ,
     (letrec
        E#6
     in
        (letrec {E#7} in (app S#9 T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]))
     )
  )

where

   Delta1 = {T#11,T#4}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {E#7} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in (app (letrec {E#7} in S#9) T#12)),
           A#10  |->  [.],
           T#11  |->  (app (letrec {E#7} in S#9) T#12),
           S#8   |->  T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {E#6} in (app (letrec {E#7} in S#9) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]))
    -cpx-in1->                    (letrec {E#6} in (app (letrec {E#7} in S#9) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]))
    ................................................................................
                                  (letrec {E#6} in (app (letrec {E#7} in S#9) T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]))
    -SR,lapp2->                   (letrec {E#6} in (letrec {E#7} in (app S#9 T#12[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#12= T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
       ;E#14
     in
        A#10[(app (letrec {E#7} in S#9) S#8)]
     )
    ,
     (letrec
        X#12= T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;E#14
     in
        A#10[(letrec {E#7} in (app S#9 S#8))]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),C#5[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#12=T#11;E#14} in A#10[(app (letrec {E#7} in S#9) S#8)]),
           E#6   |->  {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14},
           E#13  |->  {E#14}}

and instantiated rules:

                                  (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -cpx-in1->                    (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#14} in A#10[(app (letrec {E#7} in S#9) S#8)])
    ................................................................................
                                  (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {X#12=T#11[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#14} in A#10[(letrec {E#7} in (app S#9 S#8))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;E#11
     in
        A#12[(app (letrec {E#7} in C#15[(var X#1)]) S#8)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;E#11
     in
        A#12[(letrec {E#7} in (app C#15[(var X#2)] S#8))]
     )
  )

where

   Delta1 = {C#14,C#13,A#10,C#5,A#12}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),A#12[(app (letrec {E#7} in C#15) S#8)]),
             ((var X#2),A#12[(app (letrec {E#7} in C#15) S#8)]),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#12[(app (letrec {E#7} in C#15[[.]]) S#8)])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#6   |->  {X#1=(var X#2);E#11},
           E#3   |->  {E#11},
           A#10  |->  A#12,
           C#5   |->  A#12[(app (letrec {E#7} in C#15) S#8)],
           C#13  |->  (app (letrec {E#7} in C#15) S#8),
           C#14  |->  (letrec {E#7} in C#15),
           S#9   |->  C#15[(var X#2)]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#11} in A#12[(app (letrec {E#7} in C#15[(var X#2)]) S#8)])
    -cpx-in1->                    (letrec {X#1=(var X#2);E#11} in A#12[(app (letrec {E#7} in C#15[(var X#1)]) S#8)])
    ................................................................................
                                  (letrec {X#1=(var X#2);E#11} in A#12[(app (letrec {E#7} in C#15[(var X#2)]) S#8)])
    -SR,lapp2->                   (letrec {X#1=(var X#2);E#11} in A#12[(letrec {E#7} in (app C#15[(var X#2)] S#8))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;E#11
     in
        A#12[(app (letrec {X#16=C#15[(var X#1)];E#18} in S#9) S#8)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;E#11
     in
        A#12[(letrec {X#16=C#15[(var X#2)];E#18} in (app S#9 S#8))]
     )
  )

where

   Delta1 = {C#14,C#13,A#10,C#5,A#12}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),A#12[(app (letrec {X#16=C#15;E#18} in S#9) S#8)]),
             ((var X#2),A#12[(app (letrec {X#16=C#15;E#18} in S#9) S#8)]),
             (S#8,(letrec {X#16=C#15[(var X#2)];E#18} in [.])),
             ((var X#1),A#12[(app (letrec {X#16=C#15[[.]];E#18} in S#9) S#8)])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#6   |->  {X#1=(var X#2);E#11},
           E#3   |->  {E#11},
           A#10  |->  A#12,
           C#5   |->  A#12[(app (letrec {X#16=C#15;E#18} in S#9) S#8)],
           C#13  |->  (app (letrec {X#16=C#15;E#18} in S#9) S#8),
           C#14  |->  (letrec {X#16=C#15;E#18} in S#9),
           E#7   |->  {X#16=C#15[(var X#2)];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#11} in A#12[(app (letrec {X#16=C#15[(var X#2)];E#18} in S#9) S#8)])
    -cpx-in1->                    (letrec {X#1=(var X#2);E#11} in A#12[(app (letrec {X#16=C#15[(var X#1)];E#18} in S#9) S#8)])
    ................................................................................
                                  (letrec {X#1=(var X#2);E#11} in A#12[(app (letrec {X#16=C#15[(var X#2)];E#18} in S#9) S#8)])
    -SR,lapp2->                   (letrec {X#1=(var X#2);E#11} in A#12[(letrec {X#16=C#15[(var X#2)];E#18} in (app S#9 S#8))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;E#11
     in
        A#12[(app (letrec {E#7} in S#9) C#14[(var X#1)])]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;E#11
     in
        A#12[(letrec {E#7} in (app S#9 C#14[(var X#2)]))]
     )
  )

where

   Delta1 = {C#13,A#10,C#5,A#12}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),A#12[(app (letrec {E#7} in S#9) C#14)]),
             ((var X#2),A#12[(app (letrec {E#7} in S#9) C#14)]),
             (C#14[(var X#2)],(letrec {E#7} in [.])),
             ((var X#1),A#12[(app (letrec {E#7} in S#9) C#14[[.]])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#6   |->  {X#1=(var X#2);E#11},
           E#3   |->  {E#11},
           A#10  |->  A#12,
           C#5   |->  A#12[(app (letrec {E#7} in S#9) C#14)],
           C#13  |->  (app (letrec {E#7} in S#9) C#14),
           S#8   |->  C#14[(var X#2)]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#11} in A#12[(app (letrec {E#7} in S#9) C#14[(var X#2)])])
    -cpx-in1->                    (letrec {X#1=(var X#2);E#11} in A#12[(app (letrec {E#7} in S#9) C#14[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(var X#2);E#11} in A#12[(app (letrec {E#7} in S#9) C#14[(var X#2)])])
    -SR,lapp2->                   (letrec {X#1=(var X#2);E#11} in A#12[(letrec {E#7} in (app S#9 C#14[(var X#2)]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;E#11
     in
        A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] C#14[(var X#1)])]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;E#11
     in
        A#12[(app A#13[(letrec {E#7} in (app S#9 S#8))] C#14[(var X#2)])]
     )
  )

where

   Delta1 = {A#10,C#5}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] C#14)]),
             ((var X#2),A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] C#14)]),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] C#14[[.]])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#6   |->  {X#1=(var X#2);E#11},
           E#3   |->  {E#11},
           C#5   |->  A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] C#14)],
           A#10  |->  A#12[(app A#13 C#14[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#11} in A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] C#14[(var X#2)])])
    -cpx-in1->                    (letrec {X#1=(var X#2);E#11} in A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] C#14[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(var X#2);E#11} in A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] C#14[(var X#2)])])
    -SR,lapp2->                   (letrec {X#1=(var X#2);E#11} in A#12[(app A#13[(letrec {E#7} in (app S#9 S#8))] C#14[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#2);E#11} in (app (letrec {E#7} in C#13[(var X#1)]) S#8))
    ,
     (letrec {X#1=(var X#2);E#11} in (letrec {E#7} in (app C#13[(var X#2)] S#8)))
  )

where

   Delta1 = {C#12,C#5}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in C#13) S#8)),
             ((var X#2),(app (letrec {E#7} in C#13) S#8)),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in C#13[[.]]) S#8))}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#6   |->  {X#1=(var X#2);E#11},
           E#3   |->  {E#11},
           A#10  |->  [.],
           C#5   |->  (app (letrec {E#7} in C#13) S#8),
           C#12  |->  (letrec {E#7} in C#13),
           S#9   |->  C#13[(var X#2)]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#11} in (app (letrec {E#7} in C#13[(var X#2)]) S#8))
    -cpx-in1->                    (letrec {X#1=(var X#2);E#11} in (app (letrec {E#7} in C#13[(var X#1)]) S#8))
    ................................................................................
                                  (letrec {X#1=(var X#2);E#11} in (app (letrec {E#7} in C#13[(var X#2)]) S#8))
    -SR,lapp2->                   (letrec {X#1=(var X#2);E#11} in (letrec {E#7} in (app C#13[(var X#2)] S#8)))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;E#11
     in
        (app (letrec {X#14=C#13[(var X#1)];E#16} in S#9) S#8)
     )
    ,
     (letrec
        X#1= (var X#2)
       ;E#11
     in
        (letrec {X#14=C#13[(var X#2)];E#16} in (app S#9 S#8))
     )
  )

where

   Delta1 = {C#12,C#5}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),(app (letrec {X#14=C#13;E#16} in S#9) S#8)),
             ((var X#2),(app (letrec {X#14=C#13;E#16} in S#9) S#8)),
             (S#8,(letrec {X#14=C#13[(var X#2)];E#16} in [.])),
             ((var X#1),(app (letrec {X#14=C#13[[.]];E#16} in S#9) S#8))}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#6   |->  {X#1=(var X#2);E#11},
           E#3   |->  {E#11},
           A#10  |->  [.],
           C#5   |->  (app (letrec {X#14=C#13;E#16} in S#9) S#8),
           C#12  |->  (letrec {X#14=C#13;E#16} in S#9),
           E#7   |->  {X#14=C#13[(var X#2)];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#11} in (app (letrec {X#14=C#13[(var X#2)];E#16} in S#9) S#8))
    -cpx-in1->                    (letrec {X#1=(var X#2);E#11} in (app (letrec {X#14=C#13[(var X#1)];E#16} in S#9) S#8))
    ................................................................................
                                  (letrec {X#1=(var X#2);E#11} in (app (letrec {X#14=C#13[(var X#2)];E#16} in S#9) S#8))
    -SR,lapp2->                   (letrec {X#1=(var X#2);E#11} in (letrec {X#14=C#13[(var X#2)];E#16} in (app S#9 S#8)))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#2);E#11} in (app (letrec {E#7} in S#9) C#12[(var X#1)]))
    ,
     (letrec {X#1=(var X#2);E#11} in (letrec {E#7} in (app S#9 C#12[(var X#2)])))
  )

where

   Delta1 = {C#5}
   Delta2 = {E#6,E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in S#9) C#12)),
             ((var X#2),(app (letrec {E#7} in S#9) C#12)),
             (C#12[(var X#2)],(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in S#9) C#12[[.]]))}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#6,E#7}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#8,(letrec {E#7} in [.])),((var X#1),C#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#6   |->  {X#1=(var X#2);E#11},
           E#3   |->  {E#11},
           A#10  |->  [.],
           C#5   |->  (app (letrec {E#7} in S#9) C#12),
           S#8   |->  C#12[(var X#2)]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#11} in (app (letrec {E#7} in S#9) C#12[(var X#2)]))
    -cpx-in1->                    (letrec {X#1=(var X#2);E#11} in (app (letrec {E#7} in S#9) C#12[(var X#1)]))
    ................................................................................
                                  (letrec {X#1=(var X#2);E#11} in (app (letrec {E#7} in S#9) C#12[(var X#2)]))
    -SR,lapp2->                   (letrec {X#1=(var X#2);E#11} in (letrec {E#7} in (app S#9 C#12[(var X#2)])))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]
     in
        A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
     )
    ,
     (letrec
        E#7
       ;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]
     in
        A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
     )
  )

where

   Delta1 = {A#11,T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#14[(app A#15[[.]] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]),
             ((var X#6),A#14[(app A#15[[.]] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#6)] T#16)],
           A#11  |->  A#14[(app A#15 T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -cpx-in1->                    (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])])
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
       ;E#16
       ;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
       ;E#16
       ;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#14=T#13;E#16;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)]),
           E#7   |->  {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16},
           E#15  |->  {E#16;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#16;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#14=T#13[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#16;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#17[(app (letrec {E#8} in T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#9)]
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#17[(letrec {E#8} in (app T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#9))]
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#19,T#18,A#16,T#13,T#4,A#17}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#17[(app (letrec {E#8} in T#20) S#9)];E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  A#17,
           T#13         |->  A#17[(app (letrec {E#8} in T#20) S#9)],
           T#18         |->  (app (letrec {E#8} in T#20) S#9),
           T#19         |->  (letrec {E#8} in T#20),
           S#10         |->  T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#6=A#17[(app (letrec {E#8} in T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#9)];E#7} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#6=A#17[(app (letrec {E#8} in T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#9)];E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#17[(app (letrec {E#8} in T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#9)];E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=A#17[(letrec {E#8} in (app T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#9))];E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#17[(app (letrec
                           X#21= T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
                          ;E#23
                        in
                           S#10
                        ) S#9)]
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#17[(letrec
                      X#21= T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
                     ;E#23
                   in
                      (app S#10 S#9)
                   )]
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#19,T#18,A#16,T#13,T#4,A#17}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {X#21=T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#23} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#17[(app (letrec {X#21=T#20;E#23} in S#10) S#9)];E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  A#17,
           T#13         |->  A#17[(app (letrec {X#21=T#20;E#23} in S#10) S#9)],
           T#18         |->  (app (letrec {X#21=T#20;E#23} in S#10) S#9),
           T#19         |->  (letrec {X#21=T#20;E#23} in S#10),
           E#8          |->  {X#21=T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#23},
           E#22         |->  {E#23}}

and instantiated rules:

                                  (letrec {X#6=A#17[(app (letrec {X#21=T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#23} in S#10) S#9)];E#7} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#6=A#17[(app (letrec {X#21=T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#23} in S#10) S#9)];E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#17[(app (letrec {X#21=T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#23} in S#10) S#9)];E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=A#17[(letrec {X#21=T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#23} in (app S#10 S#9))];E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#17[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#9)]
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#17[(letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#9))]
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#18,A#16,T#13,T#4,A#17}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {X#1=(var X#2);E#3} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#17[(app [.] S#9)];E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  A#17,
           T#13         |->  A#17[(app [.] S#9)],
           T#18         |->  (app [.] S#9),
           T#19         |->  [.],
           S#10         |->  C#5[(var X#2)],
           E#8          |->  {X#1=(var X#2);E#3}}

and instantiated rules:

                                  (letrec {X#6=A#17[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#9)];E#7} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#6=A#17[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#9)];E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#17[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#9)];E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=A#17[(letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#9))];E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#17[(app (letrec {E#8} in S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#17[(letrec
                      E#8
                   in
                      (app S#10 T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])
                   )]
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#18,A#16,T#13,T#4,A#17}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {E#8} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#17[(app (letrec {E#8} in S#10) T#19)];E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  A#17,
           T#13         |->  A#17[(app (letrec {E#8} in S#10) T#19)],
           T#18         |->  (app (letrec {E#8} in S#10) T#19),
           S#9          |->  T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#6=A#17[(app (letrec {E#8} in S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#6=A#17[(app (letrec {E#8} in S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#17[(app (letrec {E#8} in S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=A#17[(letrec {E#8} in (app S#10 T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]))];E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#17[(app A#18[(app (letrec {E#8} in S#10) S#9)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#17[(app A#18[(letrec {E#8} in (app S#10 S#9))] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#17[(app A#18[(app (letrec {E#8} in S#10) S#9)] T#19)];E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           T#13         |->  A#17[(app A#18[(app (letrec {E#8} in S#10) S#9)] T#19)],
           A#16         |->  A#17[(app A#18 T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=A#17[(app A#18[(app (letrec {E#8} in S#10) S#9)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#6=A#17[(app A#18[(app (letrec {E#8} in S#10) S#9)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#17[(app A#18[(app (letrec {E#8} in S#10) S#9)] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=A#17[(app A#18[(letrec {E#8} in (app S#10 S#9))] T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (app (letrec {E#8} in T#18[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#9)
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= (letrec {E#8} in (app T#18[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#9))
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#17,T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(app (letrec {E#8} in T#18) S#9);E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  [.],
           T#13         |->  (app (letrec {E#8} in T#18) S#9),
           T#17         |->  (letrec {E#8} in T#18),
           S#10         |->  T#18[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#6=(app (letrec {E#8} in T#18[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#9);E#7} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#6=(app (letrec {E#8} in T#18[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#9);E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(app (letrec {E#8} in T#18[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#9);E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=(letrec {E#8} in (app T#18[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#9));E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (app (letrec
                     X#19= T#18[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
                    ;E#21
                  in
                     S#10
                  ) S#9)
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= (letrec
                X#19= T#18[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
               ;E#21
             in
                (app S#10 S#9)
             )
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#17,T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {X#19=T#18[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#21} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(app (letrec {X#19=T#18;E#21} in S#10) S#9);E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  [.],
           T#13         |->  (app (letrec {X#19=T#18;E#21} in S#10) S#9),
           T#17         |->  (letrec {X#19=T#18;E#21} in S#10),
           E#8          |->  {X#19=T#18[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#21},
           E#20         |->  {E#21}}

and instantiated rules:

                                  (letrec {X#6=(app (letrec {X#19=T#18[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#21} in S#10) S#9);E#7} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#6=(app (letrec {X#19=T#18[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#21} in S#10) S#9);E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(app (letrec {X#19=T#18[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#21} in S#10) S#9);E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=(letrec {X#19=T#18[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#21} in (app S#10 S#9));E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#9)
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= (letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#9))
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {X#1=(var X#2);E#3} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(app [.] S#9);E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  [.],
           T#13         |->  (app [.] S#9),
           T#17         |->  [.],
           S#10         |->  C#5[(var X#2)],
           E#8          |->  {X#1=(var X#2);E#3}}

and instantiated rules:

                                  (letrec {X#6=(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#9);E#7} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#6=(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#9);E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#9);E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=(letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#9));E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (app (letrec {E#8} in S#10) T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= (letrec
                E#8
             in
                (app S#10 T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])
             )
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {E#8} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(app (letrec {E#8} in S#10) T#17);E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  [.],
           T#13         |->  (app (letrec {E#8} in S#10) T#17),
           S#9          |->  T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#6=(app (letrec {E#8} in S#10) T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]);E#7} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#6=(app (letrec {E#8} in S#10) T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]);E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(app (letrec {E#8} in S#10) T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]);E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=(letrec {E#8} in (app S#10 T#17[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]));E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#7
       ;EE#18[X#17,(app (letrec {E#8} in S#10) S#9)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#7
       ;EE#18[X#17,(letrec {E#8} in (app S#10 S#9))]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#19[(app A#20[(var X#17)] T#21)];E#7;EE#18[X#17,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];EE#18[X#17,[.2]]},
           X#14         |->  X#6,
           E#15         |->  {E#7;EE#18[X#17,(app (letrec {E#8} in S#10) S#9)]},
           T#13         |->  A#19[(app A#20[(var X#17)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7;EE#18[X#17,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#7;EE#18[X#17,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7;EE#18[X#17,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7;EE#18[X#17,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#7
       ;EE#19[X#6,(var X#17)]
       ;EE#20[X#18,(app (letrec {E#8} in S#10) S#9)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#7
       ;EE#19[X#6,(var X#17)]
       ;EE#20[X#18,(letrec {E#8} in (app S#10 S#9))]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23)];E#7;EE#19[X#6,(var X#17)];EE#20[X#18,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#19[X#6,(var X#17)];EE#20[X#18,(app (letrec {E#8} in S#10) S#9)]},
           T#13         |->  A#21[(app A#22[(var X#18)] T#23)],
           A#16         |->  A#21[(app A#22 T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7;EE#19[X#6,(var X#17)];EE#20[X#18,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#7;EE#19[X#6,(var X#17)];EE#20[X#18,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7;EE#19[X#6,(var X#17)];EE#20[X#18,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7;EE#19[X#6,(var X#17)];EE#20[X#18,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app (letrec {E#8} in T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#9)]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#19[(letrec {E#8} in (app T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#9))]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#21,T#20,A#16,T#13,T#4,A#19}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app (letrec {E#8} in T#22) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[(app (letrec {E#8} in T#22) S#9)],
           T#20         |->  (app (letrec {E#8} in T#22) S#9),
           T#21         |->  (letrec {E#8} in T#22),
           S#10         |->  T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app (letrec {E#8} in T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#17=A#19[(app (letrec {E#8} in T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#19[(app (letrec {E#8} in T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=A#19[(letrec {E#8} in (app T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#9))];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app (letrec
                            X#23= T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
                           ;E#25
                         in
                            S#10
                         ) S#9)]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#19[(letrec
                       X#23= T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
                      ;E#25
                    in
                       (app S#10 S#9)
                    )]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#21,T#20,A#16,T#13,T#4,A#19}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {X#23=T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#25} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app (letrec {X#23=T#22;E#25} in S#10) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[(app (letrec {X#23=T#22;E#25} in S#10) S#9)],
           T#20         |->  (app (letrec {X#23=T#22;E#25} in S#10) S#9),
           T#21         |->  (letrec {X#23=T#22;E#25} in S#10),
           E#8          |->  {X#23=T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#25},
           E#24         |->  {E#25}}

and instantiated rules:

                                  (letrec {X#17=A#19[(app (letrec {X#23=T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#25} in S#10) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#17=A#19[(app (letrec {X#23=T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#25} in S#10) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#19[(app (letrec {X#23=T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#25} in S#10) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=A#19[(letrec {X#23=T#22[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#25} in (app S#10 S#9))];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#9)]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#19[(letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#9))]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#20,A#16,T#13,T#4,A#19}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {X#1=(var X#2);E#3} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app [.] S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[(app [.] S#9)],
           T#20         |->  (app [.] S#9),
           T#21         |->  [.],
           S#10         |->  C#5[(var X#2)],
           E#8          |->  {X#1=(var X#2);E#3}}

and instantiated rules:

                                  (letrec {X#17=A#19[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#17=A#19[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#19[(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=A#19[(letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#9))];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app (letrec {E#8} in S#10) T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#19[(letrec
                       E#8
                    in
                       (app S#10 T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])
                    )]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#20,A#16,T#13,T#4,A#19}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {E#8} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app (letrec {E#8} in S#10) T#21)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[(app (letrec {E#8} in S#10) T#21)],
           T#20         |->  (app (letrec {E#8} in S#10) T#21),
           S#9          |->  T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app (letrec {E#8} in S#10) T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#17=A#19[(app (letrec {E#8} in S#10) T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#19[(app (letrec {E#8} in S#10) T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=A#19[(letrec {E#8} in (app S#10 T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]))];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[(app (letrec {E#8} in S#10) S#9)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(letrec {E#8} in (app S#10 S#9))] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app A#20[(app (letrec {E#8} in S#10) S#9)] T#21)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           T#13         |->  A#19[(app A#20[(app (letrec {E#8} in S#10) S#9)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(app (letrec {E#8} in S#10) S#9)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#17=A#19[(app A#20[(app (letrec {E#8} in S#10) S#9)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(app (letrec {E#8} in S#10) S#9)] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=A#19[(app A#20[(letrec {E#8} in (app S#10 S#9))] T#21[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (app (letrec {E#8} in T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#9)
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= (letrec {E#8} in (app T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#9))
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#19,T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=(app (letrec {E#8} in T#20) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  (app (letrec {E#8} in T#20) S#9),
           T#19         |->  (letrec {E#8} in T#20),
           S#10         |->  T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#17=(app (letrec {E#8} in T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#17=(app (letrec {E#8} in T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=(app (letrec {E#8} in T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=(letrec {E#8} in (app T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])] S#9));E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (app (letrec
                      X#21= T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
                     ;E#23
                   in
                      S#10
                   ) S#9)
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= (letrec
                 X#21= T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
                ;E#23
              in
                 (app S#10 S#9)
              )
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#19,T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {X#21=T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#23} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=(app (letrec {X#21=T#20;E#23} in S#10) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  (app (letrec {X#21=T#20;E#23} in S#10) S#9),
           T#19         |->  (letrec {X#21=T#20;E#23} in S#10),
           E#8          |->  {X#21=T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#23},
           E#22         |->  {E#23}}

and instantiated rules:

                                  (letrec {X#17=(app (letrec {X#21=T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#23} in S#10) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#17=(app (letrec {X#21=T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])];E#23} in S#10) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=(app (letrec {X#21=T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#23} in S#10) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=(letrec {X#21=T#20[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])];E#23} in (app S#10 S#9));E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#9)
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= (letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#9))
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (S#9,(letrec {X#1=(var X#2);E#3} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=(app [.] S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  (app [.] S#9),
           T#19         |->  [.],
           S#10         |->  C#5[(var X#2)],
           E#8          |->  {X#1=(var X#2);E#3}}

and instantiated rules:

                                  (letrec {X#17=(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#17=(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#1)]) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=(app (letrec {X#1=(var X#2);E#3} in C#5[(var X#2)]) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=(letrec {X#1=(var X#2);E#3} in (app C#5[(var X#2)] S#9));E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (app (letrec {E#8} in S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])])
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= (letrec
                 E#8
              in
                 (app S#10 T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])])
              )
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {E#8}
   Delta3 = {((var X#1),C#5),
             ((var X#2),C#5),
             (T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])],(letrec {E#8} in [.])),
             ((var X#1),C#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=(app (letrec {E#8} in S#10) T#19);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  (app (letrec {E#8} in S#10) T#19),
           S#9          |->  T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#17=(app (letrec {E#8} in S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -cpx-in1->                    (letrec {X#17=(app (letrec {E#8} in S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=(app (letrec {E#8} in S#10) T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=(letrec {E#8} in (app S#10 T#19[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]));E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#6)
       ;E#13
       ;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]
     in
        A#14[(var X#1)]
     )
    ,
     (letrec
        X#1= (var X#6)
       ;E#13
       ;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]
     in
        A#14[(var X#6)]
     )
  )

where

   Delta1 = {A#11,C#5,A#14}
   Delta2 = {E#8}
   Delta3 = {((var X#1),A#14[[.]]),
             ((var X#6),A#14[[.]]),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),A#14[[.]]),
             ((var X#6),A#14[[.]]),
             ((var X#6),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#7   |->  {X#1=(var X#6);E#13},
           E#3   |->  {E#13;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]},
           A#11  |->  A#14,
           C#5   |->  A#14[[.]],
           C#15  |->  [.],
           X#2   |->  X#6}

and instantiated rules:

                                  (letrec {X#1=(var X#6);E#13;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#14[(var X#6)])
    -cpx-in1->                    (letrec {X#1=(var X#6);E#13;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#14[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#6);E#13;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#14[(var X#6)])
    -SR,lapp3->                   (letrec {X#1=(var X#6);E#13;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#14[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;E#13
       ;EE#12[X#2,(app (letrec {E#8} in S#10) S#9)]
     in
        A#14[(var X#1)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;E#13
       ;EE#12[X#2,(letrec {E#8} in (app S#10 S#9))]
     in
        A#14[(var X#2)]
     )
  )

where

   Delta1 = {A#11,C#5,A#14}
   Delta2 = {E#8}
   Delta3 = {((var X#1),A#14),
             ((var X#2),A#14),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),A#14[[.]]),
             ((var X#2),A#14[[.]]),
             ((var X#2),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#7   |->  {X#1=(var X#2);E#13},
           E#3   |->  {E#13;EE#12[X#2,(app (letrec {E#8} in S#10) S#9)]},
           A#11  |->  A#14[[.]],
           C#5   |->  A#14,
           A#15  |->  [.],
           X#6   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#13;EE#12[X#2,(app (letrec {E#8} in S#10) S#9)]} in A#14[(var X#2)])
    -cpx-in1->                    (letrec {X#1=(var X#2);E#13;EE#12[X#2,(app (letrec {E#8} in S#10) S#9)]} in A#14[(var X#1)])
    ................................................................................
                                  (letrec {X#1=(var X#2);E#13;EE#12[X#2,(app (letrec {E#8} in S#10) S#9)]} in A#14[(var X#2)])
    -SR,lapp3->                   (letrec {X#1=(var X#2);E#13;EE#12[X#2,(letrec {E#8} in (app S#10 S#9))]} in A#14[(var X#2)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;E#13
       ;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]
     in
        A#14[(app A#15[(var X#6)] C#16[(var X#1)])]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;E#13
       ;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]
     in
        A#14[(app A#15[(var X#6)] C#16[(var X#2)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {E#8}
   Delta3 = {((var X#1),A#14[(app A#15[(var X#6)] C#16)]),
             ((var X#2),A#14[(app A#15[(var X#6)] C#16)]),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),A#14[(app A#15[(var X#6)] C#16[[.]])]),
             ((var X#6),A#14[(app A#15[[.]] C#16[(var X#2)])]),
             ((var X#6),A#14[(app A#15[[.]] C#16[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#7   |->  {X#1=(var X#2);E#13},
           E#3   |->  {E#13;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]},
           C#5   |->  A#14[(app A#15[(var X#6)] C#16)],
           A#11  |->  A#14[(app A#15 C#16[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#13;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#14[(app A#15[(var X#6)] C#16[(var X#2)])])
    -cpx-in1->                    (letrec {X#1=(var X#2);E#13;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#14[(app A#15[(var X#6)] C#16[(var X#1)])])
    ................................................................................
                                  (letrec {X#1=(var X#2);E#13;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#14[(app A#15[(var X#6)] C#16[(var X#2)])])
    -SR,lapp3->                   (letrec {X#1=(var X#2);E#13;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#14[(app A#15[(var X#6)] C#16[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#2)
       ;E#13
       ;EE#12[X#2,(app (letrec {E#8} in S#10) S#9)]
     in
        (var X#1)
     )
    ,
     (letrec
        X#1= (var X#2)
       ;E#13
       ;EE#12[X#2,(letrec {E#8} in (app S#10 S#9))]
     in
        (var X#2)
     )
  )

where

   Delta1 = {}
   Delta2 = {E#8}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#7   |->  {X#1=(var X#2);E#13},
           E#3   |->  {E#13;EE#12[X#2,(app (letrec {E#8} in S#10) S#9)]},
           C#5   |->  [.],
           A#11  |->  [.],
           X#6   |->  X#2}

and instantiated rules:

                                  (letrec {X#1=(var X#2);E#13;EE#12[X#2,(app (letrec {E#8} in S#10) S#9)]} in (var X#2))
    -cpx-in1->                    (letrec {X#1=(var X#2);E#13;EE#12[X#2,(app (letrec {E#8} in S#10) S#9)]} in (var X#1))
    ................................................................................
                                  (letrec {X#1=(var X#2);E#13;EE#12[X#2,(app (letrec {E#8} in S#10) S#9)]} in (var X#2))
    -SR,lapp3->                   (letrec {X#1=(var X#2);E#13;EE#12[X#2,(letrec {E#8} in (app S#10 S#9))]} in (var X#2))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (var X#2)
       ;E#7
       ;EE#15[X#2,(app (letrec {E#8} in S#10) S#9)]
     in
        A#16[(app A#17[(var X#6)] C#18[(var X#6)])]
     )
    ,
     (letrec
        X#6= (var X#2)
       ;E#7
       ;EE#15[X#2,(letrec {E#8} in (app S#10 S#9))]
     in
        A#16[(app A#17[(var X#6)] C#18[(var X#2)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {E#8}
   Delta3 = {((var X#6),A#16[(app A#17[(var X#6)] C#18)]),
             ((var X#2),A#16[(app A#17[(var X#6)] C#18)]),
             (S#9,(letrec {E#8} in [.])),
             ((var X#6),A#16[(app A#17[(var X#6)] C#18[[.]])]),
             ((var X#6),A#16[(app A#17[[.]] C#18[(var X#2)])]),
             ((var X#6),A#16[(app A#17[[.]] C#18[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           EE#12[.1,.2] |-> {[.1]=(var X#2);EE#15[X#2,[.2]]},
           X#1          |->  X#6,
           E#3          |->  {E#7;EE#15[X#2,(app (letrec {E#8} in S#10) S#9)]},
           A#13         |->  [.],
           X#14         |->  X#2,
           C#5          |->  A#16[(app A#17[(var X#6)] C#18)],
           A#11         |->  A#16[(app A#17 C#18[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#6=(var X#2);E#7;EE#15[X#2,(app (letrec {E#8} in S#10) S#9)]} in A#16[(app A#17[(var X#6)] C#18[(var X#2)])])
    -cpx-in1->                    (letrec {X#6=(var X#2);E#7;EE#15[X#2,(app (letrec {E#8} in S#10) S#9)]} in A#16[(app A#17[(var X#6)] C#18[(var X#6)])])
    ................................................................................
                                  (letrec {X#6=(var X#2);E#7;EE#15[X#2,(app (letrec {E#8} in S#10) S#9)]} in A#16[(app A#17[(var X#6)] C#18[(var X#2)])])
    -SR,lapp3->                   (letrec {X#6=(var X#2);E#7;EE#15[X#2,(letrec {E#8} in (app S#10 S#9))]} in A#16[(app A#17[(var X#6)] C#18[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= (var X#2)
       ;E#7
       ;EE#16[X#6,(var X#14)]
       ;EE#17[X#2,(app (letrec {E#8} in S#10) S#9)]
     in
        A#18[(app A#19[(var X#6)] C#20[(var X#14)])]
     )
    ,
     (letrec
        X#14= (var X#2)
       ;E#7
       ;EE#16[X#6,(var X#14)]
       ;EE#17[X#2,(letrec {E#8} in (app S#10 S#9))]
     in
        A#18[(app A#19[(var X#6)] C#20[(var X#2)])]
     )
  )

where

   Delta1 = {A#11,C#5}
   Delta2 = {E#8}
   Delta3 = {((var X#14),A#18[(app A#19[(var X#6)] C#20)]),
             ((var X#2),A#18[(app A#19[(var X#6)] C#20)]),
             (S#9,(letrec {E#8} in [.])),
             ((var X#14),A#18[(app A#19[(var X#6)] C#20[[.]])]),
             ((var X#6),A#18[(app A#19[[.]] C#20[(var X#2)])]),
             ((var X#6),A#18[(app A#19[[.]] C#20[(var X#2)])])}
   Delta4=  {}

from overlapping -cpx-in1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
    -cpx-in1->                    T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#1)])]
    and constraints: ((var X#1),C#5), ((var X#2),C#5)
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {X#1=(var X#2);E#3} in C#5[(var X#2)])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#1),C#5),((var X#2),C#5),(S#9,(letrec {E#8} in [.])),((var X#1),C#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  [.],
           EE#12[.1,.2] |-> {X#14=(var X#2);EE#16[[.1],(var X#14)];EE#17[X#2,[.2]]},
           X#1          |->  X#14,
           E#3          |->  {E#7;EE#16[X#6,(var X#14)];EE#17[X#2,(app (letrec {E#8} in S#10) S#9)]},
           A#13         |->  [.],
           X#15         |->  X#2,
           C#5          |->  A#18[(app A#19[(var X#6)] C#20)],
           A#11         |->  A#18[(app A#19 C#20[(var X#2)])]}

and instantiated rules:

                                  (letrec {X#14=(var X#2);E#7;EE#16[X#6,(var X#14)];EE#17[X#2,(app (letrec {E#8} in S#10) S#9)]} in A#18[(app A#19[(var X#6)] C#20[(var X#2)])])
    -cpx-in1->                    (letrec {X#14=(var X#2);E#7;EE#16[X#6,(var X#14)];EE#17[X#2,(app (letrec {E#8} in S#10) S#9)]} in A#18[(app A#19[(var X#6)] C#20[(var X#14)])])
    ................................................................................
                                  (letrec {X#14=(var X#2);E#7;EE#16[X#6,(var X#14)];EE#17[X#2,(app (letrec {E#8} in S#10) S#9)]} in A#18[(app A#19[(var X#6)] C#20[(var X#2)])])
    -SR,lapp3->                   (letrec {X#14=(var X#2);E#7;EE#16[X#6,(var X#14)];EE#17[X#2,(letrec {E#8} in (app S#10 S#9))]} in A#18[(app A#19[(var X#6)] C#20[(var X#2)])])
    

================================================================================
Critical Pair:

  (
     A#12[(app (\ X#8.S#10) T#14[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
    ,
     A#12[(letrec
              X#8= T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
           in
              S#10
           )]
  )

where

   Delta1 = {T#13,A#11,T#6,A#12}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(\ X#8.[.])),
             (T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {X#8=[.]} in S#10)),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  A#11[(app (\ X#8.S#10) S#9)]
    -SR,lbeta1->                  A#11[(letrec {X#8=S#9} in S#10)]
    and constraints: (S#9,(\ X#8.[.])), (S#9,(letrec {X#8=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        A#11[(app (\ X#8.S#10) S#9)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#9,(\ X#8.[.])),(S#9,(letrec {X#8=[.]} in S#10)),((var X#2),C#7[[.]])}


and found solution:

    Sol = {A#11  |->  A#12,
           T#6   |->  A#12[(app (\ X#8.S#10) T#14)],
           T#13  |->  (app (\ X#8.S#10) T#14),
           S#9   |->  T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  A#12[(app (\ X#8.S#10) T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
    -cpx-e1->                     A#12[(app (\ X#8.S#10) T#14[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
    ................................................................................
                                  A#12[(app (\ X#8.S#10) T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
    -SR,lbeta1->                  A#12[(letrec {X#8=T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]} in S#10)]
    

================================================================================
Critical Pair:

  (
     A#12[(app A#13[(app (\ X#8.S#10) S#9)] T#14[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
    ,
     A#12[(app A#13[(letrec {X#8=S#9} in S#10)] T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
  )

where

   Delta1 = {A#11,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#9,(\ X#8.[.])),
             (S#9,(letrec {X#8=[.]} in S#10)),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  A#11[(app (\ X#8.S#10) S#9)]
    -SR,lbeta1->                  A#11[(letrec {X#8=S#9} in S#10)]
    and constraints: (S#9,(\ X#8.[.])), (S#9,(letrec {X#8=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        A#11[(app (\ X#8.S#10) S#9)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#9,(\ X#8.[.])),(S#9,(letrec {X#8=[.]} in S#10)),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  A#12[(app A#13[(app (\ X#8.S#10) S#9)] T#14)],
           A#11  |->  A#12[(app A#13 T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  A#12[(app A#13[(app (\ X#8.S#10) S#9)] T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
    -cpx-e1->                     A#12[(app A#13[(app (\ X#8.S#10) S#9)] T#14[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
    ................................................................................
                                  A#12[(app A#13[(app (\ X#8.S#10) S#9)] T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
    -SR,lbeta1->                  A#12[(app A#13[(letrec {X#8=S#9} in S#10)] T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
    

================================================================================
Critical Pair:

  (
     (app (\ X#8.S#10) T#12[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])
    ,
     (letrec
        X#8= T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
     in
        S#10
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(\ X#8.[.])),
             (T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {X#8=[.]} in S#10)),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  A#11[(app (\ X#8.S#10) S#9)]
    -SR,lbeta1->                  A#11[(letrec {X#8=S#9} in S#10)]
    and constraints: (S#9,(\ X#8.[.])), (S#9,(letrec {X#8=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        A#11[(app (\ X#8.S#10) S#9)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#9,(\ X#8.[.])),(S#9,(letrec {X#8=[.]} in S#10)),((var X#2),C#7[[.]])}


and found solution:

    Sol = {A#11  |->  [.],
           T#6   |->  (app (\ X#8.S#10) T#12),
           S#9   |->  T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (app (\ X#8.S#10) T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])
    -cpx-e1->                     (app (\ X#8.S#10) T#12[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])
    ................................................................................
                                  (app (\ X#8.S#10) T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])
    -SR,lbeta1->                  (letrec {X#8=T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]} in S#10)
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        A#14[(app (\ X#8.S#11) T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
     )
    ,
     (letrec
        E#9
     in
        A#14[(letrec
                 X#8= T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
              in
                 S#11
              )]
     )
  )

where

   Delta1 = {T#15,A#12,T#13,T#6,A#14}
   Delta2 = {E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(\ X#8.[.])),
             (T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {X#8=[.]} in S#11)),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])
    -SR,lbeta2->                  (letrec {E#9} in A#12[(letrec {X#8=S#10} in S#11)])
    and constraints: E#9/= {}, (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#9} in A#14[(app (\ X#8.S#11) T#16)]),
           A#12  |->  A#14,
           T#13  |->  A#14[(app (\ X#8.S#11) T#16)],
           T#15  |->  (app (\ X#8.S#11) T#16),
           S#10  |->  T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {E#9} in A#14[(app (\ X#8.S#11) T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -cpx-e1->                     (letrec {E#9} in A#14[(app (\ X#8.S#11) T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])])
    ................................................................................
                                  (letrec {E#9} in A#14[(app (\ X#8.S#11) T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -SR,lbeta2->                  (letrec {E#9} in A#14[(letrec {X#8=T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]} in S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        A#14[(app A#15[(app (\ X#8.S#11) S#10)] T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
     )
    ,
     (letrec
        E#9
     in
        A#14[(app A#15[(letrec {X#8=S#10} in S#11)] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#13,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])
    -SR,lbeta2->                  (letrec {E#9} in A#12[(letrec {X#8=S#10} in S#11)])
    and constraints: E#9/= {}, (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#9} in A#14[(app A#15[(app (\ X#8.S#11) S#10)] T#16)]),
           T#13  |->  A#14[(app A#15[(app (\ X#8.S#11) S#10)] T#16)],
           A#12  |->  A#14[(app A#15 T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {E#9} in A#14[(app A#15[(app (\ X#8.S#11) S#10)] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -cpx-e1->                     (letrec {E#9} in A#14[(app A#15[(app (\ X#8.S#11) S#10)] T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])])
    ................................................................................
                                  (letrec {E#9} in A#14[(app A#15[(app (\ X#8.S#11) S#10)] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -SR,lbeta2->                  (letrec {E#9} in A#14[(app A#15[(letrec {X#8=S#10} in S#11)] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        (app (\ X#8.S#11) T#14[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])
     )
    ,
     (letrec
        E#9
     in
        (letrec
           X#8= T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        in
           S#11
        )
     )
  )

where

   Delta1 = {T#13,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(\ X#8.[.])),
             (T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {X#8=[.]} in S#11)),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])
    -SR,lbeta2->                  (letrec {E#9} in A#12[(letrec {X#8=S#10} in S#11)])
    and constraints: E#9/= {}, (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#9} in (app (\ X#8.S#11) T#14)),
           A#12  |->  [.],
           T#13  |->  (app (\ X#8.S#11) T#14),
           S#10  |->  T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {E#9} in (app (\ X#8.S#11) T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]))
    -cpx-e1->                     (letrec {E#9} in (app (\ X#8.S#11) T#14[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]))
    ................................................................................
                                  (letrec {E#9} in (app (\ X#8.S#11) T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]))
    -SR,lbeta2->                  (letrec {E#9} in (letrec {X#8=T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]} in S#11))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
       ;E#16
     in
        A#12[(app (\ X#8.S#11) S#10)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;E#16
     in
        A#12[(letrec {X#8=S#10} in S#11)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])
    -SR,lbeta2->                  (letrec {E#9} in A#12[(letrec {X#8=S#10} in S#11)])
    and constraints: E#9/= {}, (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#14=T#13;E#16} in A#12[(app (\ X#8.S#11) S#10)]),
           E#9   |->  {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16} in A#12[(app (\ X#8.S#11) S#10)])
    -cpx-e1->                     (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#16} in A#12[(app (\ X#8.S#11) S#10)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16} in A#12[(app (\ X#8.S#11) S#10)])
    -SR,lbeta2->                  (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16} in A#12[(letrec {X#8=S#10} in S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#2)]
       ;X#2= (var X#3)
       ;E#14
     in
        A#12[(app (\ X#8.S#11) S#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#2= (var X#3)
       ;E#14
     in
        A#12[(letrec {X#8=S#10} in S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])
    -SR,lbeta2->                  (letrec {E#9} in A#12[(letrec {X#8=S#10} in S#11)])
    and constraints: E#9/= {}, (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(app (\ X#8.S#11) S#10)],
           E#9   |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#14},
           E#13  |->  {X#1=C#7[(var X#3)];E#14},
           E#4   |->  {E#14}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#14} in A#12[(app (\ X#8.S#11) S#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#14} in A#12[(app (\ X#8.S#11) S#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#14} in A#12[(app (\ X#8.S#11) S#10)])
    -SR,lbeta2->                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#14} in A#12[(letrec {X#8=S#10} in S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#10
       ;EE#14[X#8,(app (\ X#9.S#12) S#11)]
     in
        A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
     )
    ,
     (letrec
        E#10
       ;EE#14[X#8,(letrec {X#9=S#11} in S#12)]
     in
        A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
     )
  )

where

   Delta1 = {A#13,T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#16[(app A#17[[.]] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]),
             ((var X#8),A#16[(app A#17[[.]] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#8)] T#18)],
           A#13  |->  A#16[(app A#17 T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -cpx-e1->                     (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])])
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
       ;E#18
       ;EE#14[X#8,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;E#18
       ;EE#14[X#8,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#16=T#15;E#18;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)]),
           E#10  |->  {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18},
           E#17  |->  {E#18;EE#14[X#8,(app (\ X#9.S#12) S#11)]}}

and instantiated rules:

                                  (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#18;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#19[(app (\ X#9.S#12) T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#19[(letrec
                      X#9= T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
                   in
                      S#12
                   )]
       ;E#10
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#6,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(\ X#9.[.])),
             (T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#19[(app (\ X#9.S#12) T#21)];E#10} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#8,
           E#17         |->  {E#10},
           A#18         |->  A#19,
           T#15         |->  A#19[(app (\ X#9.S#12) T#21)],
           T#20         |->  (app (\ X#9.S#12) T#21),
           S#11         |->  T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=A#19[(app (\ X#9.S#12) T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#8=A#19[(app (\ X#9.S#12) T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#19[(app (\ X#9.S#12) T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#19[(letrec {X#9=T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]} in S#12)];E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#19[(app A#20[(app (\ X#9.S#12) S#11)] T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#19[(app A#20[(letrec {X#9=S#11} in S#12)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;E#10
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#19[(app A#20[(app (\ X#9.S#12) S#11)] T#21)];E#10} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]},
           X#16         |->  X#8,
           E#17         |->  {E#10},
           T#15         |->  A#19[(app A#20[(app (\ X#9.S#12) S#11)] T#21)],
           A#18         |->  A#19[(app A#20 T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=A#19[(app A#20[(app (\ X#9.S#12) S#11)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#8=A#19[(app A#20[(app (\ X#9.S#12) S#11)] T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#19[(app A#20[(app (\ X#9.S#12) S#11)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#19[(app A#20[(letrec {X#9=S#11} in S#12)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (app (\ X#9.S#12) T#19[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= (letrec
                X#9= T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
             in
                S#12
             )
       ;E#10
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(\ X#9.[.])),
             (T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=(app (\ X#9.S#12) T#19);E#10} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#8,
           E#17         |->  {E#10},
           A#18         |->  [.],
           T#15         |->  (app (\ X#9.S#12) T#19),
           S#11         |->  T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=(app (\ X#9.S#12) T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]);E#10} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#8=(app (\ X#9.S#12) T#19[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]);E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (\ X#9.S#12) T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]);E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=(letrec {X#9=T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]} in S#12);E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;E#10
       ;EE#20[X#19,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;E#10
       ;EE#20[X#19,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#21[(app A#22[(var X#19)] T#23)];E#10;EE#20[X#19,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];EE#20[X#19,[.2]]},
           X#16         |->  X#8,
           E#17         |->  {E#10;EE#20[X#19,(app (\ X#9.S#12) S#11)]},
           T#15         |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;EE#20[X#19,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];E#10;EE#20[X#19,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;EE#20[X#19,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;EE#20[X#19,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;E#10
       ;EE#21[X#8,(var X#19)]
       ;EE#22[X#20,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;E#10
       ;EE#21[X#8,(var X#19)]
       ;EE#22[X#20,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];E#10;EE#21[X#8,(var X#19)];EE#22[X#20,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {E#10;EE#21[X#8,(var X#19)];EE#22[X#20,(app (\ X#9.S#12) S#11)]},
           T#15         |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;EE#21[X#8,(var X#19)];EE#22[X#20,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];E#10;EE#21[X#8,(var X#19)];EE#22[X#20,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;EE#21[X#8,(var X#19)];EE#22[X#20,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;EE#21[X#8,(var X#19)];EE#22[X#20,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app (\ X#9.S#12) T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;E#10
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(letrec
                       X#9= T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
                    in
                       S#12
                    )]
       ;E#10
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#6,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(\ X#9.[.])),
             (T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app (\ X#9.S#12) T#23)];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#10;EE#20[X#8,(var X#19)]},
           A#18         |->  A#21,
           T#15         |->  A#21[(app (\ X#9.S#12) T#23)],
           T#22         |->  (app (\ X#9.S#12) T#23),
           S#11         |->  T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app (\ X#9.S#12) T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#21[(app (\ X#9.S#12) T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app (\ X#9.S#12) T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#19=A#21[(letrec {X#9=T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]} in S#12)];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(app (\ X#9.S#12) S#11)] T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;E#10
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(letrec {X#9=S#11} in S#12)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;E#10
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app A#22[(app (\ X#9.S#12) S#11)] T#23)];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#10;EE#20[X#8,(var X#19)]},
           T#15         |->  A#21[(app A#22[(app (\ X#9.S#12) S#11)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(app (\ X#9.S#12) S#11)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#21[(app A#22[(app (\ X#9.S#12) S#11)] T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(app (\ X#9.S#12) S#11)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#19=A#21[(app A#22[(letrec {X#9=S#11} in S#12)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (app (\ X#9.S#12) T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])
       ;E#10
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= (letrec
                 X#9= T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
              in
                 S#12
              )
       ;E#10
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(\ X#9.[.])),
             (T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=(app (\ X#9.S#12) T#21);E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#10;EE#20[X#8,(var X#19)]},
           A#18         |->  [.],
           T#15         |->  (app (\ X#9.S#12) T#21),
           S#11         |->  T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {X#19=(app (\ X#9.S#12) T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]);E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=(app (\ X#9.S#12) T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]);E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=(app (\ X#9.S#12) T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]);E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#19=(letrec {X#9=T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]} in S#12);E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#2)]
       ;X#2= (var X#3)
       ;E#16
       ;EE#14[X#8,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#2= (var X#3)
       ;E#16
       ;EE#14[X#8,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#8)],
           E#10  |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#16},
           E#15  |->  {X#1=C#7[(var X#3)];E#16},
           E#4   |->  {E#16;EE#14[X#8,(app (\ X#9.S#12) S#11)]}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#16;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= A#17[(app (\ X#9.C#20[(var X#2)]) S#11)]
       ;E#15
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= A#17[(letrec {X#9=S#11} in C#20[(var X#3)])]
       ;E#15
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#19,C#18,A#16,C#7,A#17}
   Delta2 = {}
   Delta3 = {((var X#2),A#17[(app (\ X#9.C#20) S#11)]),
             ((var X#3),A#17[(app (\ X#9.C#20) S#11)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in C#20[(var X#3)])),
             ((var X#2),A#17[(app (\ X#9.C#20[[.]]) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#1          |->  X#8,
           E#4          |->  {E#15},
           A#16         |->  A#17,
           C#7          |->  A#17[(app (\ X#9.C#20) S#11)],
           C#18         |->  (app (\ X#9.C#20) S#11),
           C#19         |->  (\ X#9.C#20),
           S#12         |->  C#20[(var X#3)]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=A#17[(app (\ X#9.C#20[(var X#3)]) S#11)];E#15} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=A#17[(app (\ X#9.C#20[(var X#2)]) S#11)];E#15} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=A#17[(app (\ X#9.C#20[(var X#3)]) S#11)];E#15} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#2=(var X#3);X#8=A#17[(letrec {X#9=S#11} in C#20[(var X#3)])];E#15} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= A#17[(app (\ X#9.S#12) C#19[(var X#2)])]
       ;E#15
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= A#17[(letrec {X#9=C#19[(var X#3)]} in S#12)]
       ;E#15
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#18,A#16,C#7,A#17}
   Delta2 = {}
   Delta3 = {((var X#2),A#17[(app (\ X#9.S#12) C#19)]),
             ((var X#3),A#17[(app (\ X#9.S#12) C#19)]),
             (C#19[(var X#3)],(\ X#9.[.])),
             (C#19[(var X#3)],(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#17[(app (\ X#9.S#12) C#19[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#1          |->  X#8,
           E#4          |->  {E#15},
           A#16         |->  A#17,
           C#7          |->  A#17[(app (\ X#9.S#12) C#19)],
           C#18         |->  (app (\ X#9.S#12) C#19),
           S#11         |->  C#19[(var X#3)]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=A#17[(app (\ X#9.S#12) C#19[(var X#3)])];E#15} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=A#17[(app (\ X#9.S#12) C#19[(var X#2)])];E#15} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=A#17[(app (\ X#9.S#12) C#19[(var X#3)])];E#15} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#2=(var X#3);X#8=A#17[(letrec {X#9=C#19[(var X#3)]} in S#12)];E#15} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= A#17[(app A#18[(app (\ X#9.S#12) S#11)] C#19[(var X#2)])]
       ;E#15
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= A#17[(app A#18[(letrec {X#9=S#11} in S#12)] C#19[(var X#3)])]
       ;E#15
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7}
   Delta2 = {}
   Delta3 = {((var X#2),A#17[(app A#18[(app (\ X#9.S#12) S#11)] C#19)]),
             ((var X#3),A#17[(app A#18[(app (\ X#9.S#12) S#11)] C#19)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#17[(app A#18[(app (\ X#9.S#12) S#11)] C#19[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] C#19[(var X#3)])]},
           X#1          |->  X#8,
           E#4          |->  {E#15},
           C#7          |->  A#17[(app A#18[(app (\ X#9.S#12) S#11)] C#19)],
           A#16         |->  A#17[(app A#18 C#19[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=A#17[(app A#18[(app (\ X#9.S#12) S#11)] C#19[(var X#3)])];E#15} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=A#17[(app A#18[(app (\ X#9.S#12) S#11)] C#19[(var X#2)])];E#15} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=A#17[(app A#18[(app (\ X#9.S#12) S#11)] C#19[(var X#3)])];E#15} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#2=(var X#3);X#8=A#17[(app A#18[(letrec {X#9=S#11} in S#12)] C#19[(var X#3)])];E#15} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (app (\ X#9.C#18[(var X#2)]) S#11)
       ;E#15
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= (letrec {X#9=S#11} in C#18[(var X#3)])
       ;E#15
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#17,C#7}
   Delta2 = {}
   Delta3 = {((var X#2),(app (\ X#9.C#18) S#11)),
             ((var X#3),(app (\ X#9.C#18) S#11)),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in C#18[(var X#3)])),
             ((var X#2),(app (\ X#9.C#18[[.]]) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#8,
           E#4          |->  {E#15},
           A#16         |->  [.],
           C#7          |->  (app (\ X#9.C#18) S#11),
           C#17         |->  (\ X#9.C#18),
           S#12         |->  C#18[(var X#3)]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(app (\ X#9.C#18[(var X#3)]) S#11);E#15} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(app (\ X#9.C#18[(var X#2)]) S#11);E#15} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(app (\ X#9.C#18[(var X#3)]) S#11);E#15} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#2=(var X#3);X#8=(letrec {X#9=S#11} in C#18[(var X#3)]);E#15} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (app (\ X#9.S#12) C#17[(var X#2)])
       ;E#15
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= (letrec {X#9=C#17[(var X#3)]} in S#12)
       ;E#15
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {}
   Delta3 = {((var X#2),(app (\ X#9.S#12) C#17)),
             ((var X#3),(app (\ X#9.S#12) C#17)),
             (C#17[(var X#3)],(\ X#9.[.])),
             (C#17[(var X#3)],(letrec {X#9=[.]} in S#12)),
             ((var X#2),(app (\ X#9.S#12) C#17[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#8,
           E#4          |->  {E#15},
           A#16         |->  [.],
           C#7          |->  (app (\ X#9.S#12) C#17),
           S#11         |->  C#17[(var X#3)]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(app (\ X#9.S#12) C#17[(var X#3)]);E#15} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(app (\ X#9.S#12) C#17[(var X#2)]);E#15} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(app (\ X#9.S#12) C#17[(var X#3)]);E#15} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#2=(var X#3);X#8=(letrec {X#9=C#17[(var X#3)]} in S#12);E#15} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#17)
       ;X#8= A#19[(var X#2)]
       ;E#15
       ;EE#18[X#17,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#17)
       ;X#8= A#19[(var X#17)]
       ;E#15
       ;EE#18[X#17,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[[.]]),
             ((var X#17),A#19[[.]]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#19[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#17);E#15},
           EE#14[.1,.2] |-> {[.1]=A#19[(var X#17)];EE#18[X#17,[.2]]},
           X#1          |->  X#8,
           E#4          |->  {E#15;EE#18[X#17,(app (\ X#9.S#12) S#11)]},
           A#16         |->  A#19,
           C#7          |->  A#19[[.]],
           C#20         |->  [.],
           X#3          |->  X#17}

and instantiated rules:

                                  (letrec {X#2=(var X#17);X#8=A#19[(var X#17)];E#15;EE#18[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#17);X#8=A#19[(var X#2)];E#15;EE#18[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#17);X#8=A#19[(var X#17)];E#15;EE#18[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#2=(var X#17);X#8=A#19[(var X#17)];E#15;EE#18[X#17,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= A#19[(var X#2)]
       ;E#15
       ;EE#18[X#3,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= A#19[(var X#3)]
       ;E#15
       ;EE#18[X#3,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19),
             ((var X#3),A#19),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#19[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=A#19[(var X#3)];EE#18[X#3,[.2]]},
           X#1          |->  X#8,
           E#4          |->  {E#15;EE#18[X#3,(app (\ X#9.S#12) S#11)]},
           A#16         |->  A#19[[.]],
           C#7          |->  A#19,
           A#20         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=A#19[(var X#3)];E#15;EE#18[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=A#19[(var X#2)];E#15;EE#18[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=A#19[(var X#3)];E#15;EE#18[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#2=(var X#3);X#8=A#19[(var X#3)];E#15;EE#18[X#3,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= A#19[(app A#20[(var X#17)] C#21[(var X#2)])]
       ;E#15
       ;EE#18[X#17,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= A#19[(app A#20[(var X#17)] C#21[(var X#3)])]
       ;E#15
       ;EE#18[X#17,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[(app A#20[(var X#17)] C#21)]),
             ((var X#3),A#19[(app A#20[(var X#17)] C#21)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#19[(app A#20[(var X#17)] C#21[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] C#21[(var X#3)])];EE#18[X#17,[.2]]},
           X#1          |->  X#8,
           E#4          |->  {E#15;EE#18[X#17,(app (\ X#9.S#12) S#11)]},
           C#7          |->  A#19[(app A#20[(var X#17)] C#21)],
           A#16         |->  A#19[(app A#20 C#21[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=A#19[(app A#20[(var X#17)] C#21[(var X#3)])];E#15;EE#18[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=A#19[(app A#20[(var X#17)] C#21[(var X#2)])];E#15;EE#18[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=A#19[(app A#20[(var X#17)] C#21[(var X#3)])];E#15;EE#18[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#2=(var X#3);X#8=A#19[(app A#20[(var X#17)] C#21[(var X#3)])];E#15;EE#18[X#17,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (var X#2)
       ;E#15
       ;EE#18[X#3,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= (var X#3)
       ;E#15
       ;EE#18[X#3,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#3),[.]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=(var X#3);EE#18[X#3,[.2]]},
           X#1          |->  X#8,
           E#4          |->  {E#15;EE#18[X#3,(app (\ X#9.S#12) S#11)]},
           C#7          |->  [.],
           A#16         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(var X#3);E#15;EE#18[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(var X#2);E#15;EE#18[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(var X#3);E#15;EE#18[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#2=(var X#3);X#8=(var X#3);E#15;EE#18[X#3,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(var X#2)]
       ;X#2= (var X#18)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#18,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= A#21[(var X#18)]
       ;X#2= (var X#18)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#18,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),A#21[[.]]),
             ((var X#18),A#21[[.]]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#21[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#18);E#15},
           EE#14[.1,.2] |-> {X#17=A#21[(var X#18)];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (\ X#9.S#12) S#11)]},
           A#16         |->  A#21,
           C#7          |->  A#21[[.]],
           C#22         |->  [.],
           X#3          |->  X#18}

and instantiated rules:

                                  (letrec {X#17=A#21[(var X#18)];X#2=(var X#18);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=A#21[(var X#2)];X#2=(var X#18);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=A#21[(var X#18)];X#2=(var X#18);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#17=A#21[(var X#18)];X#2=(var X#18);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(var X#2)]
       ;X#2= (var X#3)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#3,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= A#21[(var X#3)]
       ;X#2= (var X#3)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#3,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),A#21),
             ((var X#3),A#21),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#21[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=A#21[(var X#3)];EE#19[[.1],(var X#17)];EE#20[X#3,[.2]]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (\ X#9.S#12) S#11)]},
           A#16         |->  A#21[[.]],
           C#7          |->  A#21,
           A#22         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#17=A#21[(var X#3)];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=A#21[(var X#2)];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=A#21[(var X#3)];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#17=A#21[(var X#3)];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(app A#22[(var X#18)] C#23[(var X#2)])]
       ;X#2= (var X#3)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#18,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] C#23[(var X#3)])]
       ;X#2= (var X#3)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#18,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7}
   Delta2 = {}
   Delta3 = {((var X#2),A#21[(app A#22[(var X#18)] C#23)]),
             ((var X#3),A#21[(app A#22[(var X#18)] C#23)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#21[(app A#22[(var X#18)] C#23[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#3)])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (\ X#9.S#12) S#11)]},
           C#7          |->  A#21[(app A#22[(var X#18)] C#23)],
           A#16         |->  A#21[(app A#22 C#23[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#3)])];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#2)])];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#3)])];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#3)])];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#2)
       ;X#2= (var X#3)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#3,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= (var X#3)
       ;X#2= (var X#3)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#3,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#3),[.]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=(var X#3);EE#19[[.1],(var X#17)];EE#20[X#3,[.2]]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (\ X#9.S#12) S#11)]},
           C#7          |->  [.],
           A#16         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#17=(var X#3);X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=(var X#2);X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=(var X#3);X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#17=(var X#3);X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app (\ X#9.C#22[(var X#2)]) S#11)]
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= A#19[(letrec {X#9=S#11} in C#22[(var X#3)])]
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#21,C#20,A#16,C#7,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[(app (\ X#9.C#22) S#11)]),
             ((var X#3),A#19[(app (\ X#9.C#22) S#11)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in C#22[(var X#3)])),
             ((var X#2),A#19[(app (\ X#9.C#22[[.]]) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#18[X#8,(var X#17)]},
           A#16         |->  A#19,
           C#7          |->  A#19[(app (\ X#9.C#22) S#11)],
           C#20         |->  (app (\ X#9.C#22) S#11),
           C#21         |->  (\ X#9.C#22),
           S#12         |->  C#22[(var X#3)]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app (\ X#9.C#22[(var X#3)]) S#11)];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=A#19[(app (\ X#9.C#22[(var X#2)]) S#11)];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=A#19[(app (\ X#9.C#22[(var X#3)]) S#11)];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#17=A#19[(letrec {X#9=S#11} in C#22[(var X#3)])];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app (\ X#9.S#12) C#21[(var X#2)])]
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= A#19[(letrec {X#9=C#21[(var X#3)]} in S#12)]
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#20,A#16,C#7,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[(app (\ X#9.S#12) C#21)]),
             ((var X#3),A#19[(app (\ X#9.S#12) C#21)]),
             (C#21[(var X#3)],(\ X#9.[.])),
             (C#21[(var X#3)],(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#19[(app (\ X#9.S#12) C#21[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#18[X#8,(var X#17)]},
           A#16         |->  A#19,
           C#7          |->  A#19[(app (\ X#9.S#12) C#21)],
           C#20         |->  (app (\ X#9.S#12) C#21),
           S#11         |->  C#21[(var X#3)]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app (\ X#9.S#12) C#21[(var X#3)])];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=A#19[(app (\ X#9.S#12) C#21[(var X#2)])];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=A#19[(app (\ X#9.S#12) C#21[(var X#3)])];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#17=A#19[(letrec {X#9=C#21[(var X#3)]} in S#12)];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21[(var X#2)])]
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(letrec {X#9=S#11} in S#12)] C#21[(var X#3)])]
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21)]),
             ((var X#3),A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] C#21[(var X#3)])];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#18[X#8,(var X#17)]},
           C#7          |->  A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21)],
           A#16         |->  A#19[(app A#20 C#21[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21[(var X#3)])];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21[(var X#2)])];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21[(var X#3)])];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#17=A#19[(app A#20[(letrec {X#9=S#11} in S#12)] C#21[(var X#3)])];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (app (\ X#9.C#20[(var X#2)]) S#11)
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= (letrec {X#9=S#11} in C#20[(var X#3)])
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#19,C#7}
   Delta2 = {}
   Delta3 = {((var X#2),(app (\ X#9.C#20) S#11)),
             ((var X#3),(app (\ X#9.C#20) S#11)),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in C#20[(var X#3)])),
             ((var X#2),(app (\ X#9.C#20[[.]]) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#18[X#8,(var X#17)]},
           A#16         |->  [.],
           C#7          |->  (app (\ X#9.C#20) S#11),
           C#19         |->  (\ X#9.C#20),
           S#12         |->  C#20[(var X#3)]}

and instantiated rules:

                                  (letrec {X#17=(app (\ X#9.C#20[(var X#3)]) S#11);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=(app (\ X#9.C#20[(var X#2)]) S#11);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=(app (\ X#9.C#20[(var X#3)]) S#11);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#17=(letrec {X#9=S#11} in C#20[(var X#3)]);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (app (\ X#9.S#12) C#19[(var X#2)])
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= (letrec {X#9=C#19[(var X#3)]} in S#12)
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {}
   Delta3 = {((var X#2),(app (\ X#9.S#12) C#19)),
             ((var X#3),(app (\ X#9.S#12) C#19)),
             (C#19[(var X#3)],(\ X#9.[.])),
             (C#19[(var X#3)],(letrec {X#9=[.]} in S#12)),
             ((var X#2),(app (\ X#9.S#12) C#19[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#10         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#18[X#8,(var X#17)]},
           A#16         |->  [.],
           C#7          |->  (app (\ X#9.S#12) C#19),
           S#11         |->  C#19[(var X#3)]}

and instantiated rules:

                                  (letrec {X#17=(app (\ X#9.S#12) C#19[(var X#3)]);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=(app (\ X#9.S#12) C#19[(var X#2)]);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=(app (\ X#9.S#12) C#19[(var X#3)]);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#17=(letrec {X#9=C#19[(var X#3)]} in S#12);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#8)]
       ;X#8= (var X#3)
       ;E#18
       ;EE#17[X#3,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#8= (var X#3)
       ;E#18
       ;EE#17[X#3,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#8),C#7),
             ((var X#3),C#7),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#8),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=(var X#3);EE#17[X#3,[.2]]},
           X#2          |->  X#8,
           E#10         |->  {X#1=C#7[(var X#3)];E#18},
           E#4          |->  {E#18;EE#17[X#3,(app (\ X#9.S#12) S#11)]},
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#8=(var X#3);E#18;EE#17[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#8)];X#8=(var X#3);E#18;EE#17[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#8=(var X#3);E#18;EE#17[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#1=C#7[(var X#3)];X#8=(var X#3);E#18;EE#17[X#3,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= A#19[(app (\ X#9.C#22[(var X#8)]) S#11)]
       ;X#8= (var X#3)
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#3= A#19[(letrec {X#9=S#11} in C#22[(var X#3)])]
       ;X#8= (var X#3)
       ;E#10
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#21,C#20,A#18,C#7,A#19}
   Delta2 = {}
   Delta3 = {((var X#8),A#19[(app (\ X#9.C#22) S#11)]),
             ((var X#3),A#19[(app (\ X#9.C#22) S#11)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in C#22[(var X#3)])),
             ((var X#8),A#19[(app (\ X#9.C#22[[.]]) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#3=A#19[[.2]];[.1]=(var X#3)},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#1          |->  X#3,
           E#4          |->  {E#10},
           A#18         |->  A#19,
           C#7          |->  A#19[(app (\ X#9.C#22) S#11)],
           A#15         |->  [.],
           X#16         |->  X#3,
           C#20         |->  (app (\ X#9.C#22) S#11),
           C#21         |->  (\ X#9.C#22),
           S#12         |->  C#22[(var X#3)]}

and instantiated rules:

                                  (letrec {X#3=A#19[(app (\ X#9.C#22[(var X#3)]) S#11)];X#8=(var X#3);E#10} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#3=A#19[(app (\ X#9.C#22[(var X#8)]) S#11)];X#8=(var X#3);E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#3=A#19[(app (\ X#9.C#22[(var X#3)]) S#11)];X#8=(var X#3);E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#3=A#19[(letrec {X#9=S#11} in C#22[(var X#3)])];X#8=(var X#3);E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= A#19[(app (\ X#9.S#12) C#21[(var X#8)])]
       ;X#8= (var X#3)
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#3= A#19[(letrec {X#9=C#21[(var X#3)]} in S#12)]
       ;X#8= (var X#3)
       ;E#10
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#20,A#18,C#7,A#19}
   Delta2 = {}
   Delta3 = {((var X#8),A#19[(app (\ X#9.S#12) C#21)]),
             ((var X#3),A#19[(app (\ X#9.S#12) C#21)]),
             (C#21[(var X#3)],(\ X#9.[.])),
             (C#21[(var X#3)],(letrec {X#9=[.]} in S#12)),
             ((var X#8),A#19[(app (\ X#9.S#12) C#21[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#3=A#19[[.2]];[.1]=(var X#3)},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#1          |->  X#3,
           E#4          |->  {E#10},
           A#18         |->  A#19,
           C#7          |->  A#19[(app (\ X#9.S#12) C#21)],
           A#15         |->  [.],
           X#16         |->  X#3,
           C#20         |->  (app (\ X#9.S#12) C#21),
           S#11         |->  C#21[(var X#3)]}

and instantiated rules:

                                  (letrec {X#3=A#19[(app (\ X#9.S#12) C#21[(var X#3)])];X#8=(var X#3);E#10} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#3=A#19[(app (\ X#9.S#12) C#21[(var X#8)])];X#8=(var X#3);E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#3=A#19[(app (\ X#9.S#12) C#21[(var X#3)])];X#8=(var X#3);E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#3=A#19[(letrec {X#9=C#21[(var X#3)]} in S#12)];X#8=(var X#3);E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21[(var X#8)])]
       ;X#8= (var X#3)
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#3= A#19[(app A#20[(letrec {X#9=S#11} in S#12)] C#21[(var X#3)])]
       ;X#8= (var X#3)
       ;E#10
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {}
   Delta3 = {((var X#8),A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21)]),
             ((var X#3),A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#8),A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#3=A#19[(app A#20[[.2]] C#21[(var X#3)])];[.1]=(var X#3)},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] C#21[(var X#3)])]},
           X#1          |->  X#3,
           E#4          |->  {E#10},
           C#7          |->  A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21)],
           A#18         |->  A#19[(app A#20 C#21[(var X#3)])],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#3=A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21[(var X#3)])];X#8=(var X#3);E#10} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#3=A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21[(var X#8)])];X#8=(var X#3);E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#3=A#19[(app A#20[(app (\ X#9.S#12) S#11)] C#21[(var X#3)])];X#8=(var X#3);E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#3=A#19[(app A#20[(letrec {X#9=S#11} in S#12)] C#21[(var X#3)])];X#8=(var X#3);E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= (app (\ X#9.C#20[(var X#8)]) S#11)
       ;X#8= (var X#3)
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#3= (letrec {X#9=S#11} in C#20[(var X#3)])
       ;X#8= (var X#3)
       ;E#10
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#19,C#7}
   Delta2 = {}
   Delta3 = {((var X#8),(app (\ X#9.C#20) S#11)),
             ((var X#3),(app (\ X#9.C#20) S#11)),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in C#20[(var X#3)])),
             ((var X#8),(app (\ X#9.C#20[[.]]) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#3=[.2];[.1]=(var X#3)},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#3,
           E#4          |->  {E#10},
           A#18         |->  [.],
           C#7          |->  (app (\ X#9.C#20) S#11),
           C#19         |->  (\ X#9.C#20),
           S#12         |->  C#20[(var X#3)],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#3=(app (\ X#9.C#20[(var X#3)]) S#11);X#8=(var X#3);E#10} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#3=(app (\ X#9.C#20[(var X#8)]) S#11);X#8=(var X#3);E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#3=(app (\ X#9.C#20[(var X#3)]) S#11);X#8=(var X#3);E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#3=(letrec {X#9=S#11} in C#20[(var X#3)]);X#8=(var X#3);E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= (app (\ X#9.S#12) C#19[(var X#8)])
       ;X#8= (var X#3)
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#3= (letrec {X#9=C#19[(var X#3)]} in S#12)
       ;X#8= (var X#3)
       ;E#10
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {}
   Delta3 = {((var X#8),(app (\ X#9.S#12) C#19)),
             ((var X#3),(app (\ X#9.S#12) C#19)),
             (C#19[(var X#3)],(\ X#9.[.])),
             (C#19[(var X#3)],(letrec {X#9=[.]} in S#12)),
             ((var X#8),(app (\ X#9.S#12) C#19[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#3=[.2];[.1]=(var X#3)},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#3,
           E#4          |->  {E#10},
           A#18         |->  [.],
           C#7          |->  (app (\ X#9.S#12) C#19),
           S#11         |->  C#19[(var X#3)],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#3=(app (\ X#9.S#12) C#19[(var X#3)]);X#8=(var X#3);E#10} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#3=(app (\ X#9.S#12) C#19[(var X#8)]);X#8=(var X#3);E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#3=(app (\ X#9.S#12) C#19[(var X#3)]);X#8=(var X#3);E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#3=(letrec {X#9=C#19[(var X#3)]} in S#12);X#8=(var X#3);E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= A#21[(app A#22[(var X#19)] C#23[(var X#8)])]
       ;X#8= (var X#3)
       ;E#10
       ;EE#20[X#19,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#3= A#21[(app A#22[(var X#19)] C#23[(var X#3)])]
       ;X#8= (var X#3)
       ;E#10
       ;EE#20[X#19,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {}
   Delta3 = {((var X#8),A#21[(app A#22[(var X#19)] C#23)]),
             ((var X#3),A#21[(app A#22[(var X#19)] C#23)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#8),A#21[(app A#22[(var X#19)] C#23[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];[.1]=(var X#3);EE#20[X#19,[.2]]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];EE#20[X#19,[.2]]},
           X#1          |->  X#3,
           E#4          |->  {E#10;EE#20[X#19,(app (\ X#9.S#12) S#11)]},
           C#7          |->  A#21[(app A#22[(var X#19)] C#23)],
           A#18         |->  A#21[(app A#22 C#23[(var X#3)])],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];X#8=(var X#3);E#10;EE#20[X#19,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#8)])];X#8=(var X#3);E#10;EE#20[X#19,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];X#8=(var X#3);E#10;EE#20[X#19,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];X#8=(var X#3);E#10;EE#20[X#19,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] C#25[(var X#8)])]
       ;X#8= (var X#3)
       ;E#10
       ;EE#21[X#3,(var X#19)]
       ;EE#22[X#20,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] C#25[(var X#3)])]
       ;X#8= (var X#3)
       ;E#10
       ;EE#21[X#3,(var X#19)]
       ;EE#22[X#20,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {}
   Delta3 = {((var X#8),A#23[(app A#24[(var X#20)] C#25)]),
             ((var X#3),A#23[(app A#24[(var X#20)] C#25)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#8),A#23[(app A#24[(var X#20)] C#25[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];[.1]=(var X#3);EE#21[X#3,(var X#19)];EE#22[X#20,[.2]]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#1          |->  X#19,
           E#4          |->  {E#10;EE#21[X#3,(var X#19)];EE#22[X#20,(app (\ X#9.S#12) S#11)]},
           C#7          |->  A#23[(app A#24[(var X#20)] C#25)],
           A#18         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];X#8=(var X#3);E#10;EE#21[X#3,(var X#19)];EE#22[X#20,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#8)])];X#8=(var X#3);E#10;EE#21[X#3,(var X#19)];EE#22[X#20,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];X#8=(var X#3);E#10;EE#21[X#3,(var X#19)];EE#22[X#20,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];X#8=(var X#3);E#10;EE#21[X#3,(var X#19)];EE#22[X#20,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app (\ X#9.C#24[(var X#8)]) S#11)]
       ;X#8= (var X#3)
       ;E#10
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(letrec {X#9=S#11} in C#24[(var X#3)])]
       ;X#8= (var X#3)
       ;E#10
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#23,C#22,A#18,C#7,A#21}
   Delta2 = {}
   Delta3 = {((var X#8),A#21[(app (\ X#9.C#24) S#11)]),
             ((var X#3),A#21[(app (\ X#9.C#24) S#11)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in C#24[(var X#3)])),
             ((var X#8),A#21[(app (\ X#9.C#24[[.]]) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];[.1]=(var X#3);EE#20[X#3,(var X#19)]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {E#10;EE#20[X#3,(var X#19)]},
           A#18         |->  A#21,
           C#7          |->  A#21[(app (\ X#9.C#24) S#11)],
           A#15         |->  [.],
           X#16         |->  X#3,
           C#22         |->  (app (\ X#9.C#24) S#11),
           C#23         |->  (\ X#9.C#24),
           S#12         |->  C#24[(var X#3)]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app (\ X#9.C#24[(var X#3)]) S#11)];X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#21[(app (\ X#9.C#24[(var X#8)]) S#11)];X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app (\ X#9.C#24[(var X#3)]) S#11)];X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#19=A#21[(letrec {X#9=S#11} in C#24[(var X#3)])];X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app (\ X#9.S#12) C#23[(var X#8)])]
       ;X#8= (var X#3)
       ;E#10
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(letrec {X#9=C#23[(var X#3)]} in S#12)]
       ;X#8= (var X#3)
       ;E#10
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#22,A#18,C#7,A#21}
   Delta2 = {}
   Delta3 = {((var X#8),A#21[(app (\ X#9.S#12) C#23)]),
             ((var X#3),A#21[(app (\ X#9.S#12) C#23)]),
             (C#23[(var X#3)],(\ X#9.[.])),
             (C#23[(var X#3)],(letrec {X#9=[.]} in S#12)),
             ((var X#8),A#21[(app (\ X#9.S#12) C#23[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];[.1]=(var X#3);EE#20[X#3,(var X#19)]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {E#10;EE#20[X#3,(var X#19)]},
           A#18         |->  A#21,
           C#7          |->  A#21[(app (\ X#9.S#12) C#23)],
           A#15         |->  [.],
           X#16         |->  X#3,
           C#22         |->  (app (\ X#9.S#12) C#23),
           S#11         |->  C#23[(var X#3)]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app (\ X#9.S#12) C#23[(var X#3)])];X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#21[(app (\ X#9.S#12) C#23[(var X#8)])];X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app (\ X#9.S#12) C#23[(var X#3)])];X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#19=A#21[(letrec {X#9=C#23[(var X#3)]} in S#12)];X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23[(var X#8)])]
       ;X#8= (var X#3)
       ;E#10
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(letrec {X#9=S#11} in S#12)] C#23[(var X#3)])]
       ;X#8= (var X#3)
       ;E#10
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {}
   Delta3 = {((var X#8),A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23)]),
             ((var X#3),A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#8),A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] C#23[(var X#3)])];[.1]=(var X#3);EE#20[X#3,(var X#19)]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] C#23[(var X#3)])];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {E#10;EE#20[X#3,(var X#19)]},
           C#7          |->  A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23)],
           A#18         |->  A#21[(app A#22 C#23[(var X#3)])],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23[(var X#3)])];X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23[(var X#8)])];X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23[(var X#3)])];X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#19=A#21[(app A#22[(letrec {X#9=S#11} in S#12)] C#23[(var X#3)])];X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (app (\ X#9.C#22[(var X#8)]) S#11)
       ;X#8= (var X#3)
       ;E#10
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= (letrec {X#9=S#11} in C#22[(var X#3)])
       ;X#8= (var X#3)
       ;E#10
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#21,C#7}
   Delta2 = {}
   Delta3 = {((var X#8),(app (\ X#9.C#22) S#11)),
             ((var X#3),(app (\ X#9.C#22) S#11)),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in C#22[(var X#3)])),
             ((var X#8),(app (\ X#9.C#22[[.]]) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#19=[.2];[.1]=(var X#3);EE#20[X#3,(var X#19)]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {E#10;EE#20[X#3,(var X#19)]},
           A#18         |->  [.],
           C#7          |->  (app (\ X#9.C#22) S#11),
           C#21         |->  (\ X#9.C#22),
           S#12         |->  C#22[(var X#3)],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=(app (\ X#9.C#22[(var X#3)]) S#11);X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=(app (\ X#9.C#22[(var X#8)]) S#11);X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=(app (\ X#9.C#22[(var X#3)]) S#11);X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#19=(letrec {X#9=S#11} in C#22[(var X#3)]);X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (app (\ X#9.S#12) C#21[(var X#8)])
       ;X#8= (var X#3)
       ;E#10
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= (letrec {X#9=C#21[(var X#3)]} in S#12)
       ;X#8= (var X#3)
       ;E#10
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {}
   Delta3 = {((var X#8),(app (\ X#9.S#12) C#21)),
             ((var X#3),(app (\ X#9.S#12) C#21)),
             (C#21[(var X#3)],(\ X#9.[.])),
             (C#21[(var X#3)],(letrec {X#9=[.]} in S#12)),
             ((var X#8),(app (\ X#9.S#12) C#21[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#19=[.2];[.1]=(var X#3);EE#20[X#3,(var X#19)]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {E#10;EE#20[X#3,(var X#19)]},
           A#18         |->  [.],
           C#7          |->  (app (\ X#9.S#12) C#21),
           S#11         |->  C#21[(var X#3)],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=(app (\ X#9.S#12) C#21[(var X#3)]);X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=(app (\ X#9.S#12) C#21[(var X#8)]);X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=(app (\ X#9.S#12) C#21[(var X#3)]);X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#19=(letrec {X#9=C#21[(var X#3)]} in S#12);X#8=(var X#3);E#10;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#16)]
       ;X#16= (var X#3)
       ;E#20
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#3,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#16= (var X#3)
       ;E#20
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#3,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#16),C#7),
             ((var X#3),C#7),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#16),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);EE#18[[.1],(var X#16)];EE#19[X#3,[.2]]},
           X#2          |->  X#16,
           E#10         |->  {X#1=C#7[(var X#3)];E#20},
           E#4          |->  {E#20;EE#18[X#8,(var X#16)];EE#19[X#3,(app (\ X#9.S#12) S#11)]},
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#16=(var X#3);E#20;EE#18[X#8,(var X#16)];EE#19[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#16)];X#16=(var X#3);E#20;EE#18[X#8,(var X#16)];EE#19[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#16=(var X#3);E#20;EE#18[X#8,(var X#16)];EE#19[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#1=C#7[(var X#3)];X#16=(var X#3);E#20;EE#18[X#8,(var X#16)];EE#19[X#3,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#8= A#21[(app A#22[(var X#16)] C#23[(var X#16)])]
       ;E#10
       ;EE#19[X#3,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#8= A#21[(app A#22[(var X#16)] C#23[(var X#3)])]
       ;E#10
       ;EE#19[X#3,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {}
   Delta3 = {((var X#16),A#21[(app A#22[(var X#16)] C#23)]),
             ((var X#3),A#21[(app A#22[(var X#16)] C#23)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#16),A#21[(app A#22[(var X#16)] C#23[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);[.1]=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];EE#19[X#3,[.2]]},
           X#2          |->  X#16,
           EE#18[.1,.2] |-> {[.1]=A#21[(app A#22[[.2]] C#23[(var X#3)])]},
           X#1          |->  X#8,
           E#4          |->  {E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)]},
           C#7          |->  A#21[(app A#22[(var X#16)] C#23)],
           A#20         |->  A#21[(app A#22 C#23[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#8=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#8=A#21[(app A#22[(var X#16)] C#23[(var X#16)])];E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#8=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#8=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];E#10;EE#19[X#3,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#8= A#23[(app A#24[(var X#21)] C#25[(var X#16)])]
       ;E#10
       ;EE#19[X#3,(app (\ X#9.S#12) S#11)]
       ;EE#22[X#21,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#8= A#23[(app A#24[(var X#21)] C#25[(var X#3)])]
       ;E#10
       ;EE#19[X#3,(letrec {X#9=S#11} in S#12)]
       ;EE#22[X#21,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {}
   Delta3 = {((var X#16),A#23[(app A#24[(var X#21)] C#25)]),
             ((var X#3),A#23[(app A#24[(var X#21)] C#25)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#16),A#23[(app A#24[(var X#21)] C#25[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);[.1]=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];EE#19[X#3,[.2]];EE#22[X#21,(var X#16)]},
           X#2          |->  X#16,
           EE#18[.1,.2] |-> {[.1]=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];EE#22[X#21,[.2]]},
           X#1          |->  X#8,
           E#4          |->  {E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)];EE#22[X#21,(var X#16)]},
           C#7          |->  A#23[(app A#24[(var X#21)] C#25)],
           A#20         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#8=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)];EE#22[X#21,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#8=A#23[(app A#24[(var X#21)] C#25[(var X#16)])];E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)];EE#22[X#21,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#8=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)];EE#22[X#21,(var X#16)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#8=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#10;EE#19[X#3,(letrec {X#9=S#11} in S#12)];EE#22[X#21,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#25[(app A#26[(var X#22)] C#27[(var X#16)])]
       ;E#10
       ;EE#19[X#3,(app (\ X#9.S#12) S#11)]
       ;EE#23[X#8,(var X#21)]
       ;EE#24[X#22,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#25[(app A#26[(var X#22)] C#27[(var X#3)])]
       ;E#10
       ;EE#19[X#3,(letrec {X#9=S#11} in S#12)]
       ;EE#23[X#8,(var X#21)]
       ;EE#24[X#22,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {}
   Delta3 = {((var X#16),A#25[(app A#26[(var X#22)] C#27)]),
             ((var X#3),A#25[(app A#26[(var X#22)] C#27)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#16),A#25[(app A#26[(var X#22)] C#27[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];EE#19[X#3,[.2]];EE#23[[.1],(var X#21)];EE#24[X#22,(var X#16)]},
           X#2          |->  X#16,
           EE#18[.1,.2] |-> {X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];EE#23[[.1],(var X#21)];EE#24[X#22,[.2]]},
           X#1          |->  X#21,
           E#4          |->  {E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)];EE#23[X#8,(var X#21)];EE#24[X#22,(var X#16)]},
           C#7          |->  A#25[(app A#26[(var X#22)] C#27)],
           A#20         |->  A#25[(app A#26 C#27[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)];EE#23[X#8,(var X#21)];EE#24[X#22,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#16)])];E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)];EE#23[X#8,(var X#21)];EE#24[X#22,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)];EE#23[X#8,(var X#21)];EE#24[X#22,(var X#16)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#10;EE#19[X#3,(letrec {X#9=S#11} in S#12)];EE#23[X#8,(var X#21)];EE#24[X#22,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app A#24[(var X#16)] C#25[(var X#16)])]
       ;E#10
       ;EE#19[X#3,(app (\ X#9.S#12) S#11)]
       ;EE#22[X#8,(var X#21)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app A#24[(var X#16)] C#25[(var X#3)])]
       ;E#10
       ;EE#19[X#3,(letrec {X#9=S#11} in S#12)]
       ;EE#22[X#8,(var X#21)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {}
   Delta3 = {((var X#16),A#23[(app A#24[(var X#16)] C#25)]),
             ((var X#3),A#23[(app A#24[(var X#16)] C#25)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#16),A#23[(app A#24[(var X#16)] C#25[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#3)])];EE#19[X#3,[.2]];EE#22[[.1],(var X#21)]},
           X#2          |->  X#16,
           EE#18[.1,.2] |-> {X#21=A#23[(app A#24[[.2]] C#25[(var X#3)])];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)];EE#22[X#8,(var X#21)]},
           C#7          |->  A#23[(app A#24[(var X#16)] C#25)],
           A#20         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#3)])];E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)];EE#22[X#8,(var X#21)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#16)])];E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)];EE#22[X#8,(var X#21)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#3)])];E#10;EE#19[X#3,(app (\ X#9.S#12) S#11)];EE#22[X#8,(var X#21)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#3)])];E#10;EE#19[X#3,(letrec {X#9=S#11} in S#12)];EE#22[X#8,(var X#21)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(app (\ X#9.C#24[(var X#16)]) S#11)]
       ;E#10
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(letrec {X#9=S#11} in C#24[(var X#3)])]
       ;E#10
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#23,C#22,A#20,C#7,A#21}
   Delta2 = {}
   Delta3 = {((var X#16),A#21[(app (\ X#9.C#24) S#11)]),
             ((var X#3),A#21[(app (\ X#9.C#24) S#11)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in C#24[(var X#3)])),
             ((var X#16),A#21[(app (\ X#9.C#24[[.]]) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=A#21[[.2]];EE#18[[.1],(var X#16)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=A#21[[.2]]},
           X#1          |->  X#3,
           E#4          |->  {E#10;EE#18[X#8,(var X#16)]},
           A#20         |->  A#21,
           C#7          |->  A#21[(app (\ X#9.C#24) S#11)],
           A#15         |->  [.],
           X#17         |->  X#3,
           C#22         |->  (app (\ X#9.C#24) S#11),
           C#23         |->  (\ X#9.C#24),
           S#12         |->  C#24[(var X#3)]}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=A#21[(app (\ X#9.C#24[(var X#3)]) S#11)];E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=A#21[(app (\ X#9.C#24[(var X#16)]) S#11)];E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=A#21[(app (\ X#9.C#24[(var X#3)]) S#11)];E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#3=A#21[(letrec {X#9=S#11} in C#24[(var X#3)])];E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(app (\ X#9.S#12) C#23[(var X#16)])]
       ;E#10
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(letrec {X#9=C#23[(var X#3)]} in S#12)]
       ;E#10
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#22,A#20,C#7,A#21}
   Delta2 = {}
   Delta3 = {((var X#16),A#21[(app (\ X#9.S#12) C#23)]),
             ((var X#3),A#21[(app (\ X#9.S#12) C#23)]),
             (C#23[(var X#3)],(\ X#9.[.])),
             (C#23[(var X#3)],(letrec {X#9=[.]} in S#12)),
             ((var X#16),A#21[(app (\ X#9.S#12) C#23[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=A#21[[.2]];EE#18[[.1],(var X#16)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=A#21[[.2]]},
           X#1          |->  X#3,
           E#4          |->  {E#10;EE#18[X#8,(var X#16)]},
           A#20         |->  A#21,
           C#7          |->  A#21[(app (\ X#9.S#12) C#23)],
           A#15         |->  [.],
           X#17         |->  X#3,
           C#22         |->  (app (\ X#9.S#12) C#23),
           S#11         |->  C#23[(var X#3)]}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=A#21[(app (\ X#9.S#12) C#23[(var X#3)])];E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=A#21[(app (\ X#9.S#12) C#23[(var X#16)])];E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=A#21[(app (\ X#9.S#12) C#23[(var X#3)])];E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#3=A#21[(letrec {X#9=C#23[(var X#3)]} in S#12)];E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23[(var X#16)])]
       ;E#10
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(app A#22[(letrec {X#9=S#11} in S#12)] C#23[(var X#3)])]
       ;E#10
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {}
   Delta3 = {((var X#16),A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23)]),
             ((var X#3),A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#16),A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=A#21[(app A#22[[.2]] C#23[(var X#3)])];EE#18[[.1],(var X#16)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=A#21[(app A#22[[.2]] C#23[(var X#3)])]},
           X#1          |->  X#3,
           E#4          |->  {E#10;EE#18[X#8,(var X#16)]},
           C#7          |->  A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23)],
           A#20         |->  A#21[(app A#22 C#23[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23[(var X#3)])];E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23[(var X#16)])];E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=A#21[(app A#22[(app (\ X#9.S#12) S#11)] C#23[(var X#3)])];E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#3=A#21[(app A#22[(letrec {X#9=S#11} in S#12)] C#23[(var X#3)])];E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= (app (\ X#9.C#22[(var X#16)]) S#11)
       ;E#10
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= (letrec {X#9=S#11} in C#22[(var X#3)])
       ;E#10
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#21,C#7}
   Delta2 = {}
   Delta3 = {((var X#16),(app (\ X#9.C#22) S#11)),
             ((var X#3),(app (\ X#9.C#22) S#11)),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in C#22[(var X#3)])),
             ((var X#16),(app (\ X#9.C#22[[.]]) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=[.2];EE#18[[.1],(var X#16)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#3,
           E#4          |->  {E#10;EE#18[X#8,(var X#16)]},
           A#20         |->  [.],
           C#7          |->  (app (\ X#9.C#22) S#11),
           C#21         |->  (\ X#9.C#22),
           S#12         |->  C#22[(var X#3)],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=(app (\ X#9.C#22[(var X#3)]) S#11);E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=(app (\ X#9.C#22[(var X#16)]) S#11);E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=(app (\ X#9.C#22[(var X#3)]) S#11);E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#3=(letrec {X#9=S#11} in C#22[(var X#3)]);E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= (app (\ X#9.S#12) C#21[(var X#16)])
       ;E#10
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= (letrec {X#9=C#21[(var X#3)]} in S#12)
       ;E#10
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {}
   Delta3 = {((var X#16),(app (\ X#9.S#12) C#21)),
             ((var X#3),(app (\ X#9.S#12) C#21)),
             (C#21[(var X#3)],(\ X#9.[.])),
             (C#21[(var X#3)],(letrec {X#9=[.]} in S#12)),
             ((var X#16),(app (\ X#9.S#12) C#21[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=[.2];EE#18[[.1],(var X#16)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#3,
           E#4          |->  {E#10;EE#18[X#8,(var X#16)]},
           A#20         |->  [.],
           C#7          |->  (app (\ X#9.S#12) C#21),
           S#11         |->  C#21[(var X#3)],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=(app (\ X#9.S#12) C#21[(var X#3)]);E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=(app (\ X#9.S#12) C#21[(var X#16)]);E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=(app (\ X#9.S#12) C#21[(var X#3)]);E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#3=(letrec {X#9=C#21[(var X#3)]} in S#12);E#10;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= A#23[(app A#24[(var X#21)] C#25[(var X#16)])]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#21,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= A#23[(app A#24[(var X#21)] C#25[(var X#3)])]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#21,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {}
   Delta3 = {((var X#16),A#23[(app A#24[(var X#21)] C#25)]),
             ((var X#3),A#23[(app A#24[(var X#21)] C#25)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#16),A#23[(app A#24[(var X#21)] C#25[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];EE#18[[.1],(var X#16)];EE#22[X#21,[.2]]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];EE#22[X#21,[.2]]},
           X#1          |->  X#3,
           E#4          |->  {E#10;EE#18[X#8,(var X#16)];EE#22[X#21,(app (\ X#9.S#12) S#11)]},
           C#7          |->  A#23[(app A#24[(var X#21)] C#25)],
           A#20         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#10;EE#18[X#8,(var X#16)];EE#22[X#21,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#16)])];E#10;EE#18[X#8,(var X#16)];EE#22[X#21,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#10;EE#18[X#8,(var X#16)];EE#22[X#21,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#10;EE#18[X#8,(var X#16)];EE#22[X#21,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#25[(app A#26[(var X#22)] C#27[(var X#16)])]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#23[X#3,(var X#21)]
       ;EE#24[X#22,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#25[(app A#26[(var X#22)] C#27[(var X#3)])]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#23[X#3,(var X#21)]
       ;EE#24[X#22,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {}
   Delta3 = {((var X#16),A#25[(app A#26[(var X#22)] C#27)]),
             ((var X#3),A#25[(app A#26[(var X#22)] C#27)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#16),A#25[(app A#26[(var X#22)] C#27[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];EE#18[[.1],(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,[.2]]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];EE#23[[.1],(var X#21)];EE#24[X#22,[.2]]},
           X#1          |->  X#21,
           E#4          |->  {E#10;EE#18[X#8,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(app (\ X#9.S#12) S#11)]},
           C#7          |->  A#25[(app A#26[(var X#22)] C#27)],
           A#20         |->  A#25[(app A#26 C#27[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#10;EE#18[X#8,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#16)])];E#10;EE#18[X#8,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#10;EE#18[X#8,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#10;EE#18[X#8,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app (\ X#9.C#26[(var X#16)]) S#11)]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(letrec {X#9=S#11} in C#26[(var X#3)])]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#25,C#24,A#20,C#7,A#23}
   Delta2 = {}
   Delta3 = {((var X#16),A#23[(app (\ X#9.C#26) S#11)]),
             ((var X#3),A#23[(app (\ X#9.C#26) S#11)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in C#26[(var X#3)])),
             ((var X#16),A#23[(app (\ X#9.C#26[[.]]) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#23[[.2]];EE#18[[.1],(var X#16)];EE#22[X#3,(var X#21)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=A#23[[.2]];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]},
           A#20         |->  A#23,
           C#7          |->  A#23[(app (\ X#9.C#26) S#11)],
           A#15         |->  [.],
           X#17         |->  X#3,
           C#24         |->  (app (\ X#9.C#26) S#11),
           C#25         |->  (\ X#9.C#26),
           S#12         |->  C#26[(var X#3)]}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#23[(app (\ X#9.C#26[(var X#3)]) S#11)];E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#23[(app (\ X#9.C#26[(var X#16)]) S#11)];E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#23[(app (\ X#9.C#26[(var X#3)]) S#11)];E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#21=A#23[(letrec {X#9=S#11} in C#26[(var X#3)])];E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app (\ X#9.S#12) C#25[(var X#16)])]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(letrec {X#9=C#25[(var X#3)]} in S#12)]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#24,A#20,C#7,A#23}
   Delta2 = {}
   Delta3 = {((var X#16),A#23[(app (\ X#9.S#12) C#25)]),
             ((var X#3),A#23[(app (\ X#9.S#12) C#25)]),
             (C#25[(var X#3)],(\ X#9.[.])),
             (C#25[(var X#3)],(letrec {X#9=[.]} in S#12)),
             ((var X#16),A#23[(app (\ X#9.S#12) C#25[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#23[[.2]];EE#18[[.1],(var X#16)];EE#22[X#3,(var X#21)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=A#23[[.2]];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]},
           A#20         |->  A#23,
           C#7          |->  A#23[(app (\ X#9.S#12) C#25)],
           A#15         |->  [.],
           X#17         |->  X#3,
           C#24         |->  (app (\ X#9.S#12) C#25),
           S#11         |->  C#25[(var X#3)]}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#23[(app (\ X#9.S#12) C#25[(var X#3)])];E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#23[(app (\ X#9.S#12) C#25[(var X#16)])];E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#23[(app (\ X#9.S#12) C#25[(var X#3)])];E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#21=A#23[(letrec {X#9=C#25[(var X#3)]} in S#12)];E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app A#24[(app (\ X#9.S#12) S#11)] C#25[(var X#16)])]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app A#24[(letrec {X#9=S#11} in S#12)] C#25[(var X#3)])]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {}
   Delta3 = {((var X#16),A#23[(app A#24[(app (\ X#9.S#12) S#11)] C#25)]),
             ((var X#3),A#23[(app A#24[(app (\ X#9.S#12) S#11)] C#25)]),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#16),A#23[(app A#24[(app (\ X#9.S#12) S#11)] C#25[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#23[(app A#24[[.2]] C#25[(var X#3)])];EE#18[[.1],(var X#16)];EE#22[X#3,(var X#21)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=A#23[(app A#24[[.2]] C#25[(var X#3)])];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]},
           C#7          |->  A#23[(app A#24[(app (\ X#9.S#12) S#11)] C#25)],
           A#20         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(app (\ X#9.S#12) S#11)] C#25[(var X#3)])];E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(app (\ X#9.S#12) S#11)] C#25[(var X#16)])];E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(app (\ X#9.S#12) S#11)] C#25[(var X#3)])];E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(letrec {X#9=S#11} in S#12)] C#25[(var X#3)])];E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= (app (\ X#9.C#24[(var X#16)]) S#11)
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= (letrec {X#9=S#11} in C#24[(var X#3)])
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#23,C#7}
   Delta2 = {}
   Delta3 = {((var X#16),(app (\ X#9.C#24) S#11)),
             ((var X#3),(app (\ X#9.C#24) S#11)),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in C#24[(var X#3)])),
             ((var X#16),(app (\ X#9.C#24[[.]]) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=[.2];EE#18[[.1],(var X#16)];EE#22[X#3,(var X#21)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=[.2];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]},
           A#20         |->  [.],
           C#7          |->  (app (\ X#9.C#24) S#11),
           C#23         |->  (\ X#9.C#24),
           S#12         |->  C#24[(var X#3)],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=(app (\ X#9.C#24[(var X#3)]) S#11);E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=(app (\ X#9.C#24[(var X#16)]) S#11);E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=(app (\ X#9.C#24[(var X#3)]) S#11);E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#21=(letrec {X#9=S#11} in C#24[(var X#3)]);E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= (app (\ X#9.S#12) C#23[(var X#16)])
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= (letrec {X#9=C#23[(var X#3)]} in S#12)
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {}
   Delta3 = {((var X#16),(app (\ X#9.S#12) C#23)),
             ((var X#3),(app (\ X#9.S#12) C#23)),
             (C#23[(var X#3)],(\ X#9.[.])),
             (C#23[(var X#3)],(letrec {X#9=[.]} in S#12)),
             ((var X#16),(app (\ X#9.S#12) C#23[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=[.2];EE#18[[.1],(var X#16)];EE#22[X#3,(var X#21)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=[.2];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]},
           A#20         |->  [.],
           C#7          |->  (app (\ X#9.S#12) C#23),
           S#11         |->  C#23[(var X#3)],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=(app (\ X#9.S#12) C#23[(var X#3)]);E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=(app (\ X#9.S#12) C#23[(var X#16)]);E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=(app (\ X#9.S#12) C#23[(var X#3)]);E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(var X#3);X#21=(letrec {X#9=C#23[(var X#3)]} in S#12);E#10;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (\ X#9.S#11)
       ;E#10
     in
        A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
     )
    ,
     (letrec
        X#8= (\ X#9.S#11)
       ;E#10
     in
        A#14[(app A#15[(\ X#9.S#11)] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#13,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#14[(app A#15[[.]] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])
    -SR,cp-in1->                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(\ X#9.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(\ X#9.S#11);E#10} in A#14[(app A#15[(var X#8)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#8)] T#16)],
           A#12  |->  A#14[(app A#15 T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(\ X#9.S#11);E#10} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -cpx-e1->                     (letrec {X#8=(\ X#9.S#11);E#10} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])])
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#11);E#10} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -SR,cp-in1->                  (letrec {X#8=(\ X#9.S#11);E#10} in A#14[(app A#15[(\ X#9.S#11)] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
       ;X#8= (\ X#9.S#11)
       ;E#16
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;X#8= (\ X#9.S#11)
       ;E#16
     in
        A#12[(\ X#9.S#11)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])
    -SR,cp-in1->                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(\ X#9.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#14=T#13;X#8=(\ X#9.S#11);E#16} in A#12[(var X#8)]),
           E#10  |->  {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16},
           E#15  |->  {X#8=(\ X#9.S#11);E#16}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#11);E#16} in A#12[(var X#8)])
    -cpx-e1->                     (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#11);E#16} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#11);E#16} in A#12[(var X#8)])
    -SR,cp-in1->                  (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#11);E#16} in A#12[(\ X#9.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#2=(var X#3);X#8=(\ X#9.C#14[(var X#2)]);E#13} in A#12[(var X#8)])
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= (\ X#9.C#14[(var X#3)])
       ;E#13
     in
        A#12[(\ X#9.C#14[(var X#3)])]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {}
   Delta3 = {((var X#2),(\ X#9.C#14)),
             ((var X#3),(\ X#9.C#14)),
             ((var X#2),(\ X#9.C#14[[.]])),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])
    -SR,cp-in1->                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(\ X#9.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#8)],
           E#10  |->  {X#2=(var X#3);E#13},
           X#1   |->  X#8,
           E#4   |->  {E#13},
           C#7   |->  (\ X#9.C#14),
           S#11  |->  C#14[(var X#3)]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(\ X#9.C#14[(var X#3)]);E#13} in A#12[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(\ X#9.C#14[(var X#2)]);E#13} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(\ X#9.C#14[(var X#3)]);E#13} in A#12[(var X#8)])
    -SR,cp-in1->                  (letrec {X#2=(var X#3);X#8=(\ X#9.C#14[(var X#3)]);E#13} in A#12[(\ X#9.C#14[(var X#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#2)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#11)
       ;E#14
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#11)
       ;E#14
     in
        A#12[(\ X#9.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])
    -SR,cp-in1->                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(\ X#9.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#8)],
           E#10  |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#14},
           E#13  |->  {X#1=C#7[(var X#3)];E#14},
           E#4   |->  {X#8=(\ X#9.S#11);E#14}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#11);E#14} in A#12[(var X#8)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);X#8=(\ X#9.S#11);E#14} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#11);E#14} in A#12[(var X#8)])
    -SR,cp-in1->                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#11);E#14} in A#12[(\ X#9.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (\ X#9.S#12)
       ;E#11
       ;VV#14|X#10,(var X#8)|
     in
        A#16[(app A#17[(var X#10)] T#18[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
     )
    ,
     (letrec
        X#8= (\ X#9.S#12)
       ;E#11
       ;VV#14|X#10,(var X#8)|
     in
        A#16[(app A#17[(\ X#9.S#12)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
     )
  )

where

   Delta1 = {A#13,T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#16[(app A#17[[.]] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#16[(app A#17[(var X#10)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#10)] T#18)],
           A#13  |->  A#16[(app A#17 T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#16[(app A#17[(var X#10)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -cpx-e1->                     (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#16[(app A#17[(var X#10)] T#18[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])])
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#16[(app A#17[(var X#10)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#16[(app A#17[(\ X#9.S#12)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
       ;X#8= (\ X#9.S#12)
       ;E#18
       ;VV#14|X#10,(var X#8)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;X#8= (\ X#9.S#12)
       ;E#18
       ;VV#14|X#10,(var X#8)|
     in
        A#13[(\ X#9.S#12)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {X#16=T#15;X#8=(\ X#9.S#12);E#18;VV#14|X#10,(var X#8)|} in A#13[(var X#10)]),
           E#11  |->  {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18},
           E#17  |->  {X#8=(\ X#9.S#12);E#18;VV#14|X#10,(var X#8)|}}

and instantiated rules:

                                  (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#12);E#18;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -cpx-e1->                     (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#12);E#18;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#12);E#18;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#12);E#18;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (\ X#9.C#16[(var X#2)])
       ;E#15
       ;VV#14|X#10,(var X#8)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= (\ X#9.C#16[(var X#3)])
       ;E#15
       ;VV#14|X#10,(var X#8)|
     in
        A#13[(\ X#9.C#16[(var X#3)])]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {}
   Delta3 = {((var X#2),(\ X#9.C#16)),
             ((var X#3),(\ X#9.C#16)),
             ((var X#2),(\ X#9.C#16[[.]])),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#10)],
           E#11  |->  {X#2=(var X#3);E#15},
           X#1   |->  X#8,
           E#4   |->  {E#15;VV#14|X#10,(var X#8)|},
           C#7   |->  (\ X#9.C#16),
           S#12  |->  C#16[(var X#3)]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(\ X#9.C#16[(var X#3)]);E#15;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(\ X#9.C#16[(var X#2)]);E#15;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(\ X#9.C#16[(var X#3)]);E#15;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#2=(var X#3);X#8=(\ X#9.C#16[(var X#3)]);E#15;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.C#16[(var X#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#2)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;VV#14|X#10,(var X#8)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;VV#14|X#10,(var X#8)|
     in
        A#13[(\ X#9.S#12)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#10)],
           E#11  |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#16},
           E#15  |->  {X#1=C#7[(var X#3)];E#16},
           E#4   |->  {X#8=(\ X#9.S#12);E#16;VV#14|X#10,(var X#8)|}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#2)
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#15
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#8)
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#15
     in
        A#13[(\ X#9.S#12)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           E#11         |->  {X#2=(var X#8);E#15},
           VV#14|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#12);E#15},
           C#7          |->  [.],
           X#3          |->  X#8}

and instantiated rules:

                                  (letrec {X#10=(var X#8);X#2=(var X#8);X#8=(\ X#9.S#12);E#15} in A#13[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#2);X#2=(var X#8);X#8=(\ X#9.S#12);E#15} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#8);X#2=(var X#8);X#8=(\ X#9.S#12);E#15} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#10=(var X#8);X#2=(var X#8);X#8=(\ X#9.S#12);E#15} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#2)
       ;X#2= (var X#17)
       ;X#8= (\ X#9.S#12)
       ;E#15
       ;VV#18|X#17,(var X#8)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#17)
       ;X#2= (var X#17)
       ;X#8= (\ X#9.S#12)
       ;E#15
       ;VV#18|X#17,(var X#8)|
     in
        A#13[(\ X#9.S#12)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#17),[.]),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           E#11         |->  {X#2=(var X#17);E#15},
           VV#14|.1,.2| |-> {[.1]=(var X#17);VV#18|X#17,[.2]|},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#12);E#15;VV#18|X#17,(var X#8)|},
           C#7          |->  [.],
           X#3          |->  X#17}

and instantiated rules:

                                  (letrec {X#10=(var X#17);X#2=(var X#17);X#8=(\ X#9.S#12);E#15;VV#18|X#17,(var X#8)|} in A#13[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#2);X#2=(var X#17);X#8=(\ X#9.S#12);E#15;VV#18|X#17,(var X#8)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#17);X#2=(var X#17);X#8=(\ X#9.S#12);E#15;VV#18|X#17,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#10=(var X#17);X#2=(var X#17);X#8=(\ X#9.S#12);E#15;VV#18|X#17,(var X#8)|} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#2)
       ;X#2= (var X#18)
       ;X#8= (\ X#9.S#12)
       ;E#15
       ;VV#19|X#10,(var X#17)|
       ;VV#20|X#18,(var X#8)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#17= (var X#18)
       ;X#2= (var X#18)
       ;X#8= (\ X#9.S#12)
       ;E#15
       ;VV#19|X#10,(var X#17)|
       ;VV#20|X#18,(var X#8)|
     in
        A#13[(\ X#9.S#12)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#18),[.]),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           E#11         |->  {X#2=(var X#18);E#15},
           VV#14|.1,.2| |-> {X#17=(var X#18);VV#19|[.1],(var X#17)|;VV#20|X#18,[.2]|},
           X#1          |->  X#17,
           E#4          |->  {X#8=(\ X#9.S#12);E#15;VV#19|X#10,(var X#17)|;VV#20|X#18,(var X#8)|},
           C#7          |->  [.],
           X#3          |->  X#18}

and instantiated rules:

                                  (letrec {X#17=(var X#18);X#2=(var X#18);X#8=(\ X#9.S#12);E#15;VV#19|X#10,(var X#17)|;VV#20|X#18,(var X#8)|} in A#13[(var X#10)])
    -cpx-e1->                     (letrec {X#17=(var X#2);X#2=(var X#18);X#8=(\ X#9.S#12);E#15;VV#19|X#10,(var X#17)|;VV#20|X#18,(var X#8)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#17=(var X#18);X#2=(var X#18);X#8=(\ X#9.S#12);E#15;VV#19|X#10,(var X#17)|;VV#20|X#18,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#17=(var X#18);X#2=(var X#18);X#8=(\ X#9.S#12);E#15;VV#19|X#10,(var X#17)|;VV#20|X#18,(var X#8)|} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#2)
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#15
       ;VV#18|X#10,(var X#17)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#17= (var X#8)
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#15
       ;VV#18|X#10,(var X#17)|
     in
        A#13[(\ X#9.S#12)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           E#11         |->  {X#2=(var X#8);E#15},
           VV#14|.1,.2| |-> {X#17=[.2];VV#18|[.1],(var X#17)|},
           X#1          |->  X#17,
           E#4          |->  {X#8=(\ X#9.S#12);E#15;VV#18|X#10,(var X#17)|},
           C#7          |->  [.],
           X#3          |->  X#8}

and instantiated rules:

                                  (letrec {X#17=(var X#8);X#2=(var X#8);X#8=(\ X#9.S#12);E#15;VV#18|X#10,(var X#17)|} in A#13[(var X#10)])
    -cpx-e1->                     (letrec {X#17=(var X#2);X#2=(var X#8);X#8=(\ X#9.S#12);E#15;VV#18|X#10,(var X#17)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#17=(var X#8);X#2=(var X#8);X#8=(\ X#9.S#12);E#15;VV#18|X#10,(var X#17)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#17=(var X#8);X#2=(var X#8);X#8=(\ X#9.S#12);E#15;VV#18|X#10,(var X#17)|} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#10=(var X#8);X#8=(\ X#9.C#16[(var X#10)]);E#11} in A#13[(var X#10)])
    ,
     (letrec
        X#10= (var X#8)
       ;X#8= (\ X#9.C#16[(var X#8)])
       ;E#11
     in
        A#13[(\ X#9.C#16[(var X#8)])]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {}
   Delta3 = {((var X#10),(\ X#9.C#16)),
             ((var X#8),(\ X#9.C#16)),
             ((var X#10),(\ X#9.C#16[[.]])),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           VV#14|.1,.2| |-> {[.1]=[.2]},
           X#2          |->  X#10,
           X#3          |->  X#8,
           X#1          |->  X#8,
           E#4          |->  {E#11},
           C#7          |->  (\ X#9.C#16),
           S#12         |->  C#16[(var X#8)]}

and instantiated rules:

                                  (letrec {X#10=(var X#8);X#8=(\ X#9.C#16[(var X#8)]);E#11} in A#13[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#8);X#8=(\ X#9.C#16[(var X#10)]);E#11} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#8);X#8=(\ X#9.C#16[(var X#8)]);E#11} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#10=(var X#8);X#8=(\ X#9.C#16[(var X#8)]);E#11} in A#13[(\ X#9.C#16[(var X#8)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#10)]
       ;X#10= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#16
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#8)]
       ;X#10= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#16
     in
        A#13[(\ X#9.S#12)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#10),C#7),
             ((var X#8),C#7),
             ((var X#10),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           VV#14|.1,.2| |-> {[.1]=[.2]},
           X#2          |->  X#10,
           X#3          |->  X#8,
           E#11         |->  {X#1=C#7[(var X#8)];E#16},
           E#4          |->  {X#8=(\ X#9.S#12);E#16}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#8)];X#10=(var X#8);X#8=(\ X#9.S#12);E#16} in A#13[(var X#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#10)];X#10=(var X#8);X#8=(\ X#9.S#12);E#16} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#8)];X#10=(var X#8);X#8=(\ X#9.S#12);E#16} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#1=C#7[(var X#8)];X#10=(var X#8);X#8=(\ X#9.S#12);E#16} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#16)
       ;X#8= (\ X#9.C#18[(var X#10)])
       ;E#11
       ;VV#17|X#16,(var X#8)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#16)
       ;X#8= (\ X#9.C#18[(var X#16)])
       ;E#11
       ;VV#17|X#16,(var X#8)|
     in
        A#13[(\ X#9.C#18[(var X#16)])]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {}
   Delta3 = {((var X#10),(\ X#9.C#18)),
             ((var X#16),(\ X#9.C#18)),
             ((var X#10),(\ X#9.C#18[[.]])),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           VV#14|.1,.2| |-> {[.1]=(var X#16);VV#17|X#16,[.2]|},
           X#2          |->  X#10,
           X#3          |->  X#16,
           X#1          |->  X#8,
           E#4          |->  {E#11;VV#17|X#16,(var X#8)|},
           C#7          |->  (\ X#9.C#18),
           S#12         |->  C#18[(var X#16)]}

and instantiated rules:

                                  (letrec {X#10=(var X#16);X#8=(\ X#9.C#18[(var X#16)]);E#11;VV#17|X#16,(var X#8)|} in A#13[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#16);X#8=(\ X#9.C#18[(var X#10)]);E#11;VV#17|X#16,(var X#8)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#16);X#8=(\ X#9.C#18[(var X#16)]);E#11;VV#17|X#16,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#10=(var X#16);X#8=(\ X#9.C#18[(var X#16)]);E#11;VV#17|X#16,(var X#8)|} in A#13[(\ X#9.C#18[(var X#16)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#10)]
       ;X#10= (var X#16)
       ;X#8= (\ X#9.S#12)
       ;E#18
       ;VV#17|X#16,(var X#8)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#16)]
       ;X#10= (var X#16)
       ;X#8= (\ X#9.S#12)
       ;E#18
       ;VV#17|X#16,(var X#8)|
     in
        A#13[(\ X#9.S#12)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#10),C#7),
             ((var X#16),C#7),
             ((var X#10),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           VV#14|.1,.2| |-> {[.1]=(var X#16);VV#17|X#16,[.2]|},
           X#2          |->  X#10,
           X#3          |->  X#16,
           E#11         |->  {X#1=C#7[(var X#16)];E#18},
           E#4          |->  {X#8=(\ X#9.S#12);E#18;VV#17|X#16,(var X#8)|}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#16)];X#10=(var X#16);X#8=(\ X#9.S#12);E#18;VV#17|X#16,(var X#8)|} in A#13[(var X#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#10)];X#10=(var X#16);X#8=(\ X#9.S#12);E#18;VV#17|X#16,(var X#8)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#16)];X#10=(var X#16);X#8=(\ X#9.S#12);E#18;VV#17|X#16,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#1=C#7[(var X#16)];X#10=(var X#16);X#8=(\ X#9.S#12);E#18;VV#17|X#16,(var X#8)|} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#17)
       ;X#8= (\ X#9.C#20[(var X#16)])
       ;E#11
       ;VV#18|X#10,(var X#16)|
       ;VV#19|X#17,(var X#8)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#16= (var X#17)
       ;X#8= (\ X#9.C#20[(var X#17)])
       ;E#11
       ;VV#18|X#10,(var X#16)|
       ;VV#19|X#17,(var X#8)|
     in
        A#13[(\ X#9.C#20[(var X#17)])]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {}
   Delta3 = {((var X#16),(\ X#9.C#20)),
             ((var X#17),(\ X#9.C#20)),
             ((var X#16),(\ X#9.C#20[[.]])),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           VV#14|.1,.2| |-> {X#16=(var X#17);VV#18|[.1],(var X#16)|;VV#19|X#17,[.2]|},
           X#2          |->  X#16,
           X#3          |->  X#17,
           X#1          |->  X#8,
           E#4          |->  {E#11;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|},
           C#7          |->  (\ X#9.C#20),
           S#12         |->  C#20[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=(var X#17);X#8=(\ X#9.C#20[(var X#17)]);E#11;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|} in A#13[(var X#10)])
    -cpx-e1->                     (letrec {X#16=(var X#17);X#8=(\ X#9.C#20[(var X#16)]);E#11;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#16=(var X#17);X#8=(\ X#9.C#20[(var X#17)]);E#11;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#16=(var X#17);X#8=(\ X#9.C#20[(var X#17)]);E#11;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|} in A#13[(\ X#9.C#20[(var X#17)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#16)]
       ;X#16= (var X#17)
       ;X#8= (\ X#9.S#12)
       ;E#20
       ;VV#18|X#10,(var X#16)|
       ;VV#19|X#17,(var X#8)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#17)]
       ;X#16= (var X#17)
       ;X#8= (\ X#9.S#12)
       ;E#20
       ;VV#18|X#10,(var X#16)|
       ;VV#19|X#17,(var X#8)|
     in
        A#13[(\ X#9.S#12)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#16),C#7),
             ((var X#17),C#7),
             ((var X#16),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           VV#14|.1,.2| |-> {X#16=(var X#17);VV#18|[.1],(var X#16)|;VV#19|X#17,[.2]|},
           X#2          |->  X#16,
           X#3          |->  X#17,
           E#11         |->  {X#1=C#7[(var X#17)];E#20},
           E#4          |->  {X#8=(\ X#9.S#12);E#20;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#17)];X#16=(var X#17);X#8=(\ X#9.S#12);E#20;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|} in A#13[(var X#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#16)];X#16=(var X#17);X#8=(\ X#9.S#12);E#20;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#17)];X#16=(var X#17);X#8=(\ X#9.S#12);E#20;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#1=C#7[(var X#17)];X#16=(var X#17);X#8=(\ X#9.S#12);E#20;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#8)
       ;X#8= (\ X#9.C#18[(var X#16)])
       ;E#11
       ;VV#17|X#10,(var X#16)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#16= (var X#8)
       ;X#8= (\ X#9.C#18[(var X#8)])
       ;E#11
       ;VV#17|X#10,(var X#16)|
     in
        A#13[(\ X#9.C#18[(var X#8)])]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {}
   Delta3 = {((var X#16),(\ X#9.C#18)),
             ((var X#8),(\ X#9.C#18)),
             ((var X#16),(\ X#9.C#18[[.]])),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           VV#14|.1,.2| |-> {X#16=[.2];VV#17|[.1],(var X#16)|},
           X#2          |->  X#16,
           X#3          |->  X#8,
           X#1          |->  X#8,
           E#4          |->  {E#11;VV#17|X#10,(var X#16)|},
           C#7          |->  (\ X#9.C#18),
           S#12         |->  C#18[(var X#8)]}

and instantiated rules:

                                  (letrec {X#16=(var X#8);X#8=(\ X#9.C#18[(var X#8)]);E#11;VV#17|X#10,(var X#16)|} in A#13[(var X#10)])
    -cpx-e1->                     (letrec {X#16=(var X#8);X#8=(\ X#9.C#18[(var X#16)]);E#11;VV#17|X#10,(var X#16)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#16=(var X#8);X#8=(\ X#9.C#18[(var X#8)]);E#11;VV#17|X#10,(var X#16)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#16=(var X#8);X#8=(\ X#9.C#18[(var X#8)]);E#11;VV#17|X#10,(var X#16)|} in A#13[(\ X#9.C#18[(var X#8)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#16)]
       ;X#16= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#18
       ;VV#17|X#10,(var X#16)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#8)]
       ;X#16= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#18
       ;VV#17|X#10,(var X#16)|
     in
        A#13[(\ X#9.S#12)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#16),C#7),
             ((var X#8),C#7),
             ((var X#16),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           VV#14|.1,.2| |-> {X#16=[.2];VV#17|[.1],(var X#16)|},
           X#2          |->  X#16,
           X#3          |->  X#8,
           E#11         |->  {X#1=C#7[(var X#8)];E#18},
           E#4          |->  {X#8=(\ X#9.S#12);E#18;VV#17|X#10,(var X#16)|}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#8)];X#16=(var X#8);X#8=(\ X#9.S#12);E#18;VV#17|X#10,(var X#16)|} in A#13[(var X#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#16)];X#16=(var X#8);X#8=(\ X#9.S#12);E#18;VV#17|X#10,(var X#16)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#8)];X#16=(var X#8);X#8=(\ X#9.S#12);E#18;VV#17|X#10,(var X#16)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#1=C#7[(var X#8)];X#16=(var X#8);X#8=(\ X#9.S#12);E#18;VV#17|X#10,(var X#16)|} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (\ X#9.S#12)
       ;E#11
       ;EE#15[X#10,A#13[(var X#8)]]
     in
        A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
     )
    ,
     (letrec
        X#8= (\ X#9.S#12)
       ;E#11
       ;EE#15[X#10,A#13[(\ X#9.S#12)]]
     in
        A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
     )
  )

where

   Delta1 = {A#14,T#16,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#17[(app A#18[[.]] T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]),
             ((var X#10),A#17[(app A#18[[.]] T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#17[(app A#18[(var X#10)] T#19)]),
           T#16  |->  A#17[(app A#18[(var X#10)] T#19)],
           A#14  |->  A#17[(app A#18 T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -cpx-e1->                     (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])])
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
       ;X#8= (\ X#9.S#12)
       ;E#19
       ;EE#15[X#10,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;X#8= (\ X#9.S#12)
       ;E#19
       ;EE#15[X#10,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#17=T#16;X#8=(\ X#9.S#12);E#19;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)]),
           E#11  |->  {X#17=T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#19},
           E#18  |->  {X#8=(\ X#9.S#12);E#19;EE#15[X#10,A#13[(var X#8)]]}}

and instantiated rules:

                                  (letrec {X#17=T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#12);E#19;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#17=T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#12);E#19;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#12);E#19;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#12);E#19;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[A#22[(app A#23[(\ X#9.S#12)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#21,A#19,T#16,T#6,A#13,A#20}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#22[(app A#23[[.]] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#20[A#22[(app A#23[(var X#8)] T#24)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {[.1]=A#20[[.2]]},
           X#17         |->  X#10,
           E#18         |->  {X#8=(\ X#9.S#12);E#11},
           A#19         |->  A#20,
           T#16         |->  A#20[A#22[(app A#23[(var X#8)] T#24)]],
           T#21         |->  A#22[(app A#23[(var X#8)] T#24)],
           A#13         |->  A#22[(app A#23 T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#20[A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#20[A#22[(app A#23[(\ X#9.S#12)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[(app A#21[A#13[(var X#8)]] T#22[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[(app A#21[A#13[(\ X#9.S#12)]] T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,T#16,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#20[(app A#21[A#13[(var X#8)]] T#22)];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {[.1]=A#20[(app A#21[[.2]] T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]},
           X#17         |->  X#10,
           E#18         |->  {X#8=(\ X#9.S#12);E#11},
           T#16         |->  A#20[(app A#21[A#13[(var X#8)]] T#22)],
           A#19         |->  A#20[(app A#21 T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#20[(app A#21[A#13[(var X#8)]] T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[(app A#21[A#13[(var X#8)]] T#22[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[(app A#21[A#13[(var X#8)]] T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#20[(app A#21[A#13[(\ X#9.S#12)]] T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[(app A#21[(var X#8)] T#22[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[(app A#21[(\ X#9.S#12)] T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#16,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#20[(app A#21[[.]] T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#20[(app A#21[(var X#8)] T#22)];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#17         |->  X#10,
           E#18         |->  {X#8=(\ X#9.S#12);E#11},
           A#19         |->  [.],
           T#16         |->  A#20[(app A#21[(var X#8)] T#22)],
           A#13         |->  A#20[(app A#21 T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#20[(app A#21[(var X#8)] T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[(app A#21[(var X#8)] T#22[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[(app A#21[(var X#8)] T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#20[(app A#21[(\ X#9.S#12)] T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#20,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#20,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,T#16,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#22[(app A#23[(var X#20)] T#24)];X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(var X#8)]]} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {[.1]=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];EE#21[X#20,[.2]]},
           X#17         |->  X#10,
           E#18         |->  {X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(var X#8)]]},
           T#16         |->  A#22[(app A#23[(var X#20)] T#24)],
           A#19         |->  A#22[(app A#23 T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#21,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#20= A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#21,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,T#16,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26)];X#8=(\ X#9.S#12);E#11;EE#22[X#10,(var X#20)];EE#23[X#21,A#13[(var X#8)]]} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];EE#22[[.1],(var X#20)];EE#23[X#21,[.2]]},
           X#17         |->  X#20,
           E#18         |->  {X#8=(\ X#9.S#12);E#11;EE#22[X#10,(var X#20)];EE#23[X#21,A#13[(var X#8)]]},
           T#16         |->  A#24[(app A#25[(var X#21)] T#26)],
           A#19         |->  A#24[(app A#25 T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#22[X#10,(var X#20)];EE#23[X#21,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#22[X#10,(var X#20)];EE#23[X#21,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#22[X#10,(var X#20)];EE#23[X#21,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#22[X#10,(var X#20)];EE#23[X#21,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[A#24[(app A#25[(var X#8)] T#26[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#10,(var X#20)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#20= A#22[A#24[(app A#25[(\ X#9.S#12)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#10,(var X#20)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#23,A#19,T#16,T#6,A#13,A#22}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#24[(app A#25[[.]] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#20=A#22[A#24[(app A#25[(var X#8)] T#26)]];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {X#20=A#22[[.2]];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]},
           A#19         |->  A#22,
           T#16         |->  A#22[A#24[(app A#25[(var X#8)] T#26)]],
           T#23         |->  A#24[(app A#25[(var X#8)] T#26)],
           A#13         |->  A#24[(app A#25 T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#20=A#22[A#24[(app A#25[(var X#8)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#20=A#22[A#24[(app A#25[(var X#8)] T#26[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#20=A#22[A#24[(app A#25[(var X#8)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#20=A#22[A#24[(app A#25[(\ X#9.S#12)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app A#23[A#13[(var X#8)]] T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#10,(var X#20)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#20= A#22[(app A#23[A#13[(\ X#9.S#12)]] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#10,(var X#20)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,T#16,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#20=A#22[(app A#23[A#13[(var X#8)]] T#24)];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {X#20=A#22[(app A#23[[.2]] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]},
           T#16         |->  A#22[(app A#23[A#13[(var X#8)]] T#24)],
           A#19         |->  A#22[(app A#23 T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app A#23[A#13[(var X#8)]] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#20=A#22[(app A#23[A#13[(var X#8)]] T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#20=A#22[(app A#23[A#13[(var X#8)]] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#20=A#22[(app A#23[A#13[(\ X#9.S#12)]] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#10,(var X#20)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#20= A#22[(app A#23[(\ X#9.S#12)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#10,(var X#20)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#16,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#22[(app A#23[[.]] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#20=A#22[(app A#23[(var X#8)] T#24)];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]},
           A#19         |->  [.],
           T#16         |->  A#22[(app A#23[(var X#8)] T#24)],
           A#13         |->  A#22[(app A#23 T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#20=A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#20=A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#20=A#22[(app A#23[(\ X#9.S#12)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (\ X#9.C#17[(var X#2)])
       ;E#16
       ;EE#15[X#10,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= (\ X#9.C#17[(var X#3)])
       ;E#16
       ;EE#15[X#10,A#13[(\ X#9.C#17[(var X#3)])]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),(\ X#9.C#17)),
             ((var X#3),(\ X#9.C#17)),
             ((var X#2),(\ X#9.C#17[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#14[(var X#10)],
           E#11  |->  {X#2=(var X#3);E#16},
           X#1   |->  X#8,
           E#4   |->  {E#16;EE#15[X#10,A#13[(var X#8)]]},
           C#7   |->  (\ X#9.C#17),
           S#12  |->  C#17[(var X#3)]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(\ X#9.C#17[(var X#3)]);E#16;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(\ X#9.C#17[(var X#2)]);E#16;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(\ X#9.C#17[(var X#3)]);E#16;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#2=(var X#3);X#8=(\ X#9.C#17[(var X#3)]);E#16;EE#15[X#10,A#13[(\ X#9.C#17[(var X#3)])]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#2)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#17
       ;EE#15[X#10,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#17
       ;EE#15[X#10,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#14[(var X#10)],
           E#11  |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#17},
           E#16  |->  {X#1=C#7[(var X#3)];E#17},
           E#4   |->  {X#8=(\ X#9.S#12);E#17;EE#15[X#10,A#13[(var X#8)]]}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#12);E#17;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);X#8=(\ X#9.S#12);E#17;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#12);E#17;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#12);E#17;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#18[A#20[(var X#2)]]
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#16
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#18[A#20[(\ X#9.S#12)]]
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#16
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#19,A#17,C#7,A#13,A#18,A#20}
   Delta2 = {}
   Delta3 = {((var X#2),A#18[A#20[[.]]]),
             ((var X#8),A#18[A#20[[.]]]),
             ((var X#2),A#18[A#20[[.]]]),
             ((var X#8),A#20[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#8);E#16},
           EE#15[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#12);E#16},
           A#17         |->  A#18,
           C#7          |->  A#18[A#20[[.]]],
           A#13         |->  A#20,
           C#19         |->  A#20[[.]],
           C#21         |->  [.],
           X#3          |->  X#8}

and instantiated rules:

                                  (letrec {X#10=A#18[A#20[(var X#8)]];X#2=(var X#8);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#18[A#20[(var X#2)]];X#2=(var X#8);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#18[A#20[(var X#8)]];X#2=(var X#8);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#18[A#20[(\ X#9.S#12)]];X#2=(var X#8);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#18[A#20[(var X#2)]]
       ;X#2= (var X#3)
       ;X#3= (\ X#9.S#12)
       ;E#16
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#18[A#20[(\ X#9.S#12)]]
       ;X#2= (var X#3)
       ;X#3= (\ X#9.S#12)
       ;E#16
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#19,A#17,C#7,A#13,A#18,A#20}
   Delta2 = {}
   Delta3 = {((var X#2),A#18[A#20]),
             ((var X#3),A#18[A#20]),
             ((var X#2),A#18[A#20[[.]]]),
             ((var X#3),A#20[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#3=(\ X#9.S#12);E#16},
           A#17         |->  A#18,
           C#7          |->  A#18[A#20],
           A#13         |->  A#20[[.]],
           C#19         |->  A#20,
           A#21         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#10=A#18[A#20[(var X#3)]];X#2=(var X#3);X#3=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#18[A#20[(var X#2)]];X#2=(var X#3);X#3=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#18[A#20[(var X#3)]];X#2=(var X#3);X#3=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#18[A#20[(\ X#9.S#12)]];X#2=(var X#3);X#3=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#18[A#20[(app A#21[(var X#8)] C#22[(var X#2)])]]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#18[A#20[(app A#21[(\ X#9.S#12)] C#22[(var X#3)])]]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#19,A#17,C#7,A#13,A#18}
   Delta2 = {}
   Delta3 = {((var X#2),A#18[A#20[(app A#21[(var X#8)] C#22)]]),
             ((var X#3),A#18[A#20[(app A#21[(var X#8)] C#22)]]),
             ((var X#2),A#18[A#20[(app A#21[(var X#8)] C#22[[.]])]]),
             ((var X#8),A#20[(app A#21[[.]] C#22[(var X#3)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#12);E#16},
           A#17         |->  A#18,
           C#7          |->  A#18[A#20[(app A#21[(var X#8)] C#22)]],
           C#19         |->  A#20[(app A#21[(var X#8)] C#22)],
           A#13         |->  A#20[(app A#21 C#22[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#10=A#18[A#20[(app A#21[(var X#8)] C#22[(var X#3)])]];X#2=(var X#3);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#18[A#20[(app A#21[(var X#8)] C#22[(var X#2)])]];X#2=(var X#3);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#18[A#20[(app A#21[(var X#8)] C#22[(var X#3)])]];X#2=(var X#3);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#18[A#20[(app A#21[(\ X#9.S#12)] C#22[(var X#3)])]];X#2=(var X#3);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#18[(app A#19[A#13[(var X#8)]] C#20[(var X#2)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#18[(app A#19[A#13[(\ X#9.S#12)]] C#20[(var X#3)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#17,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),A#18[(app A#19[A#13[(var X#8)]] C#20)]),
             ((var X#3),A#18[(app A#19[A#13[(var X#8)]] C#20)]),
             ((var X#2),A#18[(app A#19[A#13[(var X#8)]] C#20[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] C#20[(var X#3)])]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#12);E#16},
           C#7          |->  A#18[(app A#19[A#13[(var X#8)]] C#20)],
           A#17         |->  A#18[(app A#19 C#20[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#10=A#18[(app A#19[A#13[(var X#8)]] C#20[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#18[(app A#19[A#13[(var X#8)]] C#20[(var X#2)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#18[(app A#19[A#13[(var X#8)]] C#20[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#18[(app A#19[A#13[(\ X#9.S#12)]] C#20[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#18[(var X#2)]
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#16
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#18[(\ X#9.S#12)]
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#16
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#13,A#18}
   Delta2 = {}
   Delta3 = {((var X#2),A#18[[.]]),
             ((var X#8),A#18[[.]]),
             ((var X#2),A#18[[.]]),
             ((var X#8),A#18[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#8);E#16},
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#12);E#16},
           A#17         |->  [.],
           A#13         |->  A#18,
           C#7          |->  A#18[[.]],
           C#19         |->  [.],
           X#3          |->  X#8}

and instantiated rules:

                                  (letrec {X#10=A#18[(var X#8)];X#2=(var X#8);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#18[(var X#2)];X#2=(var X#8);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#18[(var X#8)];X#2=(var X#8);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#18[(\ X#9.S#12)];X#2=(var X#8);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#18[(var X#2)]
       ;X#2= (var X#3)
       ;X#3= (\ X#9.S#12)
       ;E#16
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#18[(\ X#9.S#12)]
       ;X#2= (var X#3)
       ;X#3= (\ X#9.S#12)
       ;E#16
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#13,A#18}
   Delta2 = {}
   Delta3 = {((var X#2),A#18),
             ((var X#3),A#18),
             ((var X#2),A#18[[.]]),
             ((var X#3),A#18[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#4          |->  {X#3=(\ X#9.S#12);E#16},
           A#17         |->  [.],
           A#13         |->  A#18[[.]],
           C#7          |->  A#18,
           A#19         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#10=A#18[(var X#3)];X#2=(var X#3);X#3=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#18[(var X#2)];X#2=(var X#3);X#3=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#18[(var X#3)];X#2=(var X#3);X#3=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#18[(\ X#9.S#12)];X#2=(var X#3);X#3=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#18[(app A#19[(var X#8)] C#20[(var X#2)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#18[(app A#19[(\ X#9.S#12)] C#20[(var X#3)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),A#18[(app A#19[(var X#8)] C#20)]),
             ((var X#3),A#18[(app A#19[(var X#8)] C#20)]),
             ((var X#2),A#18[(app A#19[(var X#8)] C#20[[.]])]),
             ((var X#8),A#18[(app A#19[[.]] C#20[(var X#3)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#12);E#16},
           A#17         |->  [.],
           C#7          |->  A#18[(app A#19[(var X#8)] C#20)],
           A#13         |->  A#18[(app A#19 C#20[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#10=A#18[(app A#19[(var X#8)] C#20[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#18[(app A#19[(var X#8)] C#20[(var X#2)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#18[(app A#19[(var X#8)] C#20[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#18[(app A#19[(\ X#9.S#12)] C#20[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[(var X#2)]
       ;X#2= (var X#18)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#18,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[(var X#18)]
       ;X#2= (var X#18)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#18,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#17,C#7,A#13,A#20}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[[.]]),
             ((var X#18),A#20[[.]]),
             ((var X#2),A#20[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#18);E#16},
           EE#15[.1,.2] |-> {[.1]=A#20[(var X#18)];EE#19[X#18,[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#12);E#16;EE#19[X#18,A#13[(var X#8)]]},
           A#17         |->  A#20,
           C#7          |->  A#20[[.]],
           C#21         |->  [.],
           X#3          |->  X#18}

and instantiated rules:

                                  (letrec {X#10=A#20[(var X#18)];X#2=(var X#18);X#8=(\ X#9.S#12);E#16;EE#19[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[(var X#2)];X#2=(var X#18);X#8=(\ X#9.S#12);E#16;EE#19[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[(var X#18)];X#2=(var X#18);X#8=(\ X#9.S#12);E#16;EE#19[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#20[(var X#18)];X#2=(var X#18);X#8=(\ X#9.S#12);E#16;EE#19[X#18,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[(var X#2)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#3,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[(var X#3)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#3,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#17,C#7,A#13,A#20}
   Delta2 = {}
   Delta3 = {((var X#2),A#20),
             ((var X#3),A#20),
             ((var X#2),A#20[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {[.1]=A#20[(var X#3)];EE#19[X#3,[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#12);E#16;EE#19[X#3,A#13[(var X#8)]]},
           A#17         |->  A#20[[.]],
           C#7          |->  A#20,
           A#21         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=A#20[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[(var X#2)];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#20[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#3,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[(app A#21[(var X#18)] C#22[(var X#2)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#18,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[(app A#21[(var X#18)] C#22[(var X#3)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#18,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#17,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[(app A#21[(var X#18)] C#22)]),
             ((var X#3),A#20[(app A#21[(var X#18)] C#22)]),
             ((var X#2),A#20[(app A#21[(var X#18)] C#22[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] C#22[(var X#3)])];EE#19[X#18,[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#12);E#16;EE#19[X#18,A#13[(var X#8)]]},
           C#7          |->  A#20[(app A#21[(var X#18)] C#22)],
           A#17         |->  A#20[(app A#21 C#22[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#10=A#20[(app A#21[(var X#18)] C#22[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[(app A#21[(var X#18)] C#22[(var X#2)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[(app A#21[(var X#18)] C#22[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#20[(app A#21[(var X#18)] C#22[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#18,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#2)
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#3,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#3,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#3),[.]),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {[.1]=(var X#3);EE#19[X#3,[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#12);E#16;EE#19[X#3,A#13[(var X#8)]]},
           C#7          |->  [.],
           A#17         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#2);X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=(var X#3);X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#3,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(var X#2)]
       ;X#2= (var X#19)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#20[X#10,(var X#18)]
       ;EE#21[X#19,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#18= A#22[(var X#19)]
       ;X#2= (var X#19)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#20[X#10,(var X#18)]
       ;EE#21[X#19,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#17,C#7,A#13,A#22}
   Delta2 = {}
   Delta3 = {((var X#2),A#22[[.]]),
             ((var X#19),A#22[[.]]),
             ((var X#2),A#22[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#19);E#16},
           EE#15[.1,.2] |-> {X#18=A#22[(var X#19)];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#1          |->  X#18,
           E#4          |->  {X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#19,A#13[(var X#8)]]},
           A#17         |->  A#22,
           C#7          |->  A#22[[.]],
           C#23         |->  [.],
           X#3          |->  X#19}

and instantiated rules:

                                  (letrec {X#18=A#22[(var X#19)];X#2=(var X#19);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#19,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#18=A#22[(var X#2)];X#2=(var X#19);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#19,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#18=A#22[(var X#19)];X#2=(var X#19);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#19,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#18=A#22[(var X#19)];X#2=(var X#19);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#19,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(var X#2)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#20[X#10,(var X#18)]
       ;EE#21[X#3,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#18= A#22[(var X#3)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#20[X#10,(var X#18)]
       ;EE#21[X#3,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#17,C#7,A#13,A#22}
   Delta2 = {}
   Delta3 = {((var X#2),A#22),
             ((var X#3),A#22),
             ((var X#2),A#22[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {X#18=A#22[(var X#3)];EE#20[[.1],(var X#18)];EE#21[X#3,[.2]]},
           X#1          |->  X#18,
           E#4          |->  {X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#3,A#13[(var X#8)]]},
           A#17         |->  A#22[[.]],
           C#7          |->  A#22,
           A#23         |->  [.],
           X#19         |->  X#3}

and instantiated rules:

                                  (letrec {X#18=A#22[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#18=A#22[(var X#2)];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#18=A#22[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#18=A#22[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#3,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] C#24[(var X#2)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#20[X#10,(var X#18)]
       ;EE#21[X#19,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] C#24[(var X#3)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#20[X#10,(var X#18)]
       ;EE#21[X#19,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#17,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),A#22[(app A#23[(var X#19)] C#24)]),
             ((var X#3),A#22[(app A#23[(var X#19)] C#24)]),
             ((var X#2),A#22[(app A#23[(var X#19)] C#24[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] C#24[(var X#3)])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#1          |->  X#18,
           E#4          |->  {X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#19,A#13[(var X#8)]]},
           C#7          |->  A#22[(app A#23[(var X#19)] C#24)],
           A#17         |->  A#22[(app A#23 C#24[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#19,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(var X#2)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#19,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#19,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#18=A#22[(app A#23[(var X#19)] C#24[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#19,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (var X#2)
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#20[X#10,(var X#18)]
       ;EE#21[X#3,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#18= (var X#3)
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#20[X#10,(var X#18)]
       ;EE#21[X#3,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#3),[.]),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {X#18=(var X#3);EE#20[[.1],(var X#18)];EE#21[X#3,[.2]]},
           X#1          |->  X#18,
           E#4          |->  {X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#3,A#13[(var X#8)]]},
           C#7          |->  [.],
           A#17         |->  [.],
           X#19         |->  X#3}

and instantiated rules:

                                  (letrec {X#18=(var X#3);X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#18=(var X#2);X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#18=(var X#3);X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#18=(var X#3);X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#20[X#10,(var X#18)];EE#21[X#3,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[A#22[(var X#2)]]
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#18= A#20[A#22[(\ X#9.S#12)]]
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#21,A#17,C#7,A#13,A#20,A#22}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[A#22[[.]]]),
             ((var X#8),A#20[A#22[[.]]]),
             ((var X#2),A#20[A#22[[.]]]),
             ((var X#8),A#22[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#8);E#16},
           EE#15[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]},
           A#17         |->  A#20,
           C#7          |->  A#20[A#22[[.]]],
           A#13         |->  A#22,
           C#21         |->  A#22[[.]],
           C#23         |->  [.],
           X#3          |->  X#8}

and instantiated rules:

                                  (letrec {X#18=A#20[A#22[(var X#8)]];X#2=(var X#8);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#18=A#20[A#22[(var X#2)]];X#2=(var X#8);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#18=A#20[A#22[(var X#8)]];X#2=(var X#8);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#18=A#20[A#22[(\ X#9.S#12)]];X#2=(var X#8);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[A#22[(var X#2)]]
       ;X#2= (var X#3)
       ;X#3= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#18= A#20[A#22[(\ X#9.S#12)]]
       ;X#2= (var X#3)
       ;X#3= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#21,A#17,C#7,A#13,A#20,A#22}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[A#22]),
             ((var X#3),A#20[A#22]),
             ((var X#2),A#20[A#22[[.]]]),
             ((var X#3),A#22[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {X#3=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]},
           A#17         |->  A#20,
           C#7          |->  A#20[A#22],
           A#13         |->  A#22[[.]],
           C#21         |->  A#22,
           A#23         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#18=A#20[A#22[(var X#3)]];X#2=(var X#3);X#3=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#18=A#20[A#22[(var X#2)]];X#2=(var X#3);X#3=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#18=A#20[A#22[(var X#3)]];X#2=(var X#3);X#3=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#18=A#20[A#22[(\ X#9.S#12)]];X#2=(var X#3);X#3=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[A#22[(app A#23[(var X#8)] C#24[(var X#2)])]]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#18= A#20[A#22[(app A#23[(\ X#9.S#12)] C#24[(var X#3)])]]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#21,A#17,C#7,A#13,A#20}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[A#22[(app A#23[(var X#8)] C#24)]]),
             ((var X#3),A#20[A#22[(app A#23[(var X#8)] C#24)]]),
             ((var X#2),A#20[A#22[(app A#23[(var X#8)] C#24[[.]])]]),
             ((var X#8),A#22[(app A#23[[.]] C#24[(var X#3)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]},
           A#17         |->  A#20,
           C#7          |->  A#20[A#22[(app A#23[(var X#8)] C#24)]],
           C#21         |->  A#22[(app A#23[(var X#8)] C#24)],
           A#13         |->  A#22[(app A#23 C#24[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[A#22[(app A#23[(var X#8)] C#24[(var X#3)])]];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#18=A#20[A#22[(app A#23[(var X#8)] C#24[(var X#2)])]];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#18=A#20[A#22[(app A#23[(var X#8)] C#24[(var X#3)])]];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#18=A#20[A#22[(app A#23[(\ X#9.S#12)] C#24[(var X#3)])]];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[A#13[(var X#8)]] C#22[(var X#2)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[A#13[(\ X#9.S#12)]] C#22[(var X#3)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#17,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[(app A#21[A#13[(var X#8)]] C#22)]),
             ((var X#3),A#20[(app A#21[A#13[(var X#8)]] C#22)]),
             ((var X#2),A#20[(app A#21[A#13[(var X#8)]] C#22[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] C#22[(var X#3)])];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]},
           C#7          |->  A#20[(app A#21[A#13[(var X#8)]] C#22)],
           A#17         |->  A#20[(app A#21 C#22[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[A#13[(var X#8)]] C#22[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#18=A#20[(app A#21[A#13[(var X#8)]] C#22[(var X#2)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[A#13[(var X#8)]] C#22[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#18=A#20[(app A#21[A#13[(\ X#9.S#12)]] C#22[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(var X#2)]
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#18= A#20[(\ X#9.S#12)]
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#13,A#20}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[[.]]),
             ((var X#8),A#20[[.]]),
             ((var X#2),A#20[[.]]),
             ((var X#8),A#20[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#8);E#16},
           EE#15[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]},
           A#17         |->  [.],
           A#13         |->  A#20,
           C#7          |->  A#20[[.]],
           C#21         |->  [.],
           X#3          |->  X#8}

and instantiated rules:

                                  (letrec {X#18=A#20[(var X#8)];X#2=(var X#8);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#18=A#20[(var X#2)];X#2=(var X#8);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#18=A#20[(var X#8)];X#2=(var X#8);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#18=A#20[(\ X#9.S#12)];X#2=(var X#8);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(var X#2)]
       ;X#2= (var X#3)
       ;X#3= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#18= A#20[(\ X#9.S#12)]
       ;X#2= (var X#3)
       ;X#3= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#13,A#20}
   Delta2 = {}
   Delta3 = {((var X#2),A#20),
             ((var X#3),A#20),
             ((var X#2),A#20[[.]]),
             ((var X#3),A#20[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {X#3=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]},
           A#17         |->  [.],
           A#13         |->  A#20[[.]],
           C#7          |->  A#20,
           A#21         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#18=A#20[(var X#3)];X#2=(var X#3);X#3=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#18=A#20[(var X#2)];X#2=(var X#3);X#3=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#18=A#20[(var X#3)];X#2=(var X#3);X#3=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#18=A#20[(\ X#9.S#12)];X#2=(var X#3);X#3=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(var X#8)] C#22[(var X#2)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(\ X#9.S#12)] C#22[(var X#3)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#19[X#10,(var X#18)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[(app A#21[(var X#8)] C#22)]),
             ((var X#3),A#20[(app A#21[(var X#8)] C#22)]),
             ((var X#2),A#20[(app A#21[(var X#8)] C#22[[.]])]),
             ((var X#8),A#20[(app A#21[[.]] C#22[(var X#3)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           E#11         |->  {X#2=(var X#3);E#16},
           EE#15[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#4          |->  {X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]},
           A#17         |->  [.],
           C#7          |->  A#20[(app A#21[(var X#8)] C#22)],
           A#13         |->  A#20[(app A#21 C#22[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(var X#8)] C#22[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#18=A#20[(app A#21[(var X#8)] C#22[(var X#2)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(var X#8)] C#22[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#18=A#20[(app A#21[(\ X#9.S#12)] C#22[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#12);E#16;EE#19[X#10,(var X#18)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#8= (\ X#9.C#19[(var X#10)])
       ;E#11
       ;EE#18[X#3,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#8= (\ X#9.C#19[(var X#3)])
       ;E#11
       ;EE#18[X#3,A#13[(\ X#9.C#19[(var X#3)])]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#10),(\ X#9.C#19)),
             ((var X#3),(\ X#9.C#19)),
             ((var X#10),(\ X#9.C#19[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=(var X#3);EE#18[X#3,[.2]]},
           X#2          |->  X#10,
           X#1          |->  X#8,
           E#4          |->  {E#11;EE#18[X#3,A#13[(var X#8)]]},
           C#7          |->  (\ X#9.C#19),
           S#12         |->  C#19[(var X#3)],
           A#16         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#8=(\ X#9.C#19[(var X#3)]);E#11;EE#18[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#8=(\ X#9.C#19[(var X#10)]);E#11;EE#18[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#8=(\ X#9.C#19[(var X#3)]);E#11;EE#18[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=(var X#3);X#8=(\ X#9.C#19[(var X#3)]);E#11;EE#18[X#3,A#13[(\ X#9.C#19[(var X#3)])]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#10)]
       ;X#10= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#19
       ;EE#18[X#3,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#10= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#19
       ;EE#18[X#3,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#10),C#7),
             ((var X#3),C#7),
             ((var X#10),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=(var X#3);EE#18[X#3,[.2]]},
           X#2          |->  X#10,
           E#11         |->  {X#1=C#7[(var X#3)];E#19},
           E#4          |->  {X#8=(\ X#9.S#12);E#19;EE#18[X#3,A#13[(var X#8)]]},
           A#16         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#10=(var X#3);X#8=(\ X#9.S#12);E#19;EE#18[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#10)];X#10=(var X#3);X#8=(\ X#9.S#12);E#19;EE#18[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#10=(var X#3);X#8=(\ X#9.S#12);E#19;EE#18[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#1=C#7[(var X#3)];X#10=(var X#3);X#8=(\ X#9.S#12);E#19;EE#18[X#3,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#3= A#20[A#22[(app A#23[(var X#8)] C#24[(var X#10)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#3= A#20[A#22[(app A#23[(\ X#9.S#12)] C#24[(var X#3)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#21,A#19,C#7,A#13,A#20}
   Delta2 = {}
   Delta3 = {((var X#10),A#20[A#22[(app A#23[(var X#8)] C#24)]]),
             ((var X#3),A#20[A#22[(app A#23[(var X#8)] C#24)]]),
             ((var X#10),A#20[A#22[(app A#23[(var X#8)] C#24[[.]])]]),
             ((var X#8),A#22[(app A#23[[.]] C#24[(var X#3)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#3=A#20[[.2]];[.1]=(var X#3)},
           X#2          |->  X#10,
           EE#18[.1,.2] |-> {[.1]=A#20[[.2]]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#12);E#11},
           A#19         |->  A#20,
           C#7          |->  A#20[A#22[(app A#23[(var X#8)] C#24)]],
           A#16         |->  [.],
           X#17         |->  X#3,
           C#21         |->  A#22[(app A#23[(var X#8)] C#24)],
           A#13         |->  A#22[(app A#23 C#24[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#3=A#20[A#22[(app A#23[(var X#8)] C#24[(var X#3)])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#3=A#20[A#22[(app A#23[(var X#8)] C#24[(var X#10)])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#3=A#20[A#22[(app A#23[(var X#8)] C#24[(var X#3)])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=(var X#3);X#3=A#20[A#22[(app A#23[(\ X#9.S#12)] C#24[(var X#3)])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#3= A#20[(app A#21[A#13[(var X#8)]] C#22[(var X#10)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#3= A#20[(app A#21[A#13[(\ X#9.S#12)]] C#22[(var X#3)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#10),A#20[(app A#21[A#13[(var X#8)]] C#22)]),
             ((var X#3),A#20[(app A#21[A#13[(var X#8)]] C#22)]),
             ((var X#10),A#20[(app A#21[A#13[(var X#8)]] C#22[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#3=A#20[(app A#21[[.2]] C#22[(var X#3)])];[.1]=(var X#3)},
           X#2          |->  X#10,
           EE#18[.1,.2] |-> {[.1]=A#20[(app A#21[[.2]] C#22[(var X#3)])]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#12);E#11},
           C#7          |->  A#20[(app A#21[A#13[(var X#8)]] C#22)],
           A#19         |->  A#20[(app A#21 C#22[(var X#3)])],
           A#16         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#3=A#20[(app A#21[A#13[(var X#8)]] C#22[(var X#3)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#3=A#20[(app A#21[A#13[(var X#8)]] C#22[(var X#10)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#3=A#20[(app A#21[A#13[(var X#8)]] C#22[(var X#3)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=(var X#3);X#3=A#20[(app A#21[A#13[(\ X#9.S#12)]] C#22[(var X#3)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#3= A#20[(app A#21[(var X#8)] C#22[(var X#10)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#3= A#20[(app A#21[(\ X#9.S#12)] C#22[(var X#3)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#10),A#20[(app A#21[(var X#8)] C#22)]),
             ((var X#3),A#20[(app A#21[(var X#8)] C#22)]),
             ((var X#10),A#20[(app A#21[(var X#8)] C#22[[.]])]),
             ((var X#8),A#20[(app A#21[[.]] C#22[(var X#3)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#3=[.2];[.1]=(var X#3)},
           X#2          |->  X#10,
           EE#18[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#12);E#11},
           A#19         |->  [.],
           C#7          |->  A#20[(app A#21[(var X#8)] C#22)],
           A#13         |->  A#20[(app A#21 C#22[(var X#3)])],
           A#16         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#3=A#20[(app A#21[(var X#8)] C#22[(var X#3)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#3=A#20[(app A#21[(var X#8)] C#22[(var X#10)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#3=A#20[(app A#21[(var X#8)] C#22[(var X#3)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=(var X#3);X#3=A#20[(app A#21[(\ X#9.S#12)] C#22[(var X#3)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#3= A#22[(app A#23[(var X#20)] C#24[(var X#10)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#20,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#3= A#22[(app A#23[(var X#20)] C#24[(var X#3)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#20,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#10),A#22[(app A#23[(var X#20)] C#24)]),
             ((var X#3),A#22[(app A#23[(var X#20)] C#24)]),
             ((var X#10),A#22[(app A#23[(var X#20)] C#24[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#3=A#22[(app A#23[(var X#20)] C#24[(var X#3)])];[.1]=(var X#3);EE#21[X#20,[.2]]},
           X#2          |->  X#10,
           EE#18[.1,.2] |-> {[.1]=A#22[(app A#23[(var X#20)] C#24[(var X#3)])];EE#21[X#20,[.2]]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(var X#8)]]},
           C#7          |->  A#22[(app A#23[(var X#20)] C#24)],
           A#19         |->  A#22[(app A#23 C#24[(var X#3)])],
           A#16         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#3=A#22[(app A#23[(var X#20)] C#24[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#3=A#22[(app A#23[(var X#20)] C#24[(var X#10)])];X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#3=A#22[(app A#23[(var X#20)] C#24[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=(var X#3);X#3=A#22[(app A#23[(var X#20)] C#24[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#20= A#24[(app A#25[(var X#21)] C#26[(var X#10)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#22[X#3,(var X#20)]
       ;EE#23[X#21,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#20= A#24[(app A#25[(var X#21)] C#26[(var X#3)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#22[X#3,(var X#20)]
       ;EE#23[X#21,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#10),A#24[(app A#25[(var X#21)] C#26)]),
             ((var X#3),A#24[(app A#25[(var X#21)] C#26)]),
             ((var X#10),A#24[(app A#25[(var X#21)] C#26[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#20=A#24[(app A#25[(var X#21)] C#26[(var X#3)])];[.1]=(var X#3);EE#22[X#3,(var X#20)];EE#23[X#21,[.2]]},
           X#2          |->  X#10,
           EE#18[.1,.2] |-> {X#20=A#24[(app A#25[(var X#21)] C#26[(var X#3)])];EE#22[[.1],(var X#20)];EE#23[X#21,[.2]]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#22[X#3,(var X#20)];EE#23[X#21,A#13[(var X#8)]]},
           C#7          |->  A#24[(app A#25[(var X#21)] C#26)],
           A#19         |->  A#24[(app A#25 C#26[(var X#3)])],
           A#16         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#20=A#24[(app A#25[(var X#21)] C#26[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#22[X#3,(var X#20)];EE#23[X#21,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#20=A#24[(app A#25[(var X#21)] C#26[(var X#10)])];X#8=(\ X#9.S#12);E#11;EE#22[X#3,(var X#20)];EE#23[X#21,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#20=A#24[(app A#25[(var X#21)] C#26[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#22[X#3,(var X#20)];EE#23[X#21,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=(var X#3);X#20=A#24[(app A#25[(var X#21)] C#26[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#22[X#3,(var X#20)];EE#23[X#21,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#20= A#22[A#24[(app A#25[(var X#8)] C#26[(var X#10)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#3,(var X#20)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#20= A#22[A#24[(app A#25[(\ X#9.S#12)] C#26[(var X#3)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#3,(var X#20)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#23,A#19,C#7,A#13,A#22}
   Delta2 = {}
   Delta3 = {((var X#10),A#22[A#24[(app A#25[(var X#8)] C#26)]]),
             ((var X#3),A#22[A#24[(app A#25[(var X#8)] C#26)]]),
             ((var X#10),A#22[A#24[(app A#25[(var X#8)] C#26[[.]])]]),
             ((var X#8),A#24[(app A#25[[.]] C#26[(var X#3)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#20=A#22[[.2]];[.1]=(var X#3);EE#21[X#3,(var X#20)]},
           X#2          |->  X#10,
           EE#18[.1,.2] |-> {X#20=A#22[[.2]];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#21[X#3,(var X#20)]},
           A#19         |->  A#22,
           C#7          |->  A#22[A#24[(app A#25[(var X#8)] C#26)]],
           A#16         |->  [.],
           X#17         |->  X#3,
           C#23         |->  A#24[(app A#25[(var X#8)] C#26)],
           A#13         |->  A#24[(app A#25 C#26[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#20=A#22[A#24[(app A#25[(var X#8)] C#26[(var X#3)])]];X#8=(\ X#9.S#12);E#11;EE#21[X#3,(var X#20)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#20=A#22[A#24[(app A#25[(var X#8)] C#26[(var X#10)])]];X#8=(\ X#9.S#12);E#11;EE#21[X#3,(var X#20)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#20=A#22[A#24[(app A#25[(var X#8)] C#26[(var X#3)])]];X#8=(\ X#9.S#12);E#11;EE#21[X#3,(var X#20)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=(var X#3);X#20=A#22[A#24[(app A#25[(\ X#9.S#12)] C#26[(var X#3)])]];X#8=(\ X#9.S#12);E#11;EE#21[X#3,(var X#20)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#20= A#22[(app A#23[A#13[(var X#8)]] C#24[(var X#10)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#3,(var X#20)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#20= A#22[(app A#23[A#13[(\ X#9.S#12)]] C#24[(var X#3)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#3,(var X#20)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#10),A#22[(app A#23[A#13[(var X#8)]] C#24)]),
             ((var X#3),A#22[(app A#23[A#13[(var X#8)]] C#24)]),
             ((var X#10),A#22[(app A#23[A#13[(var X#8)]] C#24[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#20=A#22[(app A#23[[.2]] C#24[(var X#3)])];[.1]=(var X#3);EE#21[X#3,(var X#20)]},
           X#2          |->  X#10,
           EE#18[.1,.2] |-> {X#20=A#22[(app A#23[[.2]] C#24[(var X#3)])];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#21[X#3,(var X#20)]},
           C#7          |->  A#22[(app A#23[A#13[(var X#8)]] C#24)],
           A#19         |->  A#22[(app A#23 C#24[(var X#3)])],
           A#16         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#20=A#22[(app A#23[A#13[(var X#8)]] C#24[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#21[X#3,(var X#20)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#20=A#22[(app A#23[A#13[(var X#8)]] C#24[(var X#10)])];X#8=(\ X#9.S#12);E#11;EE#21[X#3,(var X#20)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#20=A#22[(app A#23[A#13[(var X#8)]] C#24[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#21[X#3,(var X#20)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=(var X#3);X#20=A#22[(app A#23[A#13[(\ X#9.S#12)]] C#24[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#21[X#3,(var X#20)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#20= A#22[(app A#23[(var X#8)] C#24[(var X#10)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#3,(var X#20)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#20= A#22[(app A#23[(\ X#9.S#12)] C#24[(var X#3)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#3,(var X#20)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#10),A#22[(app A#23[(var X#8)] C#24)]),
             ((var X#3),A#22[(app A#23[(var X#8)] C#24)]),
             ((var X#10),A#22[(app A#23[(var X#8)] C#24[[.]])]),
             ((var X#8),A#22[(app A#23[[.]] C#24[(var X#3)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#20=[.2];[.1]=(var X#3);EE#21[X#3,(var X#20)]},
           X#2          |->  X#10,
           EE#18[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#21[X#3,(var X#20)]},
           A#19         |->  [.],
           C#7          |->  A#22[(app A#23[(var X#8)] C#24)],
           A#13         |->  A#22[(app A#23 C#24[(var X#3)])],
           A#16         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#20=A#22[(app A#23[(var X#8)] C#24[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#21[X#3,(var X#20)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#20=A#22[(app A#23[(var X#8)] C#24[(var X#10)])];X#8=(\ X#9.S#12);E#11;EE#21[X#3,(var X#20)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#20=A#22[(app A#23[(var X#8)] C#24[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#21[X#3,(var X#20)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=(var X#3);X#20=A#22[(app A#23[(\ X#9.S#12)] C#24[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#21[X#3,(var X#20)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#3)
       ;X#8= (\ X#9.C#21[(var X#17)])
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#20[X#3,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= (var X#3)
       ;X#8= (\ X#9.C#21[(var X#3)])
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#20[X#3,A#13[(\ X#9.C#21[(var X#3)])]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#17),(\ X#9.C#21)),
             ((var X#3),(\ X#9.C#21)),
             ((var X#17),(\ X#9.C#21[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=(var X#3);EE#19[[.1],(var X#17)];EE#20[X#3,[.2]]},
           X#2          |->  X#17,
           X#1          |->  X#8,
           E#4          |->  {E#11;EE#19[X#10,(var X#17)];EE#20[X#3,A#13[(var X#8)]]},
           C#7          |->  (\ X#9.C#21),
           S#12         |->  C#21[(var X#3)],
           A#16         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#17=(var X#3);X#8=(\ X#9.C#21[(var X#3)]);E#11;EE#19[X#10,(var X#17)];EE#20[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#17=(var X#3);X#8=(\ X#9.C#21[(var X#17)]);E#11;EE#19[X#10,(var X#17)];EE#20[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=(var X#3);X#8=(\ X#9.C#21[(var X#3)]);E#11;EE#19[X#10,(var X#17)];EE#20[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=(var X#3);X#8=(\ X#9.C#21[(var X#3)]);E#11;EE#19[X#10,(var X#17)];EE#20[X#3,A#13[(\ X#9.C#21[(var X#3)])]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#17)]
       ;X#17= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#21
       ;EE#19[X#10,(var X#17)]
       ;EE#20[X#3,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#17= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#21
       ;EE#19[X#10,(var X#17)]
       ;EE#20[X#3,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#17),C#7),
             ((var X#3),C#7),
             ((var X#17),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=(var X#3);EE#19[[.1],(var X#17)];EE#20[X#3,[.2]]},
           X#2          |->  X#17,
           E#11         |->  {X#1=C#7[(var X#3)];E#21},
           E#4          |->  {X#8=(\ X#9.S#12);E#21;EE#19[X#10,(var X#17)];EE#20[X#3,A#13[(var X#8)]]},
           A#16         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#17=(var X#3);X#8=(\ X#9.S#12);E#21;EE#19[X#10,(var X#17)];EE#20[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#17)];X#17=(var X#3);X#8=(\ X#9.S#12);E#21;EE#19[X#10,(var X#17)];EE#20[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#17=(var X#3);X#8=(\ X#9.S#12);E#21;EE#19[X#10,(var X#17)];EE#20[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#1=C#7[(var X#3)];X#17=(var X#3);X#8=(\ X#9.S#12);E#21;EE#19[X#10,(var X#17)];EE#20[X#3,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(app A#23[(var X#17)] C#24[(var X#17)])]
       ;X#17= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#20[X#3,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(app A#23[(var X#17)] C#24[(var X#3)])]
       ;X#17= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#20[X#3,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#17),A#22[(app A#23[(var X#17)] C#24)]),
             ((var X#3),A#22[(app A#23[(var X#17)] C#24)]),
             ((var X#17),A#22[(app A#23[(var X#17)] C#24[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=(var X#3);[.1]=A#22[(app A#23[(var X#17)] C#24[(var X#3)])];EE#20[X#3,[.2]]},
           X#2          |->  X#17,
           EE#19[.1,.2] |-> {[.1]=A#22[(app A#23[[.2]] C#24[(var X#3)])]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]]},
           C#7          |->  A#22[(app A#23[(var X#17)] C#24)],
           A#21         |->  A#22[(app A#23 C#24[(var X#3)])],
           A#16         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=A#22[(app A#23[(var X#17)] C#24[(var X#3)])];X#17=(var X#3);X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#22[(app A#23[(var X#17)] C#24[(var X#17)])];X#17=(var X#3);X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(app A#23[(var X#17)] C#24[(var X#3)])];X#17=(var X#3);X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#22[(app A#23[(var X#17)] C#24[(var X#3)])];X#17=(var X#3);X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#24[(app A#25[(var X#22)] C#26[(var X#17)])]
       ;X#17= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#20[X#3,A#13[(var X#8)]]
       ;EE#23[X#22,(var X#17)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#24[(app A#25[(var X#22)] C#26[(var X#3)])]
       ;X#17= (var X#3)
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#20[X#3,A#13[(\ X#9.S#12)]]
       ;EE#23[X#22,(var X#17)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#17),A#24[(app A#25[(var X#22)] C#26)]),
             ((var X#3),A#24[(app A#25[(var X#22)] C#26)]),
             ((var X#17),A#24[(app A#25[(var X#22)] C#26[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=(var X#3);[.1]=A#24[(app A#25[(var X#22)] C#26[(var X#3)])];EE#20[X#3,[.2]];EE#23[X#22,(var X#17)]},
           X#2          |->  X#17,
           EE#19[.1,.2] |-> {[.1]=A#24[(app A#25[(var X#22)] C#26[(var X#3)])];EE#23[X#22,[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]];EE#23[X#22,(var X#17)]},
           C#7          |->  A#24[(app A#25[(var X#22)] C#26)],
           A#21         |->  A#24[(app A#25 C#26[(var X#3)])],
           A#16         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=A#24[(app A#25[(var X#22)] C#26[(var X#3)])];X#17=(var X#3);X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]];EE#23[X#22,(var X#17)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#24[(app A#25[(var X#22)] C#26[(var X#17)])];X#17=(var X#3);X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]];EE#23[X#22,(var X#17)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#24[(app A#25[(var X#22)] C#26[(var X#3)])];X#17=(var X#3);X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]];EE#23[X#22,(var X#17)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#24[(app A#25[(var X#22)] C#26[(var X#3)])];X#17=(var X#3);X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(\ X#9.S#12)]];EE#23[X#22,(var X#17)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#3)
       ;X#22= A#26[(app A#27[(var X#23)] C#28[(var X#17)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#20[X#3,A#13[(var X#8)]]
       ;EE#24[X#10,(var X#22)]
       ;EE#25[X#23,(var X#17)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= (var X#3)
       ;X#22= A#26[(app A#27[(var X#23)] C#28[(var X#3)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#20[X#3,A#13[(\ X#9.S#12)]]
       ;EE#24[X#10,(var X#22)]
       ;EE#25[X#23,(var X#17)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#17),A#26[(app A#27[(var X#23)] C#28)]),
             ((var X#3),A#26[(app A#27[(var X#23)] C#28)]),
             ((var X#17),A#26[(app A#27[(var X#23)] C#28[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=(var X#3);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#3)])];EE#20[X#3,[.2]];EE#24[[.1],(var X#22)];EE#25[X#23,(var X#17)]},
           X#2          |->  X#17,
           EE#19[.1,.2] |-> {X#22=A#26[(app A#27[(var X#23)] C#28[(var X#3)])];EE#24[[.1],(var X#22)];EE#25[X#23,[.2]]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]];EE#24[X#10,(var X#22)];EE#25[X#23,(var X#17)]},
           C#7          |->  A#26[(app A#27[(var X#23)] C#28)],
           A#21         |->  A#26[(app A#27 C#28[(var X#3)])],
           A#16         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#17=(var X#3);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]];EE#24[X#10,(var X#22)];EE#25[X#23,(var X#17)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#17=(var X#3);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#17)])];X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]];EE#24[X#10,(var X#22)];EE#25[X#23,(var X#17)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=(var X#3);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]];EE#24[X#10,(var X#22)];EE#25[X#23,(var X#17)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=(var X#3);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(\ X#9.S#12)]];EE#24[X#10,(var X#22)];EE#25[X#23,(var X#17)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#3)
       ;X#22= A#24[(app A#25[(var X#17)] C#26[(var X#17)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#20[X#3,A#13[(var X#8)]]
       ;EE#23[X#10,(var X#22)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= (var X#3)
       ;X#22= A#24[(app A#25[(var X#17)] C#26[(var X#3)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#20[X#3,A#13[(\ X#9.S#12)]]
       ;EE#23[X#10,(var X#22)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#17),A#24[(app A#25[(var X#17)] C#26)]),
             ((var X#3),A#24[(app A#25[(var X#17)] C#26)]),
             ((var X#17),A#24[(app A#25[(var X#17)] C#26[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=(var X#3);X#22=A#24[(app A#25[(var X#17)] C#26[(var X#3)])];EE#20[X#3,[.2]];EE#23[[.1],(var X#22)]},
           X#2          |->  X#17,
           EE#19[.1,.2] |-> {X#22=A#24[(app A#25[[.2]] C#26[(var X#3)])];EE#23[[.1],(var X#22)]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]];EE#23[X#10,(var X#22)]},
           C#7          |->  A#24[(app A#25[(var X#17)] C#26)],
           A#21         |->  A#24[(app A#25 C#26[(var X#3)])],
           A#16         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#17=(var X#3);X#22=A#24[(app A#25[(var X#17)] C#26[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]];EE#23[X#10,(var X#22)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#17=(var X#3);X#22=A#24[(app A#25[(var X#17)] C#26[(var X#17)])];X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]];EE#23[X#10,(var X#22)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=(var X#3);X#22=A#24[(app A#25[(var X#17)] C#26[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(var X#8)]];EE#23[X#10,(var X#22)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=(var X#3);X#22=A#24[(app A#25[(var X#17)] C#26[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#20[X#3,A#13[(\ X#9.S#12)]];EE#23[X#10,(var X#22)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#3)
       ;X#3= A#22[A#24[(app A#25[(var X#8)] C#26[(var X#17)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= (var X#3)
       ;X#3= A#22[A#24[(app A#25[(\ X#9.S#12)] C#26[(var X#3)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#23,A#21,C#7,A#13,A#22}
   Delta2 = {}
   Delta3 = {((var X#17),A#22[A#24[(app A#25[(var X#8)] C#26)]]),
             ((var X#3),A#22[A#24[(app A#25[(var X#8)] C#26)]]),
             ((var X#17),A#22[A#24[(app A#25[(var X#8)] C#26[[.]])]]),
             ((var X#8),A#24[(app A#25[[.]] C#26[(var X#3)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=(var X#3);X#3=A#22[[.2]];EE#19[[.1],(var X#17)]},
           X#2          |->  X#17,
           EE#20[.1,.2] |-> {[.1]=A#22[[.2]]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)]},
           A#21         |->  A#22,
           C#7          |->  A#22[A#24[(app A#25[(var X#8)] C#26)]],
           A#16         |->  [.],
           X#18         |->  X#3,
           C#23         |->  A#24[(app A#25[(var X#8)] C#26)],
           A#13         |->  A#24[(app A#25 C#26[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#17=(var X#3);X#3=A#22[A#24[(app A#25[(var X#8)] C#26[(var X#3)])]];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#17=(var X#3);X#3=A#22[A#24[(app A#25[(var X#8)] C#26[(var X#17)])]];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=(var X#3);X#3=A#22[A#24[(app A#25[(var X#8)] C#26[(var X#3)])]];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=(var X#3);X#3=A#22[A#24[(app A#25[(\ X#9.S#12)] C#26[(var X#3)])]];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#3)
       ;X#3= A#22[(app A#23[A#13[(var X#8)]] C#24[(var X#17)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= (var X#3)
       ;X#3= A#22[(app A#23[A#13[(\ X#9.S#12)]] C#24[(var X#3)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#17),A#22[(app A#23[A#13[(var X#8)]] C#24)]),
             ((var X#3),A#22[(app A#23[A#13[(var X#8)]] C#24)]),
             ((var X#17),A#22[(app A#23[A#13[(var X#8)]] C#24[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=(var X#3);X#3=A#22[(app A#23[[.2]] C#24[(var X#3)])];EE#19[[.1],(var X#17)]},
           X#2          |->  X#17,
           EE#20[.1,.2] |-> {[.1]=A#22[(app A#23[[.2]] C#24[(var X#3)])]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)]},
           C#7          |->  A#22[(app A#23[A#13[(var X#8)]] C#24)],
           A#21         |->  A#22[(app A#23 C#24[(var X#3)])],
           A#16         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#17=(var X#3);X#3=A#22[(app A#23[A#13[(var X#8)]] C#24[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#17=(var X#3);X#3=A#22[(app A#23[A#13[(var X#8)]] C#24[(var X#17)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=(var X#3);X#3=A#22[(app A#23[A#13[(var X#8)]] C#24[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=(var X#3);X#3=A#22[(app A#23[A#13[(\ X#9.S#12)]] C#24[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#3)
       ;X#3= A#22[(app A#23[(var X#8)] C#24[(var X#17)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= (var X#3)
       ;X#3= A#22[(app A#23[(\ X#9.S#12)] C#24[(var X#3)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#17),A#22[(app A#23[(var X#8)] C#24)]),
             ((var X#3),A#22[(app A#23[(var X#8)] C#24)]),
             ((var X#17),A#22[(app A#23[(var X#8)] C#24[[.]])]),
             ((var X#8),A#22[(app A#23[[.]] C#24[(var X#3)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=(var X#3);X#3=[.2];EE#19[[.1],(var X#17)]},
           X#2          |->  X#17,
           EE#20[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)]},
           A#21         |->  [.],
           C#7          |->  A#22[(app A#23[(var X#8)] C#24)],
           A#13         |->  A#22[(app A#23 C#24[(var X#3)])],
           A#16         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#17=(var X#3);X#3=A#22[(app A#23[(var X#8)] C#24[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#17=(var X#3);X#3=A#22[(app A#23[(var X#8)] C#24[(var X#17)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=(var X#3);X#3=A#22[(app A#23[(var X#8)] C#24[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=(var X#3);X#3=A#22[(app A#23[(\ X#9.S#12)] C#24[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#3)
       ;X#3= A#24[(app A#25[(var X#22)] C#26[(var X#17)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#23[X#22,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= (var X#3)
       ;X#3= A#24[(app A#25[(var X#22)] C#26[(var X#3)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#23[X#22,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#17),A#24[(app A#25[(var X#22)] C#26)]),
             ((var X#3),A#24[(app A#25[(var X#22)] C#26)]),
             ((var X#17),A#24[(app A#25[(var X#22)] C#26[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=(var X#3);X#3=A#24[(app A#25[(var X#22)] C#26[(var X#3)])];EE#19[[.1],(var X#17)];EE#23[X#22,[.2]]},
           X#2          |->  X#17,
           EE#20[.1,.2] |-> {[.1]=A#24[(app A#25[(var X#22)] C#26[(var X#3)])];EE#23[X#22,[.2]]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#22,A#13[(var X#8)]]},
           C#7          |->  A#24[(app A#25[(var X#22)] C#26)],
           A#21         |->  A#24[(app A#25 C#26[(var X#3)])],
           A#16         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#17=(var X#3);X#3=A#24[(app A#25[(var X#22)] C#26[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#22,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#17=(var X#3);X#3=A#24[(app A#25[(var X#22)] C#26[(var X#17)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#22,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=(var X#3);X#3=A#24[(app A#25[(var X#22)] C#26[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#22,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=(var X#3);X#3=A#24[(app A#25[(var X#22)] C#26[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#22,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#3)
       ;X#22= A#26[(app A#27[(var X#23)] C#28[(var X#17)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#24[X#3,(var X#22)]
       ;EE#25[X#23,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= (var X#3)
       ;X#22= A#26[(app A#27[(var X#23)] C#28[(var X#3)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#24[X#3,(var X#22)]
       ;EE#25[X#23,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#17),A#26[(app A#27[(var X#23)] C#28)]),
             ((var X#3),A#26[(app A#27[(var X#23)] C#28)]),
             ((var X#17),A#26[(app A#27[(var X#23)] C#28[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=(var X#3);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#3)])];EE#19[[.1],(var X#17)];EE#24[X#3,(var X#22)];EE#25[X#23,[.2]]},
           X#2          |->  X#17,
           EE#20[.1,.2] |-> {X#22=A#26[(app A#27[(var X#23)] C#28[(var X#3)])];EE#24[[.1],(var X#22)];EE#25[X#23,[.2]]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#24[X#3,(var X#22)];EE#25[X#23,A#13[(var X#8)]]},
           C#7          |->  A#26[(app A#27[(var X#23)] C#28)],
           A#21         |->  A#26[(app A#27 C#28[(var X#3)])],
           A#16         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#17=(var X#3);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#24[X#3,(var X#22)];EE#25[X#23,A#13[(var X#8)]]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#17=(var X#3);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#17)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#24[X#3,(var X#22)];EE#25[X#23,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=(var X#3);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#24[X#3,(var X#22)];EE#25[X#23,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=(var X#3);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#24[X#3,(var X#22)];EE#25[X#23,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#3)
       ;X#22= A#24[A#26[(app A#27[(var X#8)] C#28[(var X#17)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#23[X#3,(var X#22)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= (var X#3)
       ;X#22= A#24[A#26[(app A#27[(\ X#9.S#12)] C#28[(var X#3)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#23[X#3,(var X#22)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#25,A#21,C#7,A#13,A#24}
   Delta2 = {}
   Delta3 = {((var X#17),A#24[A#26[(app A#27[(var X#8)] C#28)]]),
             ((var X#3),A#24[A#26[(app A#27[(var X#8)] C#28)]]),
             ((var X#17),A#24[A#26[(app A#27[(var X#8)] C#28[[.]])]]),
             ((var X#8),A#26[(app A#27[[.]] C#28[(var X#3)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=(var X#3);X#22=A#24[[.2]];EE#19[[.1],(var X#17)];EE#23[X#3,(var X#22)]},
           X#2          |->  X#17,
           EE#20[.1,.2] |-> {X#22=A#24[[.2]];EE#23[[.1],(var X#22)]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#3,(var X#22)]},
           A#21         |->  A#24,
           C#7          |->  A#24[A#26[(app A#27[(var X#8)] C#28)]],
           A#16         |->  [.],
           X#18         |->  X#3,
           C#25         |->  A#26[(app A#27[(var X#8)] C#28)],
           A#13         |->  A#26[(app A#27 C#28[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#17=(var X#3);X#22=A#24[A#26[(app A#27[(var X#8)] C#28[(var X#3)])]];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#3,(var X#22)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#17=(var X#3);X#22=A#24[A#26[(app A#27[(var X#8)] C#28[(var X#17)])]];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#3,(var X#22)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=(var X#3);X#22=A#24[A#26[(app A#27[(var X#8)] C#28[(var X#3)])]];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#3,(var X#22)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=(var X#3);X#22=A#24[A#26[(app A#27[(\ X#9.S#12)] C#28[(var X#3)])]];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#3,(var X#22)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#3)
       ;X#22= A#24[(app A#25[A#13[(var X#8)]] C#26[(var X#17)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#23[X#3,(var X#22)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= (var X#3)
       ;X#22= A#24[(app A#25[A#13[(\ X#9.S#12)]] C#26[(var X#3)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#23[X#3,(var X#22)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#17),A#24[(app A#25[A#13[(var X#8)]] C#26)]),
             ((var X#3),A#24[(app A#25[A#13[(var X#8)]] C#26)]),
             ((var X#17),A#24[(app A#25[A#13[(var X#8)]] C#26[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=(var X#3);X#22=A#24[(app A#25[[.2]] C#26[(var X#3)])];EE#19[[.1],(var X#17)];EE#23[X#3,(var X#22)]},
           X#2          |->  X#17,
           EE#20[.1,.2] |-> {X#22=A#24[(app A#25[[.2]] C#26[(var X#3)])];EE#23[[.1],(var X#22)]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#3,(var X#22)]},
           C#7          |->  A#24[(app A#25[A#13[(var X#8)]] C#26)],
           A#21         |->  A#24[(app A#25 C#26[(var X#3)])],
           A#16         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#17=(var X#3);X#22=A#24[(app A#25[A#13[(var X#8)]] C#26[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#3,(var X#22)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#17=(var X#3);X#22=A#24[(app A#25[A#13[(var X#8)]] C#26[(var X#17)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#3,(var X#22)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=(var X#3);X#22=A#24[(app A#25[A#13[(var X#8)]] C#26[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#3,(var X#22)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=(var X#3);X#22=A#24[(app A#25[A#13[(\ X#9.S#12)]] C#26[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#3,(var X#22)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#3)
       ;X#22= A#24[(app A#25[(var X#8)] C#26[(var X#17)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#23[X#3,(var X#22)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= (var X#3)
       ;X#22= A#24[(app A#25[(\ X#9.S#12)] C#26[(var X#3)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#23[X#3,(var X#22)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#17),A#24[(app A#25[(var X#8)] C#26)]),
             ((var X#3),A#24[(app A#25[(var X#8)] C#26)]),
             ((var X#17),A#24[(app A#25[(var X#8)] C#26[[.]])]),
             ((var X#8),A#24[(app A#25[[.]] C#26[(var X#3)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=(var X#3);X#22=[.2];EE#19[[.1],(var X#17)];EE#23[X#3,(var X#22)]},
           X#2          |->  X#17,
           EE#20[.1,.2] |-> {X#22=[.2];EE#23[[.1],(var X#22)]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#3,(var X#22)]},
           A#21         |->  [.],
           C#7          |->  A#24[(app A#25[(var X#8)] C#26)],
           A#13         |->  A#24[(app A#25 C#26[(var X#3)])],
           A#16         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#17=(var X#3);X#22=A#24[(app A#25[(var X#8)] C#26[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#3,(var X#22)]} in A#14[(var X#10)])
    -cpx-e1->                     (letrec {X#17=(var X#3);X#22=A#24[(app A#25[(var X#8)] C#26[(var X#17)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#3,(var X#22)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=(var X#3);X#22=A#24[(app A#25[(var X#8)] C#26[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#3,(var X#22)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=(var X#3);X#22=A#24[(app A#25[(\ X#9.S#12)] C#26[(var X#3)])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#23[X#3,(var X#22)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (\ X#9.S#13)
       ;E#12
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#19[(app A#20[(var X#10)] T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
     )
    ,
     (letrec
        X#8= (\ X#9.S#13)
       ;E#12
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#19[(app A#20[(var X#10)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
     )
  )

where

   Delta1 = {A#15,T#18,T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#19[(app A#20[[.]] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#19[(app A#20[[.]] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#19[(app A#20[(var X#10)] T#21)]),
           T#18  |->  A#19[(app A#20[(var X#10)] T#21)],
           A#15  |->  A#19[(app A#20 T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#19[(app A#20[(var X#10)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -cpx-e1->                     (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#19[(app A#20[(var X#10)] T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])])
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#19[(app A#20[(var X#10)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#19[(app A#20[(var X#10)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= T#18[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
       ;X#8= (\ X#9.S#13)
       ;E#21
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;X#8= (\ X#9.S#13)
       ;E#21
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#19=T#18;X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           E#12  |->  {X#19=T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#21},
           E#20  |->  {X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|}}

and instantiated rules:

                                  (letrec {X#19=T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=T#18[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[A#24[(app A#25[(\ X#9.S#13)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#23,A#21,T#18,T#6,A#14,A#22}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#24[(app A#25[[.]] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#22[A#24[(app A#25[(var X#11)] T#26)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {[.1]=A#22[[.2]]},
           X#19         |->  X#10,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           A#21         |->  A#22,
           T#18         |->  A#22[A#24[(app A#25[(var X#11)] T#26)]],
           T#23         |->  A#24[(app A#25[(var X#11)] T#26)],
           A#14         |->  A#24[(app A#25 T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#22[A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[A#24[(app A#25[(\ X#9.S#13)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(app A#23[A#14[(var X#11)]] T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(app A#23[A#14[(\ X#9.S#13)]] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,T#18,T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#22[(app A#23[A#14[(var X#11)]] T#24)];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {[.1]=A#22[(app A#23[[.2]] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]},
           X#19         |->  X#10,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           T#18         |->  A#22[(app A#23[A#14[(var X#11)]] T#24)],
           A#21         |->  A#22[(app A#23 T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[(app A#23[A#14[(var X#11)]] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#22[(app A#23[A#14[(var X#11)]] T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(app A#23[A#14[(var X#11)]] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[(app A#23[A#14[(\ X#9.S#13)]] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(app A#23[(var X#11)] T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(app A#23[(\ X#9.S#13)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#18,T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#22[(app A#23[[.]] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#22[(app A#23[(var X#11)] T#24)];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#19         |->  X#10,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           A#21         |->  [.],
           T#18         |->  A#22[(app A#23[(var X#11)] T#24)],
           A#14         |->  A#22[(app A#23 T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[(app A#23[(var X#11)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#22[(app A#23[(var X#11)] T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(app A#23[(var X#11)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[(app A#23[(\ X#9.S#13)] T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#24[(app A#25[(var X#22)] T#26[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#22,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#24[(app A#25[(var X#22)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#22,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,T#18,T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#24[(app A#25[(var X#22)] T#26)];X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {[.1]=A#24[(app A#25[(var X#22)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];EE#23[X#22,[.2]]},
           X#19         |->  X#10,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           T#18         |->  A#24[(app A#25[(var X#22)] T#26)],
           A#21         |->  A#24[(app A#25 T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#24[(app A#25[(var X#22)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#24[(app A#25[(var X#22)] T#26[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#24[(app A#25[(var X#22)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#24[(app A#25[(var X#22)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#22= A#26[(app A#27[(var X#23)] T#28[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#24[X#10,(var X#22)]
       ;EE#25[X#23,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#22= A#26[(app A#27[(var X#23)] T#28[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#24[X#10,(var X#22)]
       ;EE#25[X#23,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,T#18,T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#22=A#26[(app A#27[(var X#23)] T#28)];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {X#22=A#26[(app A#27[(var X#23)] T#28[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];EE#24[[.1],(var X#22)];EE#25[X#23,[.2]]},
           X#19         |->  X#22,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           T#18         |->  A#26[(app A#27[(var X#23)] T#28)],
           A#21         |->  A#26[(app A#27 T#28[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#22=A#26[(app A#27[(var X#23)] T#28[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#22=A#26[(app A#27[(var X#23)] T#28[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#22=A#26[(app A#27[(var X#23)] T#28[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#22=A#26[(app A#27[(var X#23)] T#28[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#22= A#24[A#26[(app A#27[(var X#11)] T#28[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#22= A#24[A#26[(app A#27[(\ X#9.S#13)] T#28[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#25,A#21,T#18,T#6,A#14,A#24}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#26[(app A#27[[.]] T#28[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#22=A#24[A#26[(app A#27[(var X#11)] T#28)]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {X#22=A#24[[.2]];EE#23[[.1],(var X#22)]},
           X#19         |->  X#22,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|},
           A#21         |->  A#24,
           T#18         |->  A#24[A#26[(app A#27[(var X#11)] T#28)]],
           T#25         |->  A#26[(app A#27[(var X#11)] T#28)],
           A#14         |->  A#26[(app A#27 T#28[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#22=A#24[A#26[(app A#27[(var X#11)] T#28[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#22=A#24[A#26[(app A#27[(var X#11)] T#28[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#22=A#24[A#26[(app A#27[(var X#11)] T#28[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#22=A#24[A#26[(app A#27[(\ X#9.S#13)] T#28[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#22= A#24[(app A#25[A#14[(var X#11)]] T#26[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#22= A#24[(app A#25[A#14[(\ X#9.S#13)]] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,T#18,T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#22=A#24[(app A#25[A#14[(var X#11)]] T#26)];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {X#22=A#24[(app A#25[[.2]] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];EE#23[[.1],(var X#22)]},
           X#19         |->  X#22,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|},
           T#18         |->  A#24[(app A#25[A#14[(var X#11)]] T#26)],
           A#21         |->  A#24[(app A#25 T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#22=A#24[(app A#25[A#14[(var X#11)]] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#22=A#24[(app A#25[A#14[(var X#11)]] T#26[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#22=A#24[(app A#25[A#14[(var X#11)]] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#22=A#24[(app A#25[A#14[(\ X#9.S#13)]] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#22= A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#22= A#24[(app A#25[(\ X#9.S#13)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#18,T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#24[(app A#25[[.]] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#22=A#24[(app A#25[(var X#11)] T#26)];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {X#22=[.2];EE#23[[.1],(var X#22)]},
           X#19         |->  X#22,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|},
           A#21         |->  [.],
           T#18         |->  A#24[(app A#25[(var X#11)] T#26)],
           A#14         |->  A#24[(app A#25 T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#22=A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#22=A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#22=A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#22=A#24[(app A#25[(\ X#9.S#13)] T#26[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (\ X#9.C#19[(var X#2)])
       ;E#18
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= (\ X#9.C#19[(var X#3)])
       ;E#18
       ;EE#16[X#10,A#14[(\ X#9.C#19[(var X#3)])]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),(\ X#9.C#19)),
             ((var X#3),(\ X#9.C#19)),
             ((var X#2),(\ X#9.C#19[[.]])),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#15[(var X#10)],
           E#12  |->  {X#2=(var X#3);E#18},
           X#1   |->  X#8,
           E#4   |->  {E#18;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           C#7   |->  (\ X#9.C#19),
           S#13  |->  C#19[(var X#3)]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(\ X#9.C#19[(var X#3)]);E#18;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(\ X#9.C#19[(var X#2)]);E#18;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(\ X#9.C#19[(var X#3)]);E#18;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#2=(var X#3);X#8=(\ X#9.C#19[(var X#3)]);E#18;EE#16[X#10,A#14[(\ X#9.C#19[(var X#3)])]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#2)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#19
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#19
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#15[(var X#10)],
           E#12  |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#19},
           E#18  |->  {X#1=C#7[(var X#3)];E#19},
           E#4   |->  {X#8=(\ X#9.S#13);E#19;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#13);E#19;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);X#8=(\ X#9.S#13);E#19;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#13);E#19;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#13);E#19;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= (var X#2)
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#16[X#10,A#14[(var X#11)]]
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#11= (var X#8)
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#8);E#18},
           VV#17|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#11,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]]},
           C#7          |->  [.],
           X#3          |->  X#8}

and instantiated rules:

                                  (letrec {X#11=(var X#8);X#2=(var X#8);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]]} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#11=(var X#2);X#2=(var X#8);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]]} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#11=(var X#8);X#2=(var X#8);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]]} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#11=(var X#8);X#2=(var X#8);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(\ X#9.S#13)]]} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= (var X#2)
       ;X#2= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#21|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#11= (var X#20)
       ;X#2= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#21|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#20),[.]),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#20);E#18},
           VV#17|.1,.2| |-> {[.1]=(var X#20);VV#21|X#20,[.2]|},
           X#1          |->  X#11,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#21|X#20,(var X#8)|},
           C#7          |->  [.],
           X#3          |->  X#20}

and instantiated rules:

                                  (letrec {X#11=(var X#20);X#2=(var X#20);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#21|X#20,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#11=(var X#2);X#2=(var X#20);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#21|X#20,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#11=(var X#20);X#2=(var X#20);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#21|X#20,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#11=(var X#20);X#2=(var X#20);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#21|X#20,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#21)
       ;X#20= (var X#2)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#22|X#11,(var X#20)|
       ;VV#23|X#21,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#21)
       ;X#20= (var X#21)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#22|X#11,(var X#20)|
       ;VV#23|X#21,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#21),[.]),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#21);E#18},
           VV#17|.1,.2| |-> {X#20=(var X#21);VV#22|[.1],(var X#20)|;VV#23|X#21,[.2]|},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#22|X#11,(var X#20)|;VV#23|X#21,(var X#8)|},
           C#7          |->  [.],
           X#3          |->  X#21}

and instantiated rules:

                                  (letrec {X#2=(var X#21);X#20=(var X#21);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#22|X#11,(var X#20)|;VV#23|X#21,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#21);X#20=(var X#2);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#22|X#11,(var X#20)|;VV#23|X#21,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#21);X#20=(var X#21);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#22|X#11,(var X#20)|;VV#23|X#21,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#2=(var X#21);X#20=(var X#21);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#22|X#11,(var X#20)|;VV#23|X#21,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#8)
       ;X#20= (var X#2)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#21|X#11,(var X#20)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#8)
       ;X#20= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#21|X#11,(var X#20)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#8);E#18},
           VV#17|.1,.2| |-> {X#20=[.2];VV#21|[.1],(var X#20)|},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#20)|},
           C#7          |->  [.],
           X#3          |->  X#8}

and instantiated rules:

                                  (letrec {X#2=(var X#8);X#20=(var X#8);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#20)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#8);X#20=(var X#2);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#20)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#8);X#20=(var X#8);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#20)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#2=(var X#8);X#20=(var X#8);X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#21|X#11,(var X#20)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[A#22[(var X#2)]]
       ;X#2= (var X#11)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[A#22[(\ X#9.S#13)]]
       ;X#2= (var X#11)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#21,A#19,C#7,A#14,A#20,A#22}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[A#22[[.]]]),
             ((var X#11),A#20[A#22[[.]]]),
             ((var X#2),A#20[A#22[[.]]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#22[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#11);E#18},
           EE#16[.1,.2] |-> {[.1]=A#20[[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|},
           A#19         |->  A#20,
           C#7          |->  A#20[A#22[[.]]],
           A#14         |->  A#22,
           C#21         |->  A#22[[.]],
           C#23         |->  [.],
           X#3          |->  X#11}

and instantiated rules:

                                  (letrec {X#10=A#20[A#22[(var X#11)]];X#2=(var X#11);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[A#22[(var X#2)]];X#2=(var X#11);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[A#22[(var X#11)]];X#2=(var X#11);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#20[A#22[(\ X#9.S#13)]];X#2=(var X#11);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[A#22[(var X#2)]]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;VV#17|X#3,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[A#22[(\ X#9.S#13)]]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;VV#17|X#3,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#21,A#19,C#7,A#14,A#20,A#22}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[A#22]),
             ((var X#3),A#20[A#22]),
             ((var X#2),A#20[A#22[[.]]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#3),A#22[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {[.1]=A#20[[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;VV#17|X#3,(var X#8)|},
           A#19         |->  A#20,
           C#7          |->  A#20[A#22],
           A#14         |->  A#22[[.]],
           C#21         |->  A#22,
           A#23         |->  [.],
           X#11         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=A#20[A#22[(var X#3)]];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[A#22[(var X#2)]];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[A#22[(var X#3)]];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#20[A#22[(\ X#9.S#13)]];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[A#22[(app A#23[(var X#11)] C#24[(var X#2)])]]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[A#22[(app A#23[(\ X#9.S#13)] C#24[(var X#3)])]]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#21,A#19,C#7,A#14,A#20}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[A#22[(app A#23[(var X#11)] C#24)]]),
             ((var X#3),A#20[A#22[(app A#23[(var X#11)] C#24)]]),
             ((var X#2),A#20[A#22[(app A#23[(var X#11)] C#24[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#22[(app A#23[[.]] C#24[(var X#3)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {[.1]=A#20[[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|},
           A#19         |->  A#20,
           C#7          |->  A#20[A#22[(app A#23[(var X#11)] C#24)]],
           C#21         |->  A#22[(app A#23[(var X#11)] C#24)],
           A#14         |->  A#22[(app A#23 C#24[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#10=A#20[A#22[(app A#23[(var X#11)] C#24[(var X#3)])]];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[A#22[(app A#23[(var X#11)] C#24[(var X#2)])]];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[A#22[(app A#23[(var X#11)] C#24[(var X#3)])]];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#20[A#22[(app A#23[(\ X#9.S#13)] C#24[(var X#3)])]];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[(app A#21[A#14[(var X#11)]] C#22[(var X#2)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[(app A#21[A#14[(\ X#9.S#13)]] C#22[(var X#3)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[(app A#21[A#14[(var X#11)]] C#22)]),
             ((var X#3),A#20[(app A#21[A#14[(var X#11)]] C#22)]),
             ((var X#2),A#20[(app A#21[A#14[(var X#11)]] C#22[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {[.1]=A#20[(app A#21[[.2]] C#22[(var X#3)])]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|},
           C#7          |->  A#20[(app A#21[A#14[(var X#11)]] C#22)],
           A#19         |->  A#20[(app A#21 C#22[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#10=A#20[(app A#21[A#14[(var X#11)]] C#22[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[(app A#21[A#14[(var X#11)]] C#22[(var X#2)])];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[(app A#21[A#14[(var X#11)]] C#22[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#20[(app A#21[A#14[(\ X#9.S#13)]] C#22[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[(var X#2)]
       ;X#2= (var X#11)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[(\ X#9.S#13)]
       ;X#2= (var X#11)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14,A#20}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[[.]]),
             ((var X#11),A#20[[.]]),
             ((var X#2),A#20[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#20[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#11);E#18},
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|},
           A#19         |->  [.],
           A#14         |->  A#20,
           C#7          |->  A#20[[.]],
           C#21         |->  [.],
           X#3          |->  X#11}

and instantiated rules:

                                  (letrec {X#10=A#20[(var X#11)];X#2=(var X#11);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[(var X#2)];X#2=(var X#11);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[(var X#11)];X#2=(var X#11);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#20[(\ X#9.S#13)];X#2=(var X#11);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[(var X#2)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;VV#17|X#3,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[(\ X#9.S#13)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;VV#17|X#3,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14,A#20}
   Delta2 = {}
   Delta3 = {((var X#2),A#20),
             ((var X#3),A#20),
             ((var X#2),A#20[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#3),A#20[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;VV#17|X#3,(var X#8)|},
           A#19         |->  [.],
           A#14         |->  A#20[[.]],
           C#7          |->  A#20,
           A#21         |->  [.],
           X#11         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=A#20[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[(var X#2)];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#20[(\ X#9.S#13)];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[(app A#21[(var X#11)] C#22[(var X#2)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[(app A#21[(\ X#9.S#13)] C#22[(var X#3)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[(app A#21[(var X#11)] C#22)]),
             ((var X#3),A#20[(app A#21[(var X#11)] C#22)]),
             ((var X#2),A#20[(app A#21[(var X#11)] C#22[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#20[(app A#21[[.]] C#22[(var X#3)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|},
           A#19         |->  [.],
           C#7          |->  A#20[(app A#21[(var X#11)] C#22)],
           A#14         |->  A#20[(app A#21 C#22[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#10=A#20[(app A#21[(var X#11)] C#22[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[(app A#21[(var X#11)] C#22[(var X#2)])];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[(app A#21[(var X#11)] C#22[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#20[(app A#21[(\ X#9.S#13)] C#22[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(var X#2)]
       ;X#2= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#20,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(var X#20)]
       ;X#2= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#20,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#14,A#22}
   Delta2 = {}
   Delta3 = {((var X#2),A#22[[.]]),
             ((var X#20),A#22[[.]]),
             ((var X#2),A#22[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#20);E#18},
           EE#16[.1,.2] |-> {[.1]=A#22[(var X#20)];EE#21[X#20,[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#21[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           A#19         |->  A#22,
           C#7          |->  A#22[[.]],
           C#23         |->  [.],
           X#3          |->  X#20}

and instantiated rules:

                                  (letrec {X#10=A#22[(var X#20)];X#2=(var X#20);X#8=(\ X#9.S#13);E#18;EE#21[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#22[(var X#2)];X#2=(var X#20);X#8=(\ X#9.S#13);E#18;EE#21[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(var X#20)];X#2=(var X#20);X#8=(\ X#9.S#13);E#18;EE#21[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[(var X#20)];X#2=(var X#20);X#8=(\ X#9.S#13);E#18;EE#21[X#20,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(var X#2)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#3,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(var X#3)]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#3,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#14,A#22}
   Delta2 = {}
   Delta3 = {((var X#2),A#22),
             ((var X#3),A#22),
             ((var X#2),A#22[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {[.1]=A#22[(var X#3)];EE#21[X#3,[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#21[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           A#19         |->  A#22[[.]],
           C#7          |->  A#22,
           A#23         |->  [.],
           X#20         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=A#22[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;EE#21[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#22[(var X#2)];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;EE#21[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;EE#21[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[(var X#3)];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;EE#21[X#3,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(app A#23[(var X#20)] C#24[(var X#2)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#20,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(app A#23[(var X#20)] C#24[(var X#3)])]
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#20,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),A#22[(app A#23[(var X#20)] C#24)]),
             ((var X#3),A#22[(app A#23[(var X#20)] C#24)]),
             ((var X#2),A#22[(app A#23[(var X#20)] C#24[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {[.1]=A#22[(app A#23[(var X#20)] C#24[(var X#3)])];EE#21[X#20,[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#21[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           C#7          |->  A#22[(app A#23[(var X#20)] C#24)],
           A#19         |->  A#22[(app A#23 C#24[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[(app A#23[(var X#20)] C#24[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;EE#21[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#22[(app A#23[(var X#20)] C#24[(var X#2)])];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;EE#21[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(app A#23[(var X#20)] C#24[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;EE#21[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[(app A#23[(var X#20)] C#24[(var X#3)])];X#2=(var X#3);X#8=(\ X#9.S#13);E#18;EE#21[X#20,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#2)
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#3,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#2= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#3,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#3),[.]),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {[.1]=(var X#3);EE#21[X#3,[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#21[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           C#7          |->  [.],
           A#19         |->  [.],
           X#20         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#2=(var X#3);X#8=(\ X#9.S#13);E#18;EE#21[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#2);X#2=(var X#3);X#8=(\ X#9.S#13);E#18;EE#21[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#2=(var X#3);X#8=(\ X#9.S#13);E#18;EE#21[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=(var X#3);X#2=(var X#3);X#8=(\ X#9.S#13);E#18;EE#21[X#3,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#21)
       ;X#20= A#24[(var X#2)]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#21,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#21)
       ;X#20= A#24[(var X#21)]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#21,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#14,A#24}
   Delta2 = {}
   Delta3 = {((var X#2),A#24[[.]]),
             ((var X#21),A#24[[.]]),
             ((var X#2),A#24[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#21);E#18},
           EE#16[.1,.2] |-> {X#20=A#24[(var X#21)];EE#22[[.1],(var X#20)];EE#23[X#21,[.2]]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#21,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           A#19         |->  A#24,
           C#7          |->  A#24[[.]],
           C#25         |->  [.],
           X#3          |->  X#21}

and instantiated rules:

                                  (letrec {X#2=(var X#21);X#20=A#24[(var X#21)];X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#21,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#21);X#20=A#24[(var X#2)];X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#21,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#21);X#20=A#24[(var X#21)];X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#21,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#2=(var X#21);X#20=A#24[(var X#21)];X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#21,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#20= A#24[(var X#2)]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#3,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#20= A#24[(var X#3)]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#3,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#14,A#24}
   Delta2 = {}
   Delta3 = {((var X#2),A#24),
             ((var X#3),A#24),
             ((var X#2),A#24[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {X#20=A#24[(var X#3)];EE#22[[.1],(var X#20)];EE#23[X#3,[.2]]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           A#19         |->  A#24[[.]],
           C#7          |->  A#24,
           A#25         |->  [.],
           X#21         |->  X#3}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#20=A#24[(var X#3)];X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#20=A#24[(var X#2)];X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#20=A#24[(var X#3)];X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#2=(var X#3);X#20=A#24[(var X#3)];X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#3,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#20= A#24[(app A#25[(var X#21)] C#26[(var X#2)])]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#21,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#20= A#24[(app A#25[(var X#21)] C#26[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#21,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),A#24[(app A#25[(var X#21)] C#26)]),
             ((var X#3),A#24[(app A#25[(var X#21)] C#26)]),
             ((var X#2),A#24[(app A#25[(var X#21)] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {X#20=A#24[(app A#25[(var X#21)] C#26[(var X#3)])];EE#22[[.1],(var X#20)];EE#23[X#21,[.2]]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#21,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           C#7          |->  A#24[(app A#25[(var X#21)] C#26)],
           A#19         |->  A#24[(app A#25 C#26[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#20=A#24[(app A#25[(var X#21)] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#21,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#20=A#24[(app A#25[(var X#21)] C#26[(var X#2)])];X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#21,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#20=A#24[(app A#25[(var X#21)] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#21,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#2=(var X#3);X#20=A#24[(app A#25[(var X#21)] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#21,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#20= (var X#2)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#3,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#20= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#3,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#3),[.]),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {X#20=(var X#3);EE#22[[.1],(var X#20)];EE#23[X#3,[.2]]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           C#7          |->  [.],
           A#19         |->  [.],
           X#21         |->  X#3}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#20=(var X#3);X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#20=(var X#2);X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#20=(var X#3);X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#2=(var X#3);X#20=(var X#3);X#8=(\ X#9.S#13);E#18;EE#22[X#10,(var X#20)];EE#23[X#3,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#11)
       ;X#20= A#22[A#24[(var X#2)]]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#10,(var X#20)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#11)
       ;X#20= A#22[A#24[(\ X#9.S#13)]]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#10,(var X#20)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#23,A#19,C#7,A#14,A#22,A#24}
   Delta2 = {}
   Delta3 = {((var X#2),A#22[A#24[[.]]]),
             ((var X#11),A#22[A#24[[.]]]),
             ((var X#2),A#22[A#24[[.]]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#24[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#11);E#18},
           EE#16[.1,.2] |-> {X#20=A#22[[.2]];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|},
           A#19         |->  A#22,
           C#7          |->  A#22[A#24[[.]]],
           A#14         |->  A#24,
           C#23         |->  A#24[[.]],
           C#25         |->  [.],
           X#3          |->  X#11}

and instantiated rules:

                                  (letrec {X#2=(var X#11);X#20=A#22[A#24[(var X#11)]];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#11);X#20=A#22[A#24[(var X#2)]];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#11);X#20=A#22[A#24[(var X#11)]];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#2=(var X#11);X#20=A#22[A#24[(\ X#9.S#13)]];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#20= A#22[A#24[(var X#2)]]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#10,(var X#20)]
       ;VV#17|X#3,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#20= A#22[A#24[(\ X#9.S#13)]]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#10,(var X#20)]
       ;VV#17|X#3,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#23,A#19,C#7,A#14,A#22,A#24}
   Delta2 = {}
   Delta3 = {((var X#2),A#22[A#24]),
             ((var X#3),A#22[A#24]),
             ((var X#2),A#22[A#24[[.]]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#3),A#24[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {X#20=A#22[[.2]];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#3,(var X#8)|},
           A#19         |->  A#22,
           C#7          |->  A#22[A#24],
           A#14         |->  A#24[[.]],
           C#23         |->  A#24,
           A#25         |->  [.],
           X#11         |->  X#3}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#20=A#22[A#24[(var X#3)]];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#20=A#22[A#24[(var X#2)]];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#20=A#22[A#24[(var X#3)]];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#2=(var X#3);X#20=A#22[A#24[(\ X#9.S#13)]];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#20= A#22[A#24[(app A#25[(var X#11)] C#26[(var X#2)])]]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#10,(var X#20)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#20= A#22[A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#3)])]]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#10,(var X#20)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#23,A#19,C#7,A#14,A#22}
   Delta2 = {}
   Delta3 = {((var X#2),A#22[A#24[(app A#25[(var X#11)] C#26)]]),
             ((var X#3),A#22[A#24[(app A#25[(var X#11)] C#26)]]),
             ((var X#2),A#22[A#24[(app A#25[(var X#11)] C#26[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#24[(app A#25[[.]] C#26[(var X#3)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {X#20=A#22[[.2]];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|},
           A#19         |->  A#22,
           C#7          |->  A#22[A#24[(app A#25[(var X#11)] C#26)]],
           C#23         |->  A#24[(app A#25[(var X#11)] C#26)],
           A#14         |->  A#24[(app A#25 C#26[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#20=A#22[A#24[(app A#25[(var X#11)] C#26[(var X#3)])]];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#20=A#22[A#24[(app A#25[(var X#11)] C#26[(var X#2)])]];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#20=A#22[A#24[(app A#25[(var X#11)] C#26[(var X#3)])]];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#2=(var X#3);X#20=A#22[A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#3)])]];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#20= A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#2)])]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#10,(var X#20)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#20= A#22[(app A#23[A#14[(\ X#9.S#13)]] C#24[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#10,(var X#20)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),A#22[(app A#23[A#14[(var X#11)]] C#24)]),
             ((var X#3),A#22[(app A#23[A#14[(var X#11)]] C#24)]),
             ((var X#2),A#22[(app A#23[A#14[(var X#11)]] C#24[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {X#20=A#22[(app A#23[[.2]] C#24[(var X#3)])];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|},
           C#7          |->  A#22[(app A#23[A#14[(var X#11)]] C#24)],
           A#19         |->  A#22[(app A#23 C#24[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#20=A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#3)])];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#20=A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#2)])];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#20=A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#3)])];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#2=(var X#3);X#20=A#22[(app A#23[A#14[(\ X#9.S#13)]] C#24[(var X#3)])];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#11)
       ;X#20= A#22[(var X#2)]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#10,(var X#20)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#11)
       ;X#20= A#22[(\ X#9.S#13)]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#10,(var X#20)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14,A#22}
   Delta2 = {}
   Delta3 = {((var X#2),A#22[[.]]),
             ((var X#11),A#22[[.]]),
             ((var X#2),A#22[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#22[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#11);E#18},
           EE#16[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|},
           A#19         |->  [.],
           A#14         |->  A#22,
           C#7          |->  A#22[[.]],
           C#23         |->  [.],
           X#3          |->  X#11}

and instantiated rules:

                                  (letrec {X#2=(var X#11);X#20=A#22[(var X#11)];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#11);X#20=A#22[(var X#2)];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#11);X#20=A#22[(var X#11)];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#2=(var X#11);X#20=A#22[(\ X#9.S#13)];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#20= A#22[(var X#2)]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#10,(var X#20)]
       ;VV#17|X#3,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#20= A#22[(\ X#9.S#13)]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#10,(var X#20)]
       ;VV#17|X#3,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14,A#22}
   Delta2 = {}
   Delta3 = {((var X#2),A#22),
             ((var X#3),A#22),
             ((var X#2),A#22[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#3),A#22[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#3,(var X#8)|},
           A#19         |->  [.],
           A#14         |->  A#22[[.]],
           C#7          |->  A#22,
           A#23         |->  [.],
           X#11         |->  X#3}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#20=A#22[(var X#3)];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#20=A#22[(var X#2)];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#20=A#22[(var X#3)];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#2=(var X#3);X#20=A#22[(\ X#9.S#13)];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#3,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#20= A#22[(app A#23[(var X#11)] C#24[(var X#2)])]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#10,(var X#20)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#20= A#22[(app A#23[(\ X#9.S#13)] C#24[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#21[X#10,(var X#20)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),A#22[(app A#23[(var X#11)] C#24)]),
             ((var X#3),A#22[(app A#23[(var X#11)] C#24)]),
             ((var X#2),A#22[(app A#23[(var X#11)] C#24[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#22[(app A#23[[.]] C#24[(var X#3)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           E#12         |->  {X#2=(var X#3);E#18},
           EE#16[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|},
           A#19         |->  [.],
           C#7          |->  A#22[(app A#23[(var X#11)] C#24)],
           A#14         |->  A#22[(app A#23 C#24[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#20=A#22[(app A#23[(var X#11)] C#24[(var X#3)])];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#20=A#22[(app A#23[(var X#11)] C#24[(var X#2)])];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#20=A#22[(app A#23[(var X#11)] C#24[(var X#3)])];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#2=(var X#3);X#20=A#22[(app A#23[(\ X#9.S#13)] C#24[(var X#3)])];X#8=(\ X#9.S#13);E#18;EE#21[X#10,(var X#20)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= (var X#8)
       ;X#8= (\ X#9.C#19[(var X#11)])
       ;E#12
       ;EE#16[X#10,A#14[(var X#11)]]
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#11= (var X#8)
       ;X#8= (\ X#9.C#19[(var X#8)])
       ;E#12
       ;EE#16[X#10,A#14[(\ X#9.C#19[(var X#8)])]]
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#11),(\ X#9.C#19)),
             ((var X#8),(\ X#9.C#19)),
             ((var X#11),(\ X#9.C#19[[.]])),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=[.2]},
           X#2          |->  X#11,
           X#3          |->  X#8,
           X#1          |->  X#8,
           E#4          |->  {E#12;EE#16[X#10,A#14[(var X#11)]]},
           C#7          |->  (\ X#9.C#19),
           S#13         |->  C#19[(var X#8)]}

and instantiated rules:

                                  (letrec {X#11=(var X#8);X#8=(\ X#9.C#19[(var X#8)]);E#12;EE#16[X#10,A#14[(var X#11)]]} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#11=(var X#8);X#8=(\ X#9.C#19[(var X#11)]);E#12;EE#16[X#10,A#14[(var X#11)]]} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#11=(var X#8);X#8=(\ X#9.C#19[(var X#8)]);E#12;EE#16[X#10,A#14[(var X#11)]]} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#11=(var X#8);X#8=(\ X#9.C#19[(var X#8)]);E#12;EE#16[X#10,A#14[(\ X#9.C#19[(var X#8)])]]} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#11)]
       ;X#11= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#19
       ;EE#16[X#10,A#14[(var X#11)]]
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#8)]
       ;X#11= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#19
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#11),C#7),
             ((var X#8),C#7),
             ((var X#11),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=[.2]},
           X#2          |->  X#11,
           X#3          |->  X#8,
           E#12         |->  {X#1=C#7[(var X#8)];E#19},
           E#4          |->  {X#8=(\ X#9.S#13);E#19;EE#16[X#10,A#14[(var X#11)]]}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#8)];X#11=(var X#8);X#8=(\ X#9.S#13);E#19;EE#16[X#10,A#14[(var X#11)]]} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#11)];X#11=(var X#8);X#8=(\ X#9.S#13);E#19;EE#16[X#10,A#14[(var X#11)]]} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#8)];X#11=(var X#8);X#8=(\ X#9.S#13);E#19;EE#16[X#10,A#14[(var X#11)]]} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#1=C#7[(var X#8)];X#11=(var X#8);X#8=(\ X#9.S#13);E#19;EE#16[X#10,A#14[(\ X#9.S#13)]]} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[A#22[(app A#23[(var X#11)] C#24[(var X#11)])]]
       ;X#11= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[A#22[(app A#23[(\ X#9.S#13)] C#24[(var X#8)])]]
       ;X#11= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#21,A#19,C#7,A#14,A#20}
   Delta2 = {}
   Delta3 = {((var X#11),A#20[A#22[(app A#23[(var X#11)] C#24)]]),
             ((var X#8),A#20[A#22[(app A#23[(var X#11)] C#24)]]),
             ((var X#11),A#20[A#22[(app A#23[(var X#11)] C#24[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#22[(app A#23[[.]] C#24[(var X#8)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=[.2]},
           X#2          |->  X#11,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {[.1]=A#20[[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12},
           A#19         |->  A#20,
           C#7          |->  A#20[A#22[(app A#23[(var X#11)] C#24)]],
           C#21         |->  A#22[(app A#23[(var X#11)] C#24)],
           A#14         |->  A#22[(app A#23 C#24[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#10=A#20[A#22[(app A#23[(var X#11)] C#24[(var X#8)])]];X#11=(var X#8);X#8=(\ X#9.S#13);E#12} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[A#22[(app A#23[(var X#11)] C#24[(var X#11)])]];X#11=(var X#8);X#8=(\ X#9.S#13);E#12} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[A#22[(app A#23[(var X#11)] C#24[(var X#8)])]];X#11=(var X#8);X#8=(\ X#9.S#13);E#12} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#20[A#22[(app A#23[(\ X#9.S#13)] C#24[(var X#8)])]];X#11=(var X#8);X#8=(\ X#9.S#13);E#12} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[(app A#21[A#14[(var X#11)]] C#22[(var X#11)])]
       ;X#11= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[(app A#21[A#14[(\ X#9.S#13)]] C#22[(var X#8)])]
       ;X#11= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#11),A#20[(app A#21[A#14[(var X#11)]] C#22)]),
             ((var X#8),A#20[(app A#21[A#14[(var X#11)]] C#22)]),
             ((var X#11),A#20[(app A#21[A#14[(var X#11)]] C#22[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=[.2]},
           X#2          |->  X#11,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {[.1]=A#20[(app A#21[[.2]] C#22[(var X#8)])]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12},
           C#7          |->  A#20[(app A#21[A#14[(var X#11)]] C#22)],
           A#19         |->  A#20[(app A#21 C#22[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#10=A#20[(app A#21[A#14[(var X#11)]] C#22[(var X#8)])];X#11=(var X#8);X#8=(\ X#9.S#13);E#12} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[(app A#21[A#14[(var X#11)]] C#22[(var X#11)])];X#11=(var X#8);X#8=(\ X#9.S#13);E#12} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[(app A#21[A#14[(var X#11)]] C#22[(var X#8)])];X#11=(var X#8);X#8=(\ X#9.S#13);E#12} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#20[(app A#21[A#14[(\ X#9.S#13)]] C#22[(var X#8)])];X#11=(var X#8);X#8=(\ X#9.S#13);E#12} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[(app A#21[(var X#11)] C#22[(var X#11)])]
       ;X#11= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[(app A#21[(\ X#9.S#13)] C#22[(var X#8)])]
       ;X#11= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#11),A#20[(app A#21[(var X#11)] C#22)]),
             ((var X#8),A#20[(app A#21[(var X#11)] C#22)]),
             ((var X#11),A#20[(app A#21[(var X#11)] C#22[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#20[(app A#21[[.]] C#22[(var X#8)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=[.2]},
           X#2          |->  X#11,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12},
           A#19         |->  [.],
           C#7          |->  A#20[(app A#21[(var X#11)] C#22)],
           A#14         |->  A#20[(app A#21 C#22[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#10=A#20[(app A#21[(var X#11)] C#22[(var X#8)])];X#11=(var X#8);X#8=(\ X#9.S#13);E#12} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#20[(app A#21[(var X#11)] C#22[(var X#11)])];X#11=(var X#8);X#8=(\ X#9.S#13);E#12} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[(app A#21[(var X#11)] C#22[(var X#8)])];X#11=(var X#8);X#8=(\ X#9.S#13);E#12} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#20[(app A#21[(\ X#9.S#13)] C#22[(var X#8)])];X#11=(var X#8);X#8=(\ X#9.S#13);E#12} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(app A#23[(var X#20)] C#24[(var X#11)])]
       ;X#11= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#20,A#14[(var X#11)]]
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(app A#23[(var X#20)] C#24[(var X#8)])]
       ;X#11= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#20,A#14[(\ X#9.S#13)]]
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#11),A#22[(app A#23[(var X#20)] C#24)]),
             ((var X#8),A#22[(app A#23[(var X#20)] C#24)]),
             ((var X#11),A#22[(app A#23[(var X#20)] C#24[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=[.2]},
           X#2          |->  X#11,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {[.1]=A#22[(app A#23[(var X#20)] C#24[(var X#8)])];EE#21[X#20,[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#20,A#14[(var X#11)]]},
           C#7          |->  A#22[(app A#23[(var X#20)] C#24)],
           A#19         |->  A#22[(app A#23 C#24[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[(app A#23[(var X#20)] C#24[(var X#8)])];X#11=(var X#8);X#8=(\ X#9.S#13);E#12;EE#21[X#20,A#14[(var X#11)]]} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#22[(app A#23[(var X#20)] C#24[(var X#11)])];X#11=(var X#8);X#8=(\ X#9.S#13);E#12;EE#21[X#20,A#14[(var X#11)]]} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(app A#23[(var X#20)] C#24[(var X#8)])];X#11=(var X#8);X#8=(\ X#9.S#13);E#12;EE#21[X#20,A#14[(var X#11)]]} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[(app A#23[(var X#20)] C#24[(var X#8)])];X#11=(var X#8);X#8=(\ X#9.S#13);E#12;EE#21[X#20,A#14[(\ X#9.S#13)]]} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= (var X#8)
       ;X#20= A#24[(app A#25[(var X#21)] C#26[(var X#11)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#21,A#14[(var X#11)]]
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#11= (var X#8)
       ;X#20= A#24[(app A#25[(var X#21)] C#26[(var X#8)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#21,A#14[(\ X#9.S#13)]]
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#11),A#24[(app A#25[(var X#21)] C#26)]),
             ((var X#8),A#24[(app A#25[(var X#21)] C#26)]),
             ((var X#11),A#24[(app A#25[(var X#21)] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=[.2]},
           X#2          |->  X#11,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {X#20=A#24[(app A#25[(var X#21)] C#26[(var X#8)])];EE#22[[.1],(var X#20)];EE#23[X#21,[.2]]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#22[X#10,(var X#20)];EE#23[X#21,A#14[(var X#11)]]},
           C#7          |->  A#24[(app A#25[(var X#21)] C#26)],
           A#19         |->  A#24[(app A#25 C#26[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#11=(var X#8);X#20=A#24[(app A#25[(var X#21)] C#26[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#22[X#10,(var X#20)];EE#23[X#21,A#14[(var X#11)]]} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#11=(var X#8);X#20=A#24[(app A#25[(var X#21)] C#26[(var X#11)])];X#8=(\ X#9.S#13);E#12;EE#22[X#10,(var X#20)];EE#23[X#21,A#14[(var X#11)]]} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#11=(var X#8);X#20=A#24[(app A#25[(var X#21)] C#26[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#22[X#10,(var X#20)];EE#23[X#21,A#14[(var X#11)]]} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#11=(var X#8);X#20=A#24[(app A#25[(var X#21)] C#26[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#22[X#10,(var X#20)];EE#23[X#21,A#14[(\ X#9.S#13)]]} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= (var X#8)
       ;X#20= A#22[A#24[(app A#25[(var X#11)] C#26[(var X#11)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#20)]
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#11= (var X#8)
       ;X#20= A#22[A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#8)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#20)]
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#23,A#19,C#7,A#14,A#22}
   Delta2 = {}
   Delta3 = {((var X#11),A#22[A#24[(app A#25[(var X#11)] C#26)]]),
             ((var X#8),A#22[A#24[(app A#25[(var X#11)] C#26)]]),
             ((var X#11),A#22[A#24[(app A#25[(var X#11)] C#26[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#24[(app A#25[[.]] C#26[(var X#8)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=[.2]},
           X#2          |->  X#11,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {X#20=A#22[[.2]];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#20)]},
           A#19         |->  A#22,
           C#7          |->  A#22[A#24[(app A#25[(var X#11)] C#26)]],
           C#23         |->  A#24[(app A#25[(var X#11)] C#26)],
           A#14         |->  A#24[(app A#25 C#26[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#11=(var X#8);X#20=A#22[A#24[(app A#25[(var X#11)] C#26[(var X#8)])]];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#20)]} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#11=(var X#8);X#20=A#22[A#24[(app A#25[(var X#11)] C#26[(var X#11)])]];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#20)]} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#11=(var X#8);X#20=A#22[A#24[(app A#25[(var X#11)] C#26[(var X#8)])]];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#20)]} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#11=(var X#8);X#20=A#22[A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#8)])]];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#20)]} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= (var X#8)
       ;X#20= A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#11)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#20)]
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#11= (var X#8)
       ;X#20= A#22[(app A#23[A#14[(\ X#9.S#13)]] C#24[(var X#8)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#20)]
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#19,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#11),A#22[(app A#23[A#14[(var X#11)]] C#24)]),
             ((var X#8),A#22[(app A#23[A#14[(var X#11)]] C#24)]),
             ((var X#11),A#22[(app A#23[A#14[(var X#11)]] C#24[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=[.2]},
           X#2          |->  X#11,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {X#20=A#22[(app A#23[[.2]] C#24[(var X#8)])];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#20)]},
           C#7          |->  A#22[(app A#23[A#14[(var X#11)]] C#24)],
           A#19         |->  A#22[(app A#23 C#24[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#11=(var X#8);X#20=A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#20)]} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#11=(var X#8);X#20=A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#11)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#20)]} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#11=(var X#8);X#20=A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#20)]} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#11=(var X#8);X#20=A#22[(app A#23[A#14[(\ X#9.S#13)]] C#24[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#20)]} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= (var X#8)
       ;X#20= A#22[(app A#23[(var X#11)] C#24[(var X#11)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#20)]
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#11= (var X#8)
       ;X#20= A#22[(app A#23[(\ X#9.S#13)] C#24[(var X#8)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#20)]
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#11),A#22[(app A#23[(var X#11)] C#24)]),
             ((var X#8),A#22[(app A#23[(var X#11)] C#24)]),
             ((var X#11),A#22[(app A#23[(var X#11)] C#24[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#22[(app A#23[[.]] C#24[(var X#8)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=[.2]},
           X#2          |->  X#11,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#20)]},
           A#19         |->  [.],
           C#7          |->  A#22[(app A#23[(var X#11)] C#24)],
           A#14         |->  A#22[(app A#23 C#24[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#11=(var X#8);X#20=A#22[(app A#23[(var X#11)] C#24[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#20)]} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#11=(var X#8);X#20=A#22[(app A#23[(var X#11)] C#24[(var X#11)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#20)]} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#11=(var X#8);X#20=A#22[(app A#23[(var X#11)] C#24[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#20)]} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#11=(var X#8);X#20=A#22[(app A#23[(\ X#9.S#13)] C#24[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#20)]} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= (var X#19)
       ;X#8= (\ X#9.C#21[(var X#11)])
       ;E#12
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#11= (var X#19)
       ;X#8= (\ X#9.C#21[(var X#19)])
       ;E#12
       ;EE#16[X#10,A#14[(\ X#9.C#21[(var X#19)])]]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#11),(\ X#9.C#21)),
             ((var X#19),(\ X#9.C#21)),
             ((var X#11),(\ X#9.C#21[[.]])),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=(var X#19);VV#20|X#19,[.2]|},
           X#2          |->  X#11,
           X#3          |->  X#19,
           X#1          |->  X#8,
           E#4          |->  {E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#19,(var X#8)|},
           C#7          |->  (\ X#9.C#21),
           S#13         |->  C#21[(var X#19)]}

and instantiated rules:

                                  (letrec {X#11=(var X#19);X#8=(\ X#9.C#21[(var X#19)]);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#11=(var X#19);X#8=(\ X#9.C#21[(var X#11)]);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#11=(var X#19);X#8=(\ X#9.C#21[(var X#19)]);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#11=(var X#19);X#8=(\ X#9.C#21[(var X#19)]);E#12;EE#16[X#10,A#14[(\ X#9.C#21[(var X#19)])]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#11)]
       ;X#11= (var X#19)
       ;X#8= (\ X#9.S#13)
       ;E#21
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#19)]
       ;X#11= (var X#19)
       ;X#8= (\ X#9.S#13)
       ;E#21
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#11),C#7),
             ((var X#19),C#7),
             ((var X#11),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=(var X#19);VV#20|X#19,[.2]|},
           X#2          |->  X#11,
           X#3          |->  X#19,
           E#12         |->  {X#1=C#7[(var X#19)];E#21},
           E#4          |->  {X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#20|X#19,(var X#8)|}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#19)];X#11=(var X#19);X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#11)];X#11=(var X#19);X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#19)];X#11=(var X#19);X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#1=C#7[(var X#19)];X#11=(var X#19);X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[A#24[(app A#25[(var X#11)] C#26[(var X#11)])]]
       ;X#11= (var X#19)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#19)])]]
       ;X#11= (var X#19)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#23,A#21,C#7,A#14,A#22}
   Delta2 = {}
   Delta3 = {((var X#11),A#22[A#24[(app A#25[(var X#11)] C#26)]]),
             ((var X#19),A#22[A#24[(app A#25[(var X#11)] C#26)]]),
             ((var X#11),A#22[A#24[(app A#25[(var X#11)] C#26[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#24[(app A#25[[.]] C#26[(var X#19)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=(var X#19);VV#20|X#19,[.2]|},
           X#2          |->  X#11,
           X#3          |->  X#19,
           EE#16[.1,.2] |-> {[.1]=A#22[[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;VV#20|X#19,(var X#8)|},
           A#21         |->  A#22,
           C#7          |->  A#22[A#24[(app A#25[(var X#11)] C#26)]],
           C#23         |->  A#24[(app A#25[(var X#11)] C#26)],
           A#14         |->  A#24[(app A#25 C#26[(var X#19)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[A#24[(app A#25[(var X#11)] C#26[(var X#19)])]];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#22[A#24[(app A#25[(var X#11)] C#26[(var X#11)])]];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[A#24[(app A#25[(var X#11)] C#26[(var X#19)])]];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#19)])]];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#11)])]
       ;X#11= (var X#19)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(app A#23[A#14[(\ X#9.S#13)]] C#24[(var X#19)])]
       ;X#11= (var X#19)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#11),A#22[(app A#23[A#14[(var X#11)]] C#24)]),
             ((var X#19),A#22[(app A#23[A#14[(var X#11)]] C#24)]),
             ((var X#11),A#22[(app A#23[A#14[(var X#11)]] C#24[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=(var X#19);VV#20|X#19,[.2]|},
           X#2          |->  X#11,
           X#3          |->  X#19,
           EE#16[.1,.2] |-> {[.1]=A#22[(app A#23[[.2]] C#24[(var X#19)])]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;VV#20|X#19,(var X#8)|},
           C#7          |->  A#22[(app A#23[A#14[(var X#11)]] C#24)],
           A#21         |->  A#22[(app A#23 C#24[(var X#19)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#19)])];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#11)])];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#19)])];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[(app A#23[A#14[(\ X#9.S#13)]] C#24[(var X#19)])];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(app A#23[(var X#11)] C#24[(var X#11)])]
       ;X#11= (var X#19)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(app A#23[(\ X#9.S#13)] C#24[(var X#19)])]
       ;X#11= (var X#19)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#11),A#22[(app A#23[(var X#11)] C#24)]),
             ((var X#19),A#22[(app A#23[(var X#11)] C#24)]),
             ((var X#11),A#22[(app A#23[(var X#11)] C#24[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#22[(app A#23[[.]] C#24[(var X#19)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=(var X#19);VV#20|X#19,[.2]|},
           X#2          |->  X#11,
           X#3          |->  X#19,
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;VV#20|X#19,(var X#8)|},
           A#21         |->  [.],
           C#7          |->  A#22[(app A#23[(var X#11)] C#24)],
           A#14         |->  A#22[(app A#23 C#24[(var X#19)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[(app A#23[(var X#11)] C#24[(var X#19)])];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#22[(app A#23[(var X#11)] C#24[(var X#11)])];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(app A#23[(var X#11)] C#24[(var X#19)])];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[(app A#23[(\ X#9.S#13)] C#24[(var X#19)])];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#24[(app A#25[(var X#22)] C#26[(var X#11)])]
       ;X#11= (var X#19)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#22,A#14[(var X#11)]]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#24[(app A#25[(var X#22)] C#26[(var X#19)])]
       ;X#11= (var X#19)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#22,A#14[(\ X#9.S#13)]]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#11),A#24[(app A#25[(var X#22)] C#26)]),
             ((var X#19),A#24[(app A#25[(var X#22)] C#26)]),
             ((var X#11),A#24[(app A#25[(var X#22)] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=(var X#19);VV#20|X#19,[.2]|},
           X#2          |->  X#11,
           X#3          |->  X#19,
           EE#16[.1,.2] |-> {[.1]=A#24[(app A#25[(var X#22)] C#26[(var X#19)])];EE#23[X#22,[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#20|X#19,(var X#8)|},
           C#7          |->  A#24[(app A#25[(var X#22)] C#26)],
           A#21         |->  A#24[(app A#25 C#26[(var X#19)])]}

and instantiated rules:

                                  (letrec {X#10=A#24[(app A#25[(var X#22)] C#26[(var X#19)])];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#24[(app A#25[(var X#22)] C#26[(var X#11)])];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#24[(app A#25[(var X#22)] C#26[(var X#19)])];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#24[(app A#25[(var X#22)] C#26[(var X#19)])];X#11=(var X#19);X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(\ X#9.S#13)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= (var X#19)
       ;X#22= A#26[(app A#27[(var X#23)] C#28[(var X#11)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#24[X#10,(var X#22)]
       ;EE#25[X#23,A#14[(var X#11)]]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#11= (var X#19)
       ;X#22= A#26[(app A#27[(var X#23)] C#28[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#24[X#10,(var X#22)]
       ;EE#25[X#23,A#14[(\ X#9.S#13)]]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#11),A#26[(app A#27[(var X#23)] C#28)]),
             ((var X#19),A#26[(app A#27[(var X#23)] C#28)]),
             ((var X#11),A#26[(app A#27[(var X#23)] C#28[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=(var X#19);VV#20|X#19,[.2]|},
           X#2          |->  X#11,
           X#3          |->  X#19,
           EE#16[.1,.2] |-> {X#22=A#26[(app A#27[(var X#23)] C#28[(var X#19)])];EE#24[[.1],(var X#22)];EE#25[X#23,[.2]]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#20|X#19,(var X#8)|},
           C#7          |->  A#26[(app A#27[(var X#23)] C#28)],
           A#21         |->  A#26[(app A#27 C#28[(var X#19)])]}

and instantiated rules:

                                  (letrec {X#11=(var X#19);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#11=(var X#19);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#11)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#11=(var X#19);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#11=(var X#19);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(\ X#9.S#13)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= (var X#19)
       ;X#22= A#24[A#26[(app A#27[(var X#11)] C#28[(var X#11)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#11= (var X#19)
       ;X#22= A#24[A#26[(app A#27[(\ X#9.S#13)] C#28[(var X#19)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#25,A#21,C#7,A#14,A#24}
   Delta2 = {}
   Delta3 = {((var X#11),A#24[A#26[(app A#27[(var X#11)] C#28)]]),
             ((var X#19),A#24[A#26[(app A#27[(var X#11)] C#28)]]),
             ((var X#11),A#24[A#26[(app A#27[(var X#11)] C#28[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#26[(app A#27[[.]] C#28[(var X#19)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=(var X#19);VV#20|X#19,[.2]|},
           X#2          |->  X#11,
           X#3          |->  X#19,
           EE#16[.1,.2] |-> {X#22=A#24[[.2]];EE#23[[.1],(var X#22)]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#19,(var X#8)|},
           A#21         |->  A#24,
           C#7          |->  A#24[A#26[(app A#27[(var X#11)] C#28)]],
           C#25         |->  A#26[(app A#27[(var X#11)] C#28)],
           A#14         |->  A#26[(app A#27 C#28[(var X#19)])]}

and instantiated rules:

                                  (letrec {X#11=(var X#19);X#22=A#24[A#26[(app A#27[(var X#11)] C#28[(var X#19)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#11=(var X#19);X#22=A#24[A#26[(app A#27[(var X#11)] C#28[(var X#11)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#11=(var X#19);X#22=A#24[A#26[(app A#27[(var X#11)] C#28[(var X#19)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#11=(var X#19);X#22=A#24[A#26[(app A#27[(\ X#9.S#13)] C#28[(var X#19)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= (var X#19)
       ;X#22= A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#11)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#11= (var X#19)
       ;X#22= A#24[(app A#25[A#14[(\ X#9.S#13)]] C#26[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#11),A#24[(app A#25[A#14[(var X#11)]] C#26)]),
             ((var X#19),A#24[(app A#25[A#14[(var X#11)]] C#26)]),
             ((var X#11),A#24[(app A#25[A#14[(var X#11)]] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=(var X#19);VV#20|X#19,[.2]|},
           X#2          |->  X#11,
           X#3          |->  X#19,
           EE#16[.1,.2] |-> {X#22=A#24[(app A#25[[.2]] C#26[(var X#19)])];EE#23[[.1],(var X#22)]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#19,(var X#8)|},
           C#7          |->  A#24[(app A#25[A#14[(var X#11)]] C#26)],
           A#21         |->  A#24[(app A#25 C#26[(var X#19)])]}

and instantiated rules:

                                  (letrec {X#11=(var X#19);X#22=A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#11=(var X#19);X#22=A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#11)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#11=(var X#19);X#22=A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#11=(var X#19);X#22=A#24[(app A#25[A#14[(\ X#9.S#13)]] C#26[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= (var X#19)
       ;X#22= A#24[(app A#25[(var X#11)] C#26[(var X#11)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#11= (var X#19)
       ;X#22= A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#11),A#24[(app A#25[(var X#11)] C#26)]),
             ((var X#19),A#24[(app A#25[(var X#11)] C#26)]),
             ((var X#11),A#24[(app A#25[(var X#11)] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#24[(app A#25[[.]] C#26[(var X#19)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=(var X#19);VV#20|X#19,[.2]|},
           X#2          |->  X#11,
           X#3          |->  X#19,
           EE#16[.1,.2] |-> {X#22=[.2];EE#23[[.1],(var X#22)]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#19,(var X#8)|},
           A#21         |->  [.],
           C#7          |->  A#24[(app A#25[(var X#11)] C#26)],
           A#14         |->  A#24[(app A#25 C#26[(var X#19)])]}

and instantiated rules:

                                  (letrec {X#11=(var X#19);X#22=A#24[(app A#25[(var X#11)] C#26[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#11=(var X#19);X#22=A#24[(app A#25[(var X#11)] C#26[(var X#11)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#11=(var X#19);X#22=A#24[(app A#25[(var X#11)] C#26[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#11=(var X#19);X#22=A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#20)
       ;X#8= (\ X#9.C#23[(var X#19)])
       ;E#12
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#20)
       ;X#8= (\ X#9.C#23[(var X#20)])
       ;E#12
       ;EE#16[X#10,A#14[(\ X#9.C#23[(var X#20)])]]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),(\ X#9.C#23)),
             ((var X#20),(\ X#9.C#23)),
             ((var X#19),(\ X#9.C#23[[.]])),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=(var X#20);VV#21|[.1],(var X#19)|;VV#22|X#20,[.2]|},
           X#2          |->  X#19,
           X#3          |->  X#20,
           X#1          |->  X#8,
           E#4          |->  {E#12;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|},
           C#7          |->  (\ X#9.C#23),
           S#13         |->  C#23[(var X#20)]}

and instantiated rules:

                                  (letrec {X#19=(var X#20);X#8=(\ X#9.C#23[(var X#20)]);E#12;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#20);X#8=(\ X#9.C#23[(var X#19)]);E#12;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#20);X#8=(\ X#9.C#23[(var X#20)]);E#12;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#20);X#8=(\ X#9.C#23[(var X#20)]);E#12;EE#16[X#10,A#14[(\ X#9.C#23[(var X#20)])]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#19)]
       ;X#19= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#23
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#20)]
       ;X#19= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#23
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#19),C#7),
             ((var X#20),C#7),
             ((var X#19),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=(var X#20);VV#21|[.1],(var X#19)|;VV#22|X#20,[.2]|},
           X#2          |->  X#19,
           X#3          |->  X#20,
           E#12         |->  {X#1=C#7[(var X#20)];E#23},
           E#4          |->  {X#8=(\ X#9.S#13);E#23;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#20)];X#19=(var X#20);X#8=(\ X#9.S#13);E#23;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#19)];X#19=(var X#20);X#8=(\ X#9.S#13);E#23;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#20)];X#19=(var X#20);X#8=(\ X#9.S#13);E#23;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#1=C#7[(var X#20)];X#19=(var X#20);X#8=(\ X#9.S#13);E#23;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#24[A#26[(app A#27[(var X#11)] C#28[(var X#19)])]]
       ;X#19= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#24[A#26[(app A#27[(\ X#9.S#13)] C#28[(var X#20)])]]
       ;X#19= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#25,A#23,C#7,A#14,A#24}
   Delta2 = {}
   Delta3 = {((var X#19),A#24[A#26[(app A#27[(var X#11)] C#28)]]),
             ((var X#20),A#24[A#26[(app A#27[(var X#11)] C#28)]]),
             ((var X#19),A#24[A#26[(app A#27[(var X#11)] C#28[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#26[(app A#27[[.]] C#28[(var X#20)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=(var X#20);VV#21|[.1],(var X#19)|;VV#22|X#20,[.2]|},
           X#2          |->  X#19,
           X#3          |->  X#20,
           EE#16[.1,.2] |-> {[.1]=A#24[[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|},
           A#23         |->  A#24,
           C#7          |->  A#24[A#26[(app A#27[(var X#11)] C#28)]],
           C#25         |->  A#26[(app A#27[(var X#11)] C#28)],
           A#14         |->  A#26[(app A#27 C#28[(var X#20)])]}

and instantiated rules:

                                  (letrec {X#10=A#24[A#26[(app A#27[(var X#11)] C#28[(var X#20)])]];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#24[A#26[(app A#27[(var X#11)] C#28[(var X#19)])]];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#24[A#26[(app A#27[(var X#11)] C#28[(var X#20)])]];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#24[A#26[(app A#27[(\ X#9.S#13)] C#28[(var X#20)])]];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#19)])]
       ;X#19= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#24[(app A#25[A#14[(\ X#9.S#13)]] C#26[(var X#20)])]
       ;X#19= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#23,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#24[(app A#25[A#14[(var X#11)]] C#26)]),
             ((var X#20),A#24[(app A#25[A#14[(var X#11)]] C#26)]),
             ((var X#19),A#24[(app A#25[A#14[(var X#11)]] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=(var X#20);VV#21|[.1],(var X#19)|;VV#22|X#20,[.2]|},
           X#2          |->  X#19,
           X#3          |->  X#20,
           EE#16[.1,.2] |-> {[.1]=A#24[(app A#25[[.2]] C#26[(var X#20)])]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|},
           C#7          |->  A#24[(app A#25[A#14[(var X#11)]] C#26)],
           A#23         |->  A#24[(app A#25 C#26[(var X#20)])]}

and instantiated rules:

                                  (letrec {X#10=A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#20)])];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#19)])];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#20)])];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#24[(app A#25[A#14[(\ X#9.S#13)]] C#26[(var X#20)])];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#24[(app A#25[(var X#11)] C#26[(var X#19)])]
       ;X#19= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#20)])]
       ;X#19= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#24[(app A#25[(var X#11)] C#26)]),
             ((var X#20),A#24[(app A#25[(var X#11)] C#26)]),
             ((var X#19),A#24[(app A#25[(var X#11)] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#24[(app A#25[[.]] C#26[(var X#20)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=(var X#20);VV#21|[.1],(var X#19)|;VV#22|X#20,[.2]|},
           X#2          |->  X#19,
           X#3          |->  X#20,
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|},
           A#23         |->  [.],
           C#7          |->  A#24[(app A#25[(var X#11)] C#26)],
           A#14         |->  A#24[(app A#25 C#26[(var X#20)])]}

and instantiated rules:

                                  (letrec {X#10=A#24[(app A#25[(var X#11)] C#26[(var X#20)])];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#24[(app A#25[(var X#11)] C#26[(var X#19)])];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#24[(app A#25[(var X#11)] C#26[(var X#20)])];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#20)])];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#26[(app A#27[(var X#24)] C#28[(var X#19)])]
       ;X#19= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#25[X#24,A#14[(var X#11)]]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#26[(app A#27[(var X#24)] C#28[(var X#20)])]
       ;X#19= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#25[X#24,A#14[(\ X#9.S#13)]]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#23,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#26[(app A#27[(var X#24)] C#28)]),
             ((var X#20),A#26[(app A#27[(var X#24)] C#28)]),
             ((var X#19),A#26[(app A#27[(var X#24)] C#28[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=(var X#20);VV#21|[.1],(var X#19)|;VV#22|X#20,[.2]|},
           X#2          |->  X#19,
           X#3          |->  X#20,
           EE#16[.1,.2] |-> {[.1]=A#26[(app A#27[(var X#24)] C#28[(var X#20)])];EE#25[X#24,[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#25[X#24,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|},
           C#7          |->  A#26[(app A#27[(var X#24)] C#28)],
           A#23         |->  A#26[(app A#27 C#28[(var X#20)])]}

and instantiated rules:

                                  (letrec {X#10=A#26[(app A#27[(var X#24)] C#28[(var X#20)])];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;EE#25[X#24,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#26[(app A#27[(var X#24)] C#28[(var X#19)])];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;EE#25[X#24,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#26[(app A#27[(var X#24)] C#28[(var X#20)])];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;EE#25[X#24,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#26[(app A#27[(var X#24)] C#28[(var X#20)])];X#19=(var X#20);X#8=(\ X#9.S#13);E#12;EE#25[X#24,A#14[(\ X#9.S#13)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#20)
       ;X#24= A#28[(app A#29[(var X#25)] C#30[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#26[X#10,(var X#24)]
       ;EE#27[X#25,A#14[(var X#11)]]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#20)
       ;X#24= A#28[(app A#29[(var X#25)] C#30[(var X#20)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#26[X#10,(var X#24)]
       ;EE#27[X#25,A#14[(\ X#9.S#13)]]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#23,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#28[(app A#29[(var X#25)] C#30)]),
             ((var X#20),A#28[(app A#29[(var X#25)] C#30)]),
             ((var X#19),A#28[(app A#29[(var X#25)] C#30[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=(var X#20);VV#21|[.1],(var X#19)|;VV#22|X#20,[.2]|},
           X#2          |->  X#19,
           X#3          |->  X#20,
           EE#16[.1,.2] |-> {X#24=A#28[(app A#29[(var X#25)] C#30[(var X#20)])];EE#26[[.1],(var X#24)];EE#27[X#25,[.2]]},
           X#1          |->  X#24,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#26[X#10,(var X#24)];EE#27[X#25,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|},
           C#7          |->  A#28[(app A#29[(var X#25)] C#30)],
           A#23         |->  A#28[(app A#29 C#30[(var X#20)])]}

and instantiated rules:

                                  (letrec {X#19=(var X#20);X#24=A#28[(app A#29[(var X#25)] C#30[(var X#20)])];X#8=(\ X#9.S#13);E#12;EE#26[X#10,(var X#24)];EE#27[X#25,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#20);X#24=A#28[(app A#29[(var X#25)] C#30[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#26[X#10,(var X#24)];EE#27[X#25,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#20);X#24=A#28[(app A#29[(var X#25)] C#30[(var X#20)])];X#8=(\ X#9.S#13);E#12;EE#26[X#10,(var X#24)];EE#27[X#25,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#20);X#24=A#28[(app A#29[(var X#25)] C#30[(var X#20)])];X#8=(\ X#9.S#13);E#12;EE#26[X#10,(var X#24)];EE#27[X#25,A#14[(\ X#9.S#13)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#20)
       ;X#24= A#26[A#28[(app A#29[(var X#11)] C#30[(var X#19)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#25[X#10,(var X#24)]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#20)
       ;X#24= A#26[A#28[(app A#29[(\ X#9.S#13)] C#30[(var X#20)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#25[X#10,(var X#24)]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#27,A#23,C#7,A#14,A#26}
   Delta2 = {}
   Delta3 = {((var X#19),A#26[A#28[(app A#29[(var X#11)] C#30)]]),
             ((var X#20),A#26[A#28[(app A#29[(var X#11)] C#30)]]),
             ((var X#19),A#26[A#28[(app A#29[(var X#11)] C#30[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#28[(app A#29[[.]] C#30[(var X#20)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=(var X#20);VV#21|[.1],(var X#19)|;VV#22|X#20,[.2]|},
           X#2          |->  X#19,
           X#3          |->  X#20,
           EE#16[.1,.2] |-> {X#24=A#26[[.2]];EE#25[[.1],(var X#24)]},
           X#1          |->  X#24,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#25[X#10,(var X#24)];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|},
           A#23         |->  A#26,
           C#7          |->  A#26[A#28[(app A#29[(var X#11)] C#30)]],
           C#27         |->  A#28[(app A#29[(var X#11)] C#30)],
           A#14         |->  A#28[(app A#29 C#30[(var X#20)])]}

and instantiated rules:

                                  (letrec {X#19=(var X#20);X#24=A#26[A#28[(app A#29[(var X#11)] C#30[(var X#20)])]];X#8=(\ X#9.S#13);E#12;EE#25[X#10,(var X#24)];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#20);X#24=A#26[A#28[(app A#29[(var X#11)] C#30[(var X#19)])]];X#8=(\ X#9.S#13);E#12;EE#25[X#10,(var X#24)];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#20);X#24=A#26[A#28[(app A#29[(var X#11)] C#30[(var X#20)])]];X#8=(\ X#9.S#13);E#12;EE#25[X#10,(var X#24)];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#20);X#24=A#26[A#28[(app A#29[(\ X#9.S#13)] C#30[(var X#20)])]];X#8=(\ X#9.S#13);E#12;EE#25[X#10,(var X#24)];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#20)
       ;X#24= A#26[(app A#27[A#14[(var X#11)]] C#28[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#25[X#10,(var X#24)]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#20)
       ;X#24= A#26[(app A#27[A#14[(\ X#9.S#13)]] C#28[(var X#20)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#25[X#10,(var X#24)]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#23,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#26[(app A#27[A#14[(var X#11)]] C#28)]),
             ((var X#20),A#26[(app A#27[A#14[(var X#11)]] C#28)]),
             ((var X#19),A#26[(app A#27[A#14[(var X#11)]] C#28[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=(var X#20);VV#21|[.1],(var X#19)|;VV#22|X#20,[.2]|},
           X#2          |->  X#19,
           X#3          |->  X#20,
           EE#16[.1,.2] |-> {X#24=A#26[(app A#27[[.2]] C#28[(var X#20)])];EE#25[[.1],(var X#24)]},
           X#1          |->  X#24,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#25[X#10,(var X#24)];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|},
           C#7          |->  A#26[(app A#27[A#14[(var X#11)]] C#28)],
           A#23         |->  A#26[(app A#27 C#28[(var X#20)])]}

and instantiated rules:

                                  (letrec {X#19=(var X#20);X#24=A#26[(app A#27[A#14[(var X#11)]] C#28[(var X#20)])];X#8=(\ X#9.S#13);E#12;EE#25[X#10,(var X#24)];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#20);X#24=A#26[(app A#27[A#14[(var X#11)]] C#28[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#25[X#10,(var X#24)];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#20);X#24=A#26[(app A#27[A#14[(var X#11)]] C#28[(var X#20)])];X#8=(\ X#9.S#13);E#12;EE#25[X#10,(var X#24)];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#20);X#24=A#26[(app A#27[A#14[(\ X#9.S#13)]] C#28[(var X#20)])];X#8=(\ X#9.S#13);E#12;EE#25[X#10,(var X#24)];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#20)
       ;X#24= A#26[(app A#27[(var X#11)] C#28[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#25[X#10,(var X#24)]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#20)
       ;X#24= A#26[(app A#27[(\ X#9.S#13)] C#28[(var X#20)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#25[X#10,(var X#24)]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#26[(app A#27[(var X#11)] C#28)]),
             ((var X#20),A#26[(app A#27[(var X#11)] C#28)]),
             ((var X#19),A#26[(app A#27[(var X#11)] C#28[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#26[(app A#27[[.]] C#28[(var X#20)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=(var X#20);VV#21|[.1],(var X#19)|;VV#22|X#20,[.2]|},
           X#2          |->  X#19,
           X#3          |->  X#20,
           EE#16[.1,.2] |-> {X#24=[.2];EE#25[[.1],(var X#24)]},
           X#1          |->  X#24,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#25[X#10,(var X#24)];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|},
           A#23         |->  [.],
           C#7          |->  A#26[(app A#27[(var X#11)] C#28)],
           A#14         |->  A#26[(app A#27 C#28[(var X#20)])]}

and instantiated rules:

                                  (letrec {X#19=(var X#20);X#24=A#26[(app A#27[(var X#11)] C#28[(var X#20)])];X#8=(\ X#9.S#13);E#12;EE#25[X#10,(var X#24)];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#20);X#24=A#26[(app A#27[(var X#11)] C#28[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#25[X#10,(var X#24)];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#20);X#24=A#26[(app A#27[(var X#11)] C#28[(var X#20)])];X#8=(\ X#9.S#13);E#12;EE#25[X#10,(var X#24)];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#20);X#24=A#26[(app A#27[(\ X#9.S#13)] C#28[(var X#20)])];X#8=(\ X#9.S#13);E#12;EE#25[X#10,(var X#24)];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#8)
       ;X#8= (\ X#9.C#21[(var X#19)])
       ;E#12
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#8)
       ;X#8= (\ X#9.C#21[(var X#8)])
       ;E#12
       ;EE#16[X#10,A#14[(\ X#9.C#21[(var X#8)])]]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),(\ X#9.C#21)),
             ((var X#8),(\ X#9.C#21)),
             ((var X#19),(\ X#9.C#21[[.]])),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=[.2];VV#20|[.1],(var X#19)|},
           X#2          |->  X#19,
           X#3          |->  X#8,
           X#1          |->  X#8,
           E#4          |->  {E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#11,(var X#19)|},
           C#7          |->  (\ X#9.C#21),
           S#13         |->  C#21[(var X#8)]}

and instantiated rules:

                                  (letrec {X#19=(var X#8);X#8=(\ X#9.C#21[(var X#8)]);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#8);X#8=(\ X#9.C#21[(var X#19)]);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#8);X#8=(\ X#9.C#21[(var X#8)]);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#8);X#8=(\ X#9.C#21[(var X#8)]);E#12;EE#16[X#10,A#14[(\ X#9.C#21[(var X#8)])]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#19)]
       ;X#19= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#21
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#8)]
       ;X#19= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#21
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#19),C#7),
             ((var X#8),C#7),
             ((var X#19),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=[.2];VV#20|[.1],(var X#19)|},
           X#2          |->  X#19,
           X#3          |->  X#8,
           E#12         |->  {X#1=C#7[(var X#8)];E#21},
           E#4          |->  {X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#20|X#11,(var X#19)|}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#8)];X#19=(var X#8);X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#19)];X#19=(var X#8);X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#8)];X#19=(var X#8);X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#1=C#7[(var X#8)];X#19=(var X#8);X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[A#24[(app A#25[(var X#11)] C#26[(var X#19)])]]
       ;X#19= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#8)])]]
       ;X#19= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#23,A#21,C#7,A#14,A#22}
   Delta2 = {}
   Delta3 = {((var X#19),A#22[A#24[(app A#25[(var X#11)] C#26)]]),
             ((var X#8),A#22[A#24[(app A#25[(var X#11)] C#26)]]),
             ((var X#19),A#22[A#24[(app A#25[(var X#11)] C#26[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#24[(app A#25[[.]] C#26[(var X#8)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=[.2];VV#20|[.1],(var X#19)|},
           X#2          |->  X#19,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {[.1]=A#22[[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;VV#20|X#11,(var X#19)|},
           A#21         |->  A#22,
           C#7          |->  A#22[A#24[(app A#25[(var X#11)] C#26)]],
           C#23         |->  A#24[(app A#25[(var X#11)] C#26)],
           A#14         |->  A#24[(app A#25 C#26[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[A#24[(app A#25[(var X#11)] C#26[(var X#8)])]];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#22[A#24[(app A#25[(var X#11)] C#26[(var X#19)])]];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[A#24[(app A#25[(var X#11)] C#26[(var X#8)])]];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#8)])]];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#19)])]
       ;X#19= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(app A#23[A#14[(\ X#9.S#13)]] C#24[(var X#8)])]
       ;X#19= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#22[(app A#23[A#14[(var X#11)]] C#24)]),
             ((var X#8),A#22[(app A#23[A#14[(var X#11)]] C#24)]),
             ((var X#19),A#22[(app A#23[A#14[(var X#11)]] C#24[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=[.2];VV#20|[.1],(var X#19)|},
           X#2          |->  X#19,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {[.1]=A#22[(app A#23[[.2]] C#24[(var X#8)])]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;VV#20|X#11,(var X#19)|},
           C#7          |->  A#22[(app A#23[A#14[(var X#11)]] C#24)],
           A#21         |->  A#22[(app A#23 C#24[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#8)])];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#19)])];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#8)])];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[(app A#23[A#14[(\ X#9.S#13)]] C#24[(var X#8)])];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(app A#23[(var X#11)] C#24[(var X#19)])]
       ;X#19= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(app A#23[(\ X#9.S#13)] C#24[(var X#8)])]
       ;X#19= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#22[(app A#23[(var X#11)] C#24)]),
             ((var X#8),A#22[(app A#23[(var X#11)] C#24)]),
             ((var X#19),A#22[(app A#23[(var X#11)] C#24[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#22[(app A#23[[.]] C#24[(var X#8)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=[.2];VV#20|[.1],(var X#19)|},
           X#2          |->  X#19,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;VV#20|X#11,(var X#19)|},
           A#21         |->  [.],
           C#7          |->  A#22[(app A#23[(var X#11)] C#24)],
           A#14         |->  A#22[(app A#23 C#24[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[(app A#23[(var X#11)] C#24[(var X#8)])];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#22[(app A#23[(var X#11)] C#24[(var X#19)])];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(app A#23[(var X#11)] C#24[(var X#8)])];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[(app A#23[(\ X#9.S#13)] C#24[(var X#8)])];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#24[(app A#25[(var X#22)] C#26[(var X#19)])]
       ;X#19= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#22,A#14[(var X#11)]]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#24[(app A#25[(var X#22)] C#26[(var X#8)])]
       ;X#19= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#22,A#14[(\ X#9.S#13)]]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#24[(app A#25[(var X#22)] C#26)]),
             ((var X#8),A#24[(app A#25[(var X#22)] C#26)]),
             ((var X#19),A#24[(app A#25[(var X#22)] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=[.2];VV#20|[.1],(var X#19)|},
           X#2          |->  X#19,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {[.1]=A#24[(app A#25[(var X#22)] C#26[(var X#8)])];EE#23[X#22,[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#20|X#11,(var X#19)|},
           C#7          |->  A#24[(app A#25[(var X#22)] C#26)],
           A#21         |->  A#24[(app A#25 C#26[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#10=A#24[(app A#25[(var X#22)] C#26[(var X#8)])];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#24[(app A#25[(var X#22)] C#26[(var X#19)])];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#24[(app A#25[(var X#22)] C#26[(var X#8)])];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#24[(app A#25[(var X#22)] C#26[(var X#8)])];X#19=(var X#8);X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(\ X#9.S#13)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#8)
       ;X#22= A#26[(app A#27[(var X#23)] C#28[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#24[X#10,(var X#22)]
       ;EE#25[X#23,A#14[(var X#11)]]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#8)
       ;X#22= A#26[(app A#27[(var X#23)] C#28[(var X#8)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#24[X#10,(var X#22)]
       ;EE#25[X#23,A#14[(\ X#9.S#13)]]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#26[(app A#27[(var X#23)] C#28)]),
             ((var X#8),A#26[(app A#27[(var X#23)] C#28)]),
             ((var X#19),A#26[(app A#27[(var X#23)] C#28[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=[.2];VV#20|[.1],(var X#19)|},
           X#2          |->  X#19,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {X#22=A#26[(app A#27[(var X#23)] C#28[(var X#8)])];EE#24[[.1],(var X#22)];EE#25[X#23,[.2]]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#20|X#11,(var X#19)|},
           C#7          |->  A#26[(app A#27[(var X#23)] C#28)],
           A#21         |->  A#26[(app A#27 C#28[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#19=(var X#8);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#8);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#8);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#8);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(\ X#9.S#13)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#8)
       ;X#22= A#24[A#26[(app A#27[(var X#11)] C#28[(var X#19)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#8)
       ;X#22= A#24[A#26[(app A#27[(\ X#9.S#13)] C#28[(var X#8)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#25,A#21,C#7,A#14,A#24}
   Delta2 = {}
   Delta3 = {((var X#19),A#24[A#26[(app A#27[(var X#11)] C#28)]]),
             ((var X#8),A#24[A#26[(app A#27[(var X#11)] C#28)]]),
             ((var X#19),A#24[A#26[(app A#27[(var X#11)] C#28[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#26[(app A#27[[.]] C#28[(var X#8)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=[.2];VV#20|[.1],(var X#19)|},
           X#2          |->  X#19,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {X#22=A#24[[.2]];EE#23[[.1],(var X#22)]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#11,(var X#19)|},
           A#21         |->  A#24,
           C#7          |->  A#24[A#26[(app A#27[(var X#11)] C#28)]],
           C#25         |->  A#26[(app A#27[(var X#11)] C#28)],
           A#14         |->  A#26[(app A#27 C#28[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#19=(var X#8);X#22=A#24[A#26[(app A#27[(var X#11)] C#28[(var X#8)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#8);X#22=A#24[A#26[(app A#27[(var X#11)] C#28[(var X#19)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#8);X#22=A#24[A#26[(app A#27[(var X#11)] C#28[(var X#8)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#8);X#22=A#24[A#26[(app A#27[(\ X#9.S#13)] C#28[(var X#8)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#8)
       ;X#22= A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#8)
       ;X#22= A#24[(app A#25[A#14[(\ X#9.S#13)]] C#26[(var X#8)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#24[(app A#25[A#14[(var X#11)]] C#26)]),
             ((var X#8),A#24[(app A#25[A#14[(var X#11)]] C#26)]),
             ((var X#19),A#24[(app A#25[A#14[(var X#11)]] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=[.2];VV#20|[.1],(var X#19)|},
           X#2          |->  X#19,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {X#22=A#24[(app A#25[[.2]] C#26[(var X#8)])];EE#23[[.1],(var X#22)]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#11,(var X#19)|},
           C#7          |->  A#24[(app A#25[A#14[(var X#11)]] C#26)],
           A#21         |->  A#24[(app A#25 C#26[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#19=(var X#8);X#22=A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#8);X#22=A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#8);X#22=A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#8);X#22=A#24[(app A#25[A#14[(\ X#9.S#13)]] C#26[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#8)
       ;X#22= A#24[(app A#25[(var X#11)] C#26[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#8)
       ;X#22= A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#8)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#24[(app A#25[(var X#11)] C#26)]),
             ((var X#8),A#24[(app A#25[(var X#11)] C#26)]),
             ((var X#19),A#24[(app A#25[(var X#11)] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#24[(app A#25[[.]] C#26[(var X#8)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=[.2];VV#20|[.1],(var X#19)|},
           X#2          |->  X#19,
           X#3          |->  X#8,
           EE#16[.1,.2] |-> {X#22=[.2];EE#23[[.1],(var X#22)]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#11,(var X#19)|},
           A#21         |->  [.],
           C#7          |->  A#24[(app A#25[(var X#11)] C#26)],
           A#14         |->  A#24[(app A#25 C#26[(var X#8)])]}

and instantiated rules:

                                  (letrec {X#19=(var X#8);X#22=A#24[(app A#25[(var X#11)] C#26[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#8);X#22=A#24[(app A#25[(var X#11)] C#26[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#8);X#22=A#24[(app A#25[(var X#11)] C#26[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#8);X#22=A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#8)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#8= (\ X#9.C#21[(var X#10)])
       ;E#12
       ;EE#20[X#3,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#8= (\ X#9.C#21[(var X#3)])
       ;E#12
       ;EE#20[X#3,A#14[(\ X#9.C#21[(var X#3)])]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#10),(\ X#9.C#21)),
             ((var X#3),(\ X#9.C#21)),
             ((var X#10),(\ X#9.C#21[[.]])),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=(var X#3);EE#20[X#3,[.2]]},
           X#2          |->  X#10,
           X#1          |->  X#8,
           E#4          |->  {E#12;EE#20[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           C#7          |->  (\ X#9.C#21),
           S#13         |->  C#21[(var X#3)],
           A#18         |->  [.],
           X#19         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#8=(\ X#9.C#21[(var X#3)]);E#12;EE#20[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#8=(\ X#9.C#21[(var X#10)]);E#12;EE#20[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#8=(\ X#9.C#21[(var X#3)]);E#12;EE#20[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=(var X#3);X#8=(\ X#9.C#21[(var X#3)]);E#12;EE#20[X#3,A#14[(\ X#9.C#21[(var X#3)])]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#10)]
       ;X#10= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#21
       ;EE#20[X#3,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#10= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#21
       ;EE#20[X#3,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#10),C#7),
             ((var X#3),C#7),
             ((var X#10),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=(var X#3);EE#20[X#3,[.2]]},
           X#2          |->  X#10,
           E#12         |->  {X#1=C#7[(var X#3)];E#21},
           E#4          |->  {X#8=(\ X#9.S#13);E#21;EE#20[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           A#18         |->  [.],
           X#19         |->  X#3}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#10=(var X#3);X#8=(\ X#9.S#13);E#21;EE#20[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#10)];X#10=(var X#3);X#8=(\ X#9.S#13);E#21;EE#20[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#10=(var X#3);X#8=(\ X#9.S#13);E#21;EE#20[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#1=C#7[(var X#3)];X#10=(var X#3);X#8=(\ X#9.S#13);E#21;EE#20[X#3,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#3= A#22[A#24[(app A#25[(var X#11)] C#26[(var X#10)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#3= A#22[A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#3)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#23,A#21,C#7,A#14,A#22}
   Delta2 = {}
   Delta3 = {((var X#10),A#22[A#24[(app A#25[(var X#11)] C#26)]]),
             ((var X#3),A#22[A#24[(app A#25[(var X#11)] C#26)]]),
             ((var X#10),A#22[A#24[(app A#25[(var X#11)] C#26[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#24[(app A#25[[.]] C#26[(var X#3)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#3=A#22[[.2]];[.1]=(var X#3)},
           X#2          |->  X#10,
           EE#20[.1,.2] |-> {[.1]=A#22[[.2]]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           A#21         |->  A#22,
           C#7          |->  A#22[A#24[(app A#25[(var X#11)] C#26)]],
           A#18         |->  [.],
           X#19         |->  X#3,
           C#23         |->  A#24[(app A#25[(var X#11)] C#26)],
           A#14         |->  A#24[(app A#25 C#26[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#3=A#22[A#24[(app A#25[(var X#11)] C#26[(var X#3)])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#3=A#22[A#24[(app A#25[(var X#11)] C#26[(var X#10)])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#3=A#22[A#24[(app A#25[(var X#11)] C#26[(var X#3)])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=(var X#3);X#3=A#22[A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#3)])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#3= A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#10)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#3= A#22[(app A#23[A#14[(\ X#9.S#13)]] C#24[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#10),A#22[(app A#23[A#14[(var X#11)]] C#24)]),
             ((var X#3),A#22[(app A#23[A#14[(var X#11)]] C#24)]),
             ((var X#10),A#22[(app A#23[A#14[(var X#11)]] C#24[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#3=A#22[(app A#23[[.2]] C#24[(var X#3)])];[.1]=(var X#3)},
           X#2          |->  X#10,
           EE#20[.1,.2] |-> {[.1]=A#22[(app A#23[[.2]] C#24[(var X#3)])]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           C#7          |->  A#22[(app A#23[A#14[(var X#11)]] C#24)],
           A#21         |->  A#22[(app A#23 C#24[(var X#3)])],
           A#18         |->  [.],
           X#19         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#3=A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#3)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#3=A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#10)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#3=A#22[(app A#23[A#14[(var X#11)]] C#24[(var X#3)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=(var X#3);X#3=A#22[(app A#23[A#14[(\ X#9.S#13)]] C#24[(var X#3)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#3= A#22[(app A#23[(var X#11)] C#24[(var X#10)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#3= A#22[(app A#23[(\ X#9.S#13)] C#24[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#10),A#22[(app A#23[(var X#11)] C#24)]),
             ((var X#3),A#22[(app A#23[(var X#11)] C#24)]),
             ((var X#10),A#22[(app A#23[(var X#11)] C#24[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#22[(app A#23[[.]] C#24[(var X#3)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#3=[.2];[.1]=(var X#3)},
           X#2          |->  X#10,
           EE#20[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           A#21         |->  [.],
           C#7          |->  A#22[(app A#23[(var X#11)] C#24)],
           A#14         |->  A#22[(app A#23 C#24[(var X#3)])],
           A#18         |->  [.],
           X#19         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#3=A#22[(app A#23[(var X#11)] C#24[(var X#3)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#3=A#22[(app A#23[(var X#11)] C#24[(var X#10)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#3=A#22[(app A#23[(var X#11)] C#24[(var X#3)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=(var X#3);X#3=A#22[(app A#23[(\ X#9.S#13)] C#24[(var X#3)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#3= A#24[(app A#25[(var X#22)] C#26[(var X#10)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#22,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#3= A#24[(app A#25[(var X#22)] C#26[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#22,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#10),A#24[(app A#25[(var X#22)] C#26)]),
             ((var X#3),A#24[(app A#25[(var X#22)] C#26)]),
             ((var X#10),A#24[(app A#25[(var X#22)] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#3=A#24[(app A#25[(var X#22)] C#26[(var X#3)])];[.1]=(var X#3);EE#23[X#22,[.2]]},
           X#2          |->  X#10,
           EE#20[.1,.2] |-> {[.1]=A#24[(app A#25[(var X#22)] C#26[(var X#3)])];EE#23[X#22,[.2]]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           C#7          |->  A#24[(app A#25[(var X#22)] C#26)],
           A#21         |->  A#24[(app A#25 C#26[(var X#3)])],
           A#18         |->  [.],
           X#19         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#3=A#24[(app A#25[(var X#22)] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#3=A#24[(app A#25[(var X#22)] C#26[(var X#10)])];X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#3=A#24[(app A#25[(var X#22)] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=(var X#3);X#3=A#24[(app A#25[(var X#22)] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#22= A#26[(app A#27[(var X#23)] C#28[(var X#10)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#24[X#3,(var X#22)]
       ;EE#25[X#23,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#22= A#26[(app A#27[(var X#23)] C#28[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#24[X#3,(var X#22)]
       ;EE#25[X#23,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#10),A#26[(app A#27[(var X#23)] C#28)]),
             ((var X#3),A#26[(app A#27[(var X#23)] C#28)]),
             ((var X#10),A#26[(app A#27[(var X#23)] C#28[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#22=A#26[(app A#27[(var X#23)] C#28[(var X#3)])];[.1]=(var X#3);EE#24[X#3,(var X#22)];EE#25[X#23,[.2]]},
           X#2          |->  X#10,
           EE#20[.1,.2] |-> {X#22=A#26[(app A#27[(var X#23)] C#28[(var X#3)])];EE#24[[.1],(var X#22)];EE#25[X#23,[.2]]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#24[X#3,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           C#7          |->  A#26[(app A#27[(var X#23)] C#28)],
           A#21         |->  A#26[(app A#27 C#28[(var X#3)])],
           A#18         |->  [.],
           X#19         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#24[X#3,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#10)])];X#8=(\ X#9.S#13);E#12;EE#24[X#3,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#24[X#3,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=(var X#3);X#22=A#26[(app A#27[(var X#23)] C#28[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#24[X#3,(var X#22)];EE#25[X#23,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#22= A#24[A#26[(app A#27[(var X#11)] C#28[(var X#10)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#3,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#22= A#24[A#26[(app A#27[(\ X#9.S#13)] C#28[(var X#3)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#3,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#25,A#21,C#7,A#14,A#24}
   Delta2 = {}
   Delta3 = {((var X#10),A#24[A#26[(app A#27[(var X#11)] C#28)]]),
             ((var X#3),A#24[A#26[(app A#27[(var X#11)] C#28)]]),
             ((var X#10),A#24[A#26[(app A#27[(var X#11)] C#28[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#26[(app A#27[[.]] C#28[(var X#3)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#22=A#24[[.2]];[.1]=(var X#3);EE#23[X#3,(var X#22)]},
           X#2          |->  X#10,
           EE#20[.1,.2] |-> {X#22=A#24[[.2]];EE#23[[.1],(var X#22)]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#3,(var X#22)];VV#17|X#11,(var X#8)|},
           A#21         |->  A#24,
           C#7          |->  A#24[A#26[(app A#27[(var X#11)] C#28)]],
           A#18         |->  [.],
           X#19         |->  X#3,
           C#25         |->  A#26[(app A#27[(var X#11)] C#28)],
           A#14         |->  A#26[(app A#27 C#28[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#22=A#24[A#26[(app A#27[(var X#11)] C#28[(var X#3)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#3,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#22=A#24[A#26[(app A#27[(var X#11)] C#28[(var X#10)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#3,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#22=A#24[A#26[(app A#27[(var X#11)] C#28[(var X#3)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#3,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=(var X#3);X#22=A#24[A#26[(app A#27[(\ X#9.S#13)] C#28[(var X#3)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#3,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#22= A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#10)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#3,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#22= A#24[(app A#25[A#14[(\ X#9.S#13)]] C#26[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#3,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#10),A#24[(app A#25[A#14[(var X#11)]] C#26)]),
             ((var X#3),A#24[(app A#25[A#14[(var X#11)]] C#26)]),
             ((var X#10),A#24[(app A#25[A#14[(var X#11)]] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#22=A#24[(app A#25[[.2]] C#26[(var X#3)])];[.1]=(var X#3);EE#23[X#3,(var X#22)]},
           X#2          |->  X#10,
           EE#20[.1,.2] |-> {X#22=A#24[(app A#25[[.2]] C#26[(var X#3)])];EE#23[[.1],(var X#22)]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#3,(var X#22)];VV#17|X#11,(var X#8)|},
           C#7          |->  A#24[(app A#25[A#14[(var X#11)]] C#26)],
           A#21         |->  A#24[(app A#25 C#26[(var X#3)])],
           A#18         |->  [.],
           X#19         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#22=A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#23[X#3,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#22=A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#10)])];X#8=(\ X#9.S#13);E#12;EE#23[X#3,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#22=A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#23[X#3,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=(var X#3);X#22=A#24[(app A#25[A#14[(\ X#9.S#13)]] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#23[X#3,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#3)
       ;X#22= A#24[(app A#25[(var X#11)] C#26[(var X#10)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#3,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#3)
       ;X#22= A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#3,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#10),A#24[(app A#25[(var X#11)] C#26)]),
             ((var X#3),A#24[(app A#25[(var X#11)] C#26)]),
             ((var X#10),A#24[(app A#25[(var X#11)] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#24[(app A#25[[.]] C#26[(var X#3)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#22=[.2];[.1]=(var X#3);EE#23[X#3,(var X#22)]},
           X#2          |->  X#10,
           EE#20[.1,.2] |-> {X#22=[.2];EE#23[[.1],(var X#22)]},
           X#1          |->  X#22,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#3,(var X#22)];VV#17|X#11,(var X#8)|},
           A#21         |->  [.],
           C#7          |->  A#24[(app A#25[(var X#11)] C#26)],
           A#14         |->  A#24[(app A#25 C#26[(var X#3)])],
           A#18         |->  [.],
           X#19         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=(var X#3);X#22=A#24[(app A#25[(var X#11)] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#23[X#3,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=(var X#3);X#22=A#24[(app A#25[(var X#11)] C#26[(var X#10)])];X#8=(\ X#9.S#13);E#12;EE#23[X#3,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#3);X#22=A#24[(app A#25[(var X#11)] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#23[X#3,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=(var X#3);X#22=A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#23[X#3,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#3)
       ;X#8= (\ X#9.C#23[(var X#19)])
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#22[X#3,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#3)
       ;X#8= (\ X#9.C#23[(var X#3)])
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#22[X#3,A#14[(\ X#9.C#23[(var X#3)])]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),(\ X#9.C#23)),
             ((var X#3),(\ X#9.C#23)),
             ((var X#19),(\ X#9.C#23[[.]])),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=(var X#3);EE#21[[.1],(var X#19)];EE#22[X#3,[.2]]},
           X#2          |->  X#19,
           X#1          |->  X#8,
           E#4          |->  {E#12;EE#21[X#10,(var X#19)];EE#22[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           C#7          |->  (\ X#9.C#23),
           S#13         |->  C#23[(var X#3)],
           A#18         |->  [.],
           X#20         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=(var X#3);X#8=(\ X#9.C#23[(var X#3)]);E#12;EE#21[X#10,(var X#19)];EE#22[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#3);X#8=(\ X#9.C#23[(var X#19)]);E#12;EE#21[X#10,(var X#19)];EE#22[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#3);X#8=(\ X#9.C#23[(var X#3)]);E#12;EE#21[X#10,(var X#19)];EE#22[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#3);X#8=(\ X#9.C#23[(var X#3)]);E#12;EE#21[X#10,(var X#19)];EE#22[X#3,A#14[(\ X#9.C#23[(var X#3)])]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#19)]
       ;X#19= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#23
       ;EE#21[X#10,(var X#19)]
       ;EE#22[X#3,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#19= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#23
       ;EE#21[X#10,(var X#19)]
       ;EE#22[X#3,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#19),C#7),
             ((var X#3),C#7),
             ((var X#19),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=(var X#3);EE#21[[.1],(var X#19)];EE#22[X#3,[.2]]},
           X#2          |->  X#19,
           E#12         |->  {X#1=C#7[(var X#3)];E#23},
           E#4          |->  {X#8=(\ X#9.S#13);E#23;EE#21[X#10,(var X#19)];EE#22[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           A#18         |->  [.],
           X#20         |->  X#3}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#19=(var X#3);X#8=(\ X#9.S#13);E#23;EE#21[X#10,(var X#19)];EE#22[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#19)];X#19=(var X#3);X#8=(\ X#9.S#13);E#23;EE#21[X#10,(var X#19)];EE#22[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#19=(var X#3);X#8=(\ X#9.S#13);E#23;EE#21[X#10,(var X#19)];EE#22[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#1=C#7[(var X#3)];X#19=(var X#3);X#8=(\ X#9.S#13);E#23;EE#21[X#10,(var X#19)];EE#22[X#3,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#24[(app A#25[(var X#19)] C#26[(var X#19)])]
       ;X#19= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#22[X#3,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#24[(app A#25[(var X#19)] C#26[(var X#3)])]
       ;X#19= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#22[X#3,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#23,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#24[(app A#25[(var X#19)] C#26)]),
             ((var X#3),A#24[(app A#25[(var X#19)] C#26)]),
             ((var X#19),A#24[(app A#25[(var X#19)] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=(var X#3);[.1]=A#24[(app A#25[(var X#19)] C#26[(var X#3)])];EE#22[X#3,[.2]]},
           X#2          |->  X#19,
           EE#21[.1,.2] |-> {[.1]=A#24[(app A#25[[.2]] C#26[(var X#3)])]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           C#7          |->  A#24[(app A#25[(var X#19)] C#26)],
           A#23         |->  A#24[(app A#25 C#26[(var X#3)])],
           A#18         |->  [.],
           X#20         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=A#24[(app A#25[(var X#19)] C#26[(var X#3)])];X#19=(var X#3);X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#24[(app A#25[(var X#19)] C#26[(var X#19)])];X#19=(var X#3);X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#24[(app A#25[(var X#19)] C#26[(var X#3)])];X#19=(var X#3);X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#24[(app A#25[(var X#19)] C#26[(var X#3)])];X#19=(var X#3);X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#26[(app A#27[(var X#24)] C#28[(var X#19)])]
       ;X#19= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#22[X#3,A#14[(var X#11)]]
       ;EE#25[X#24,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#26[(app A#27[(var X#24)] C#28[(var X#3)])]
       ;X#19= (var X#3)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#22[X#3,A#14[(\ X#9.S#13)]]
       ;EE#25[X#24,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#23,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#26[(app A#27[(var X#24)] C#28)]),
             ((var X#3),A#26[(app A#27[(var X#24)] C#28)]),
             ((var X#19),A#26[(app A#27[(var X#24)] C#28[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=(var X#3);[.1]=A#26[(app A#27[(var X#24)] C#28[(var X#3)])];EE#22[X#3,[.2]];EE#25[X#24,(var X#19)]},
           X#2          |->  X#19,
           EE#21[.1,.2] |-> {[.1]=A#26[(app A#27[(var X#24)] C#28[(var X#3)])];EE#25[X#24,[.2]]},
           X#1          |->  X#10,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];EE#25[X#24,(var X#19)];VV#17|X#11,(var X#8)|},
           C#7          |->  A#26[(app A#27[(var X#24)] C#28)],
           A#23         |->  A#26[(app A#27 C#28[(var X#3)])],
           A#18         |->  [.],
           X#20         |->  X#3}

and instantiated rules:

                                  (letrec {X#10=A#26[(app A#27[(var X#24)] C#28[(var X#3)])];X#19=(var X#3);X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];EE#25[X#24,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#10=A#26[(app A#27[(var X#24)] C#28[(var X#19)])];X#19=(var X#3);X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];EE#25[X#24,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#26[(app A#27[(var X#24)] C#28[(var X#3)])];X#19=(var X#3);X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];EE#25[X#24,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#26[(app A#27[(var X#24)] C#28[(var X#3)])];X#19=(var X#3);X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(\ X#9.S#13)]];EE#25[X#24,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#3)
       ;X#24= A#28[(app A#29[(var X#25)] C#30[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#22[X#3,A#14[(var X#11)]]
       ;EE#26[X#10,(var X#24)]
       ;EE#27[X#25,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#3)
       ;X#24= A#28[(app A#29[(var X#25)] C#30[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#22[X#3,A#14[(\ X#9.S#13)]]
       ;EE#26[X#10,(var X#24)]
       ;EE#27[X#25,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#23,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#28[(app A#29[(var X#25)] C#30)]),
             ((var X#3),A#28[(app A#29[(var X#25)] C#30)]),
             ((var X#19),A#28[(app A#29[(var X#25)] C#30[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=(var X#3);X#24=A#28[(app A#29[(var X#25)] C#30[(var X#3)])];EE#22[X#3,[.2]];EE#26[[.1],(var X#24)];EE#27[X#25,(var X#19)]},
           X#2          |->  X#19,
           EE#21[.1,.2] |-> {X#24=A#28[(app A#29[(var X#25)] C#30[(var X#3)])];EE#26[[.1],(var X#24)];EE#27[X#25,[.2]]},
           X#1          |->  X#24,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];EE#26[X#10,(var X#24)];EE#27[X#25,(var X#19)];VV#17|X#11,(var X#8)|},
           C#7          |->  A#28[(app A#29[(var X#25)] C#30)],
           A#23         |->  A#28[(app A#29 C#30[(var X#3)])],
           A#18         |->  [.],
           X#20         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=(var X#3);X#24=A#28[(app A#29[(var X#25)] C#30[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];EE#26[X#10,(var X#24)];EE#27[X#25,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#3);X#24=A#28[(app A#29[(var X#25)] C#30[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];EE#26[X#10,(var X#24)];EE#27[X#25,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#3);X#24=A#28[(app A#29[(var X#25)] C#30[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];EE#26[X#10,(var X#24)];EE#27[X#25,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#3);X#24=A#28[(app A#29[(var X#25)] C#30[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(\ X#9.S#13)]];EE#26[X#10,(var X#24)];EE#27[X#25,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#3)
       ;X#24= A#26[(app A#27[(var X#19)] C#28[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#22[X#3,A#14[(var X#11)]]
       ;EE#25[X#10,(var X#24)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#3)
       ;X#24= A#26[(app A#27[(var X#19)] C#28[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#22[X#3,A#14[(\ X#9.S#13)]]
       ;EE#25[X#10,(var X#24)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#23,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#26[(app A#27[(var X#19)] C#28)]),
             ((var X#3),A#26[(app A#27[(var X#19)] C#28)]),
             ((var X#19),A#26[(app A#27[(var X#19)] C#28[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=(var X#3);X#24=A#26[(app A#27[(var X#19)] C#28[(var X#3)])];EE#22[X#3,[.2]];EE#25[[.1],(var X#24)]},
           X#2          |->  X#19,
           EE#21[.1,.2] |-> {X#24=A#26[(app A#27[[.2]] C#28[(var X#3)])];EE#25[[.1],(var X#24)]},
           X#1          |->  X#24,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];EE#25[X#10,(var X#24)];VV#17|X#11,(var X#8)|},
           C#7          |->  A#26[(app A#27[(var X#19)] C#28)],
           A#23         |->  A#26[(app A#27 C#28[(var X#3)])],
           A#18         |->  [.],
           X#20         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=(var X#3);X#24=A#26[(app A#27[(var X#19)] C#28[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];EE#25[X#10,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#3);X#24=A#26[(app A#27[(var X#19)] C#28[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];EE#25[X#10,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#3);X#24=A#26[(app A#27[(var X#19)] C#28[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(var X#11)]];EE#25[X#10,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#3);X#24=A#26[(app A#27[(var X#19)] C#28[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#22[X#3,A#14[(\ X#9.S#13)]];EE#25[X#10,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#3)
       ;X#3= A#24[A#26[(app A#27[(var X#11)] C#28[(var X#19)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#3)
       ;X#3= A#24[A#26[(app A#27[(\ X#9.S#13)] C#28[(var X#3)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#25,A#23,C#7,A#14,A#24}
   Delta2 = {}
   Delta3 = {((var X#19),A#24[A#26[(app A#27[(var X#11)] C#28)]]),
             ((var X#3),A#24[A#26[(app A#27[(var X#11)] C#28)]]),
             ((var X#19),A#24[A#26[(app A#27[(var X#11)] C#28[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#26[(app A#27[[.]] C#28[(var X#3)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=(var X#3);X#3=A#24[[.2]];EE#21[[.1],(var X#19)]},
           X#2          |->  X#19,
           EE#22[.1,.2] |-> {[.1]=A#24[[.2]]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];VV#17|X#11,(var X#8)|},
           A#23         |->  A#24,
           C#7          |->  A#24[A#26[(app A#27[(var X#11)] C#28)]],
           A#18         |->  [.],
           X#20         |->  X#3,
           C#25         |->  A#26[(app A#27[(var X#11)] C#28)],
           A#14         |->  A#26[(app A#27 C#28[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#19=(var X#3);X#3=A#24[A#26[(app A#27[(var X#11)] C#28[(var X#3)])]];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#3);X#3=A#24[A#26[(app A#27[(var X#11)] C#28[(var X#19)])]];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#3);X#3=A#24[A#26[(app A#27[(var X#11)] C#28[(var X#3)])]];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#3);X#3=A#24[A#26[(app A#27[(\ X#9.S#13)] C#28[(var X#3)])]];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#3)
       ;X#3= A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#3)
       ;X#3= A#24[(app A#25[A#14[(\ X#9.S#13)]] C#26[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#23,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#24[(app A#25[A#14[(var X#11)]] C#26)]),
             ((var X#3),A#24[(app A#25[A#14[(var X#11)]] C#26)]),
             ((var X#19),A#24[(app A#25[A#14[(var X#11)]] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=(var X#3);X#3=A#24[(app A#25[[.2]] C#26[(var X#3)])];EE#21[[.1],(var X#19)]},
           X#2          |->  X#19,
           EE#22[.1,.2] |-> {[.1]=A#24[(app A#25[[.2]] C#26[(var X#3)])]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];VV#17|X#11,(var X#8)|},
           C#7          |->  A#24[(app A#25[A#14[(var X#11)]] C#26)],
           A#23         |->  A#24[(app A#25 C#26[(var X#3)])],
           A#18         |->  [.],
           X#20         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=(var X#3);X#3=A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#3);X#3=A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#3);X#3=A#24[(app A#25[A#14[(var X#11)]] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#3);X#3=A#24[(app A#25[A#14[(\ X#9.S#13)]] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#3)
       ;X#3= A#24[(app A#25[(var X#11)] C#26[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#3)
       ;X#3= A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#24[(app A#25[(var X#11)] C#26)]),
             ((var X#3),A#24[(app A#25[(var X#11)] C#26)]),
             ((var X#19),A#24[(app A#25[(var X#11)] C#26[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#24[(app A#25[[.]] C#26[(var X#3)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=(var X#3);X#3=[.2];EE#21[[.1],(var X#19)]},
           X#2          |->  X#19,
           EE#22[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];VV#17|X#11,(var X#8)|},
           A#23         |->  [.],
           C#7          |->  A#24[(app A#25[(var X#11)] C#26)],
           A#14         |->  A#24[(app A#25 C#26[(var X#3)])],
           A#18         |->  [.],
           X#20         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=(var X#3);X#3=A#24[(app A#25[(var X#11)] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#3);X#3=A#24[(app A#25[(var X#11)] C#26[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#3);X#3=A#24[(app A#25[(var X#11)] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#3);X#3=A#24[(app A#25[(\ X#9.S#13)] C#26[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#3)
       ;X#3= A#26[(app A#27[(var X#24)] C#28[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#25[X#24,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#3)
       ;X#3= A#26[(app A#27[(var X#24)] C#28[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#25[X#24,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#23,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#26[(app A#27[(var X#24)] C#28)]),
             ((var X#3),A#26[(app A#27[(var X#24)] C#28)]),
             ((var X#19),A#26[(app A#27[(var X#24)] C#28[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=(var X#3);X#3=A#26[(app A#27[(var X#24)] C#28[(var X#3)])];EE#21[[.1],(var X#19)];EE#25[X#24,[.2]]},
           X#2          |->  X#19,
           EE#22[.1,.2] |-> {[.1]=A#26[(app A#27[(var X#24)] C#28[(var X#3)])];EE#25[X#24,[.2]]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#24,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           C#7          |->  A#26[(app A#27[(var X#24)] C#28)],
           A#23         |->  A#26[(app A#27 C#28[(var X#3)])],
           A#18         |->  [.],
           X#20         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=(var X#3);X#3=A#26[(app A#27[(var X#24)] C#28[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#24,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#3);X#3=A#26[(app A#27[(var X#24)] C#28[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#24,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#3);X#3=A#26[(app A#27[(var X#24)] C#28[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#24,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#3);X#3=A#26[(app A#27[(var X#24)] C#28[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#24,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#3)
       ;X#24= A#28[(app A#29[(var X#25)] C#30[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#26[X#3,(var X#24)]
       ;EE#27[X#25,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#3)
       ;X#24= A#28[(app A#29[(var X#25)] C#30[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#26[X#3,(var X#24)]
       ;EE#27[X#25,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#23,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#28[(app A#29[(var X#25)] C#30)]),
             ((var X#3),A#28[(app A#29[(var X#25)] C#30)]),
             ((var X#19),A#28[(app A#29[(var X#25)] C#30[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=(var X#3);X#24=A#28[(app A#29[(var X#25)] C#30[(var X#3)])];EE#21[[.1],(var X#19)];EE#26[X#3,(var X#24)];EE#27[X#25,[.2]]},
           X#2          |->  X#19,
           EE#22[.1,.2] |-> {X#24=A#28[(app A#29[(var X#25)] C#30[(var X#3)])];EE#26[[.1],(var X#24)];EE#27[X#25,[.2]]},
           X#1          |->  X#24,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#26[X#3,(var X#24)];EE#27[X#25,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           C#7          |->  A#28[(app A#29[(var X#25)] C#30)],
           A#23         |->  A#28[(app A#29 C#30[(var X#3)])],
           A#18         |->  [.],
           X#20         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=(var X#3);X#24=A#28[(app A#29[(var X#25)] C#30[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#26[X#3,(var X#24)];EE#27[X#25,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#3);X#24=A#28[(app A#29[(var X#25)] C#30[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#26[X#3,(var X#24)];EE#27[X#25,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#3);X#24=A#28[(app A#29[(var X#25)] C#30[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#26[X#3,(var X#24)];EE#27[X#25,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#3);X#24=A#28[(app A#29[(var X#25)] C#30[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#26[X#3,(var X#24)];EE#27[X#25,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#3)
       ;X#24= A#26[A#28[(app A#29[(var X#11)] C#30[(var X#19)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#25[X#3,(var X#24)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#3)
       ;X#24= A#26[A#28[(app A#29[(\ X#9.S#13)] C#30[(var X#3)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#25[X#3,(var X#24)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#27,A#23,C#7,A#14,A#26}
   Delta2 = {}
   Delta3 = {((var X#19),A#26[A#28[(app A#29[(var X#11)] C#30)]]),
             ((var X#3),A#26[A#28[(app A#29[(var X#11)] C#30)]]),
             ((var X#19),A#26[A#28[(app A#29[(var X#11)] C#30[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#28[(app A#29[[.]] C#30[(var X#3)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=(var X#3);X#24=A#26[[.2]];EE#21[[.1],(var X#19)];EE#25[X#3,(var X#24)]},
           X#2          |->  X#19,
           EE#22[.1,.2] |-> {X#24=A#26[[.2]];EE#25[[.1],(var X#24)]},
           X#1          |->  X#24,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#3,(var X#24)];VV#17|X#11,(var X#8)|},
           A#23         |->  A#26,
           C#7          |->  A#26[A#28[(app A#29[(var X#11)] C#30)]],
           A#18         |->  [.],
           X#20         |->  X#3,
           C#27         |->  A#28[(app A#29[(var X#11)] C#30)],
           A#14         |->  A#28[(app A#29 C#30[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#19=(var X#3);X#24=A#26[A#28[(app A#29[(var X#11)] C#30[(var X#3)])]];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#3,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#3);X#24=A#26[A#28[(app A#29[(var X#11)] C#30[(var X#19)])]];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#3,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#3);X#24=A#26[A#28[(app A#29[(var X#11)] C#30[(var X#3)])]];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#3,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#3);X#24=A#26[A#28[(app A#29[(\ X#9.S#13)] C#30[(var X#3)])]];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#3,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#3)
       ;X#24= A#26[(app A#27[A#14[(var X#11)]] C#28[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#25[X#3,(var X#24)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#3)
       ;X#24= A#26[(app A#27[A#14[(\ X#9.S#13)]] C#28[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#25[X#3,(var X#24)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#23,C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#26[(app A#27[A#14[(var X#11)]] C#28)]),
             ((var X#3),A#26[(app A#27[A#14[(var X#11)]] C#28)]),
             ((var X#19),A#26[(app A#27[A#14[(var X#11)]] C#28[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=(var X#3);X#24=A#26[(app A#27[[.2]] C#28[(var X#3)])];EE#21[[.1],(var X#19)];EE#25[X#3,(var X#24)]},
           X#2          |->  X#19,
           EE#22[.1,.2] |-> {X#24=A#26[(app A#27[[.2]] C#28[(var X#3)])];EE#25[[.1],(var X#24)]},
           X#1          |->  X#24,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#3,(var X#24)];VV#17|X#11,(var X#8)|},
           C#7          |->  A#26[(app A#27[A#14[(var X#11)]] C#28)],
           A#23         |->  A#26[(app A#27 C#28[(var X#3)])],
           A#18         |->  [.],
           X#20         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=(var X#3);X#24=A#26[(app A#27[A#14[(var X#11)]] C#28[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#3,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#3);X#24=A#26[(app A#27[A#14[(var X#11)]] C#28[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#3,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#3);X#24=A#26[(app A#27[A#14[(var X#11)]] C#28[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#3,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#3);X#24=A#26[(app A#27[A#14[(\ X#9.S#13)]] C#28[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#3,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#3)
       ;X#24= A#26[(app A#27[(var X#11)] C#28[(var X#19)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#25[X#3,(var X#24)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#3)
       ;X#24= A#26[(app A#27[(\ X#9.S#13)] C#28[(var X#3)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#25[X#3,(var X#24)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {C#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#19),A#26[(app A#27[(var X#11)] C#28)]),
             ((var X#3),A#26[(app A#27[(var X#11)] C#28)]),
             ((var X#19),A#26[(app A#27[(var X#11)] C#28[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#26[(app A#27[[.]] C#28[(var X#3)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#2),C#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=(var X#3);X#24=[.2];EE#21[[.1],(var X#19)];EE#25[X#3,(var X#24)]},
           X#2          |->  X#19,
           EE#22[.1,.2] |-> {X#24=[.2];EE#25[[.1],(var X#24)]},
           X#1          |->  X#24,
           E#4          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#3,(var X#24)];VV#17|X#11,(var X#8)|},
           A#23         |->  [.],
           C#7          |->  A#26[(app A#27[(var X#11)] C#28)],
           A#14         |->  A#26[(app A#27 C#28[(var X#3)])],
           A#18         |->  [.],
           X#20         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=(var X#3);X#24=A#26[(app A#27[(var X#11)] C#28[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#3,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -cpx-e1->                     (letrec {X#19=(var X#3);X#24=A#26[(app A#27[(var X#11)] C#28[(var X#19)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#3,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#3);X#24=A#26[(app A#27[(var X#11)] C#28[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#3,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#3);X#24=A#26[(app A#27[(\ X#9.S#13)] C#28[(var X#3)])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#25[X#3,(var X#24)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        (letrec {E#9} in T#12[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])
     )
    ,
     (letrec
        E#8
       ;E#9
     in
        T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
     )
  )

where

   Delta1 = {T#11,T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             [{E#8},(letrec {E#9} in [.])],
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in (letrec {E#9} in S#10))
    -SR,llet-in1->                (letrec {E#8;E#9} in S#10)
    and constraints: E#8/= {}, E#9/= {}, ({E#8},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in (letrec {E#9} in S#10))}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),[{E#8},(letrec {E#9} in [.])],((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in (letrec {E#9} in T#12)),
           T#11  |->  (letrec {E#9} in T#12),
           S#10  |->  T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {E#8} in (letrec {E#9} in T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]))
    -cpx-e1->                     (letrec {E#8} in (letrec {E#9} in T#12[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]))
    ................................................................................
                                  (letrec {E#8} in (letrec {E#9} in T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]))
    -SR,llet-in1->                (letrec {E#8;E#9} in T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        (letrec
           X#13= T#12[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
          ;E#15
        in
           S#10
        )
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;E#15
       ;E#8
     in
        S#10
     )
  )

where

   Delta1 = {T#11,T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             [{E#8},(letrec {X#13=T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#15} in [.])],
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in (letrec {E#9} in S#10))
    -SR,llet-in1->                (letrec {E#8;E#9} in S#10)
    and constraints: E#8/= {}, E#9/= {}, ({E#8},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in (letrec {E#9} in S#10))}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),[{E#8},(letrec {E#9} in [.])],((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in (letrec {X#13=T#12;E#15} in S#10)),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#10),
           E#9   |->  {X#13=T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {E#8} in (letrec {X#13=T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#15} in S#10))
    -cpx-e1->                     (letrec {E#8} in (letrec {X#13=T#12[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#15} in S#10))
    ................................................................................
                                  (letrec {E#8} in (letrec {X#13=T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#15} in S#10))
    -SR,llet-in1->                (letrec {X#13=T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#15;E#8} in S#10)
    

================================================================================
Critical Pair:

  (
     (letrec {E#8} in (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#13} in S#10))
    ,
     (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#13;E#8} in S#10)
  )

where

   Delta1 = {T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             [{E#8},(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#13} in [.])],
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in (letrec {E#9} in S#10))
    -SR,llet-in1->                (letrec {E#8;E#9} in S#10)
    and constraints: E#8/= {}, E#9/= {}, ({E#8},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in (letrec {E#9} in S#10))}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),[{E#8},(letrec {E#9} in [.])],((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in [.]),
           T#11  |->  [.],
           S#5   |->  S#10,
           E#9   |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#13},
           E#12  |->  {X#1=C#7[(var X#3)];E#13},
           E#4   |->  {E#13}}

and instantiated rules:

                                  (letrec {E#8} in (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#13} in S#10))
    -cpx-e1->                     (letrec {E#8} in (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#13} in S#10))
    ................................................................................
                                  (letrec {E#8} in (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#13} in S#10))
    -SR,llet-in1->                (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#13;E#8} in S#10)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#12= T#11[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
       ;E#14
     in
        (letrec {E#9} in S#10)
     )
    ,
     (letrec
        X#12= T#11[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;E#14
       ;E#9
     in
        S#10
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             [{X#12=T#11[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#14},(letrec {E#9} in [.])],
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in (letrec {E#9} in S#10))
    -SR,llet-in1->                (letrec {E#8;E#9} in S#10)
    and constraints: E#8/= {}, E#9/= {}, ({E#8},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in (letrec {E#9} in S#10))}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),[{E#8},(letrec {E#9} in [.])],((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#12=T#11;E#14} in (letrec {E#9} in S#10)),
           E#8   |->  {X#12=T#11[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#14},
           E#13  |->  {E#14}}

and instantiated rules:

                                  (letrec {X#12=T#11[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#14} in (letrec {E#9} in S#10))
    -cpx-e1->                     (letrec {X#12=T#11[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#14} in (letrec {E#9} in S#10))
    ................................................................................
                                  (letrec {X#12=T#11[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#14} in (letrec {E#9} in S#10))
    -SR,llet-in1->                (letrec {X#12=T#11[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#14;E#9} in S#10)
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#12} in (letrec {E#9} in S#10))
    ,
     (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#12;E#9} in S#10)
  )

where

   Delta1 = {}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             [{X#1=C#7[(var X#3)];X#2=(var X#3);E#12},(letrec {E#9} in [.])],
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in (letrec {E#9} in S#10))
    -SR,llet-in1->                (letrec {E#8;E#9} in S#10)
    and constraints: E#8/= {}, E#9/= {}, ({E#8},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in (letrec {E#9} in S#10))}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),[{E#8},(letrec {E#9} in [.])],((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  (letrec {E#9} in S#10),
           E#8   |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#12},
           E#11  |->  {X#1=C#7[(var X#3)];E#12},
           E#4   |->  {E#12}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#12} in (letrec {E#9} in S#10))
    -cpx-e1->                     (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#12} in (letrec {E#9} in S#10))
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#12} in (letrec {E#9} in S#10))
    -SR,llet-in1->                (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#12;E#9} in S#10)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {E#9} in S#11)
       ;E#10
     in
        A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
     )
    ,
     (letrec
        X#8= S#11
       ;E#10
       ;E#9
     in
        A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#13,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])],(letrec {E#9} in [.])),
             [{E#10},(letrec {E#9} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),A#14[(app A#15[[.]] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]),
             ((var X#8),A#14[(app A#15[[.]] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),C#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#14[(app A#15[(var X#8)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#8)] T#16)],
           A#12  |->  A#14[(app A#15 T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -cpx-e1->                     (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])])
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {E#9} in T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])
       ;E#10
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#8= T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;E#10
       ;E#9
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#13,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{E#10},(letrec {E#9} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),C#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(letrec {E#9} in T#16);E#10} in A#12[(var X#8)]),
           X#14  |->  X#8,
           E#15  |->  {E#10},
           T#13  |->  (letrec {E#9} in T#16),
           S#11  |->  T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#9} in T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]);E#10} in A#12[(var X#8)])
    -cpx-e1->                     (letrec {X#8=(letrec {E#9} in T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]);E#10} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#10;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec
                X#17= T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
               ;E#19
             in
                S#11
             )
       ;E#10
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#17= T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;X#8= S#11
       ;E#10
       ;E#19
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#13,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (A#12[(var X#8)],(letrec {X#17=T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#19} in [.])),
             [{E#10},(letrec {X#17=T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#19} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),C#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(letrec {X#17=T#16;E#19} in S#11);E#10} in A#12[(var X#8)]),
           X#14  |->  X#8,
           E#15  |->  {E#10},
           T#13  |->  (letrec {X#17=T#16;E#19} in S#11),
           E#9   |->  {X#17=T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#19},
           E#18  |->  {E#19}}

and instantiated rules:

                                  (letrec {X#8=(letrec {X#17=T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#19} in S#11);E#10} in A#12[(var X#8)])
    -cpx-e1->                     (letrec {X#8=(letrec {X#17=T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#19} in S#11);E#10} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(letrec {X#17=T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#19} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#17=T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=S#11;E#10;E#19} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#17} in S#11)
       ;E#10
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#2= (var X#3)
       ;X#8= S#11
       ;E#10
       ;E#17
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (A#12[(var X#8)],(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#17} in [.])),
             [{E#10},(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#17} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),C#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=[.];E#10} in A#12[(var X#8)]),
           X#14  |->  X#8,
           E#15  |->  {E#10},
           T#13  |->  [.],
           S#5   |->  S#11,
           E#9   |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#17},
           E#16  |->  {X#1=C#7[(var X#3)];E#17},
           E#4   |->  {E#17}}

and instantiated rules:

                                  (letrec {X#8=(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#17} in S#11);E#10} in A#12[(var X#8)])
    -cpx-e1->                     (letrec {X#8=(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#17} in S#11);E#10} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#17} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=S#11;E#10;E#17} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
       ;X#8= (letrec {E#9} in S#11)
       ;E#16
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;X#8= S#11
       ;E#16
       ;E#9
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16},(letrec {E#9} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),C#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#14=T#13;X#8=(letrec {E#9} in S#11);E#16} in A#12[(var X#8)]),
           E#10  |->  {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16},
           E#15  |->  {X#8=(letrec {E#9} in S#11);E#16}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(letrec {E#9} in S#11);E#16} in A#12[(var X#8)])
    -cpx-e1->                     (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];X#8=(letrec {E#9} in S#11);E#16} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(letrec {E#9} in S#11);E#16} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=S#11;E#16;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (letrec {E#9} in C#14[(var X#2)])
       ;E#13
     in
        A#12[(var X#8)]
     )
    ,
     (letrec {X#2=(var X#3);X#8=C#14[(var X#3)];E#13;E#9} in A#12[(var X#8)])
  )

where

   Delta1 = {C#7}
   Delta2 = {E#9}
   Delta3 = {((var X#2),(letrec {E#9} in C#14)),
             ((var X#3),(letrec {E#9} in C#14)),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#2=(var X#3);E#13},(letrec {E#9} in [.])],
             ((var X#2),(letrec {E#9} in C#14[[.]])),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),C#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#8)],
           E#10  |->  {X#2=(var X#3);E#13},
           X#1   |->  X#8,
           E#4   |->  {E#13},
           C#7   |->  (letrec {E#9} in C#14),
           S#11  |->  C#14[(var X#3)]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(letrec {E#9} in C#14[(var X#3)]);E#13} in A#12[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(letrec {E#9} in C#14[(var X#2)]);E#13} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(letrec {E#9} in C#14[(var X#3)]);E#13} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#2=(var X#3);X#8=C#14[(var X#3)];E#13;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (letrec {X#15=C#14[(var X#2)];E#17} in S#11)
       ;E#13
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= C#14[(var X#3)]
       ;X#2= (var X#3)
       ;X#8= S#11
       ;E#13
       ;E#17
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#9}
   Delta3 = {((var X#2),(letrec {X#15=C#14;E#17} in S#11)),
             ((var X#3),(letrec {X#15=C#14;E#17} in S#11)),
             (A#12[(var X#8)],(letrec {X#15=C#14[(var X#3)];E#17} in [.])),
             [{X#2=(var X#3);E#13},(letrec {X#15=C#14[(var X#3)];E#17} in [.])],
             ((var X#2),(letrec {X#15=C#14[[.]];E#17} in S#11)),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),C#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#8)],
           E#10  |->  {X#2=(var X#3);E#13},
           X#1   |->  X#8,
           E#4   |->  {E#13},
           C#7   |->  (letrec {X#15=C#14;E#17} in S#11),
           E#9   |->  {X#15=C#14[(var X#3)];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(letrec {X#15=C#14[(var X#3)];E#17} in S#11);E#13} in A#12[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(letrec {X#15=C#14[(var X#2)];E#17} in S#11);E#13} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(letrec {X#15=C#14[(var X#3)];E#17} in S#11);E#13} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#15=C#14[(var X#3)];X#2=(var X#3);X#8=S#11;E#13;E#17} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#2)]
       ;X#2= (var X#3)
       ;X#8= (letrec {E#9} in S#11)
       ;E#14
     in
        A#12[(var X#8)]
     )
    ,
     (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=S#11;E#14;E#9} in A#12[(var X#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#1=C#7[(var X#3)];X#2=(var X#3);E#14},(letrec {E#9} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),C#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#8)],
           E#10  |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#14},
           E#13  |->  {X#1=C#7[(var X#3)];E#14},
           E#4   |->  {X#8=(letrec {E#9} in S#11);E#14}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(letrec {E#9} in S#11);E#14} in A#12[(var X#8)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);X#8=(letrec {E#9} in S#11);E#14} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(letrec {E#9} in S#11);E#14} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=S#11;E#14;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#14[X#9,(var X#8)]
     in
        A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
     )
    ,
     (letrec
        X#8= S#12
       ;E#10
       ;E#11
       ;EE#14[X#9,(var X#8)]
     in
        A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
     )
  )

where

   Delta1 = {A#13,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),
             (A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])],(letrec {E#10} in [.])),
             [{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#16[(app A#17[[.]] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]),
             ((var X#8),[.]),
             ((var X#9),A#16[(app A#17[[.]] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#16[(app A#17[(var X#9)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#9)] T#18)],
           A#13  |->  A#16[(app A#17 T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -cpx-e1->                     (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {E#10} in T#18[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])
       ;E#11
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#8= T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;E#10
       ;E#11
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(letrec {E#10} in T#18);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)]),
           X#16  |->  X#8,
           E#17  |->  {E#11;EE#14[X#9,(var X#8)]},
           T#15  |->  (letrec {E#10} in T#18),
           S#12  |->  T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#8=(letrec {E#10} in T#18[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec
                X#19= T#18[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
               ;E#21
             in
                S#12
             )
       ;E#11
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;X#8= S#12
       ;E#11
       ;E#21
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#8),(letrec {X#19=T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#11;E#21;EE#14[X#9,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {X#19=T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#21} in [.])),
             [{E#11;EE#14[X#9,(var X#8)]},(letrec {X#19=T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#21} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(letrec {X#19=T#18;E#21} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)]),
           X#16  |->  X#8,
           E#17  |->  {E#11;EE#14[X#9,(var X#8)]},
           T#15  |->  (letrec {X#19=T#18;E#21} in S#12),
           E#10  |->  {X#19=T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#21},
           E#20  |->  {E#21}}

and instantiated rules:

                                  (letrec {X#8=(letrec {X#19=T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#21} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#8=(letrec {X#19=T#18[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#21} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {X#19=T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#21} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#19=T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=S#12;E#11;E#21;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#19} in S#12)
       ;E#11
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#2= (var X#3)
       ;X#8= S#12
       ;E#11
       ;E#19
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#8),(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#11;E#19;EE#14[X#9,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#19} in [.])),
             [{E#11;EE#14[X#9,(var X#8)]},(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#19} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=[.];E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)]),
           X#16  |->  X#8,
           E#17  |->  {E#11;EE#14[X#9,(var X#8)]},
           T#15  |->  [.],
           S#5   |->  S#12,
           E#10  |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#19},
           E#18  |->  {X#1=C#7[(var X#3)];E#19},
           E#4   |->  {E#19}}

and instantiated rules:

                                  (letrec {X#8=(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#19} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#8=(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#19} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#19} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=S#12;E#11;E#19;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
       ;X#8= (letrec {E#10} in S#12)
       ;E#18
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;X#8= S#12
       ;E#10
       ;E#18
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#8),(letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#10;E#18;EE#14[X#9,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#16=T#15;X#8=(letrec {E#10} in S#12);E#18;EE#14[X#9,(var X#8)]} in A#13[(var X#9)]),
           E#11  |->  {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18},
           E#17  |->  {X#8=(letrec {E#10} in S#12);E#18;EE#14[X#9,(var X#8)]}}

and instantiated rules:

                                  (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(letrec {E#10} in S#12);E#18;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];X#8=(letrec {E#10} in S#12);E#18;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=(letrec {E#10} in S#12);E#18;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];X#8=S#12;E#10;E#18;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {E#10} in S#12)
       ;X#9= A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;E#11
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#8= S#12
       ;X#9= A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;E#10
       ;E#11
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#8),(letrec {X#9=A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;E#11} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#9=A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#11},(letrec {E#10} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#19[(app A#20[(var X#8)] T#21)];E#11} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]},
           X#16         |->  X#9,
           E#17         |->  {X#8=(letrec {E#10} in S#12);E#11},
           T#15         |->  A#19[(app A#20[(var X#8)] T#21)],
           A#18         |->  A#19[(app A#20 T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#11} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#8=(letrec {E#10} in S#12);X#9=A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];E#11} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#11} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;X#9=A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;E#11} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {E#10} in S#12)
       ;X#9= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;E#11
       ;EE#20[X#19,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#8= S#12
       ;X#9= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;E#10
       ;E#11
       ;EE#20[X#19,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#8),(letrec {X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;E#11;EE#20[X#19,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#11;EE#20[X#19,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#21[(app A#22[(var X#19)] T#23)];E#11;EE#20[X#19,(var X#8)]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];EE#20[X#19,[.2]]},
           X#16         |->  X#9,
           E#17         |->  {X#8=(letrec {E#10} in S#12);E#11;EE#20[X#19,(var X#8)]},
           T#15         |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#11;EE#20[X#19,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#8=(letrec {E#10} in S#12);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];E#11;EE#20[X#19,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#11;EE#20[X#19,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;E#11;EE#20[X#19,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#21[X#9,(var X#19)]
       ;EE#22[X#20,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#21[X#9,(var X#19)]
       ;EE#22[X#20,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#8),(letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];X#8=(letrec {E#10} in S#12);E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#8=(letrec {E#10} in S#12);E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]},
           T#15         |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(letrec {E#10} in S#12);E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];X#8=(letrec {E#10} in S#12);E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(letrec {E#10} in S#12);E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=S#12;E#10;E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#8),(letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#10;E#11;EE#20[X#9,(var X#19)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#11;EE#20[X#9,(var X#19)]},(letrec {E#10} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23)];X#8=(letrec {E#10} in S#12);E#11;EE#20[X#9,(var X#19)]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#8=(letrec {E#10} in S#12);E#11;EE#20[X#9,(var X#19)]},
           T#15         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(letrec {E#10} in S#12);E#11;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];X#8=(letrec {E#10} in S#12);E#11;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=(letrec {E#10} in S#12);E#11;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];X#8=S#12;E#10;E#11;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (letrec {E#10} in C#16[(var X#2)])
       ;E#15
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= C#16[(var X#3)]
       ;E#10
       ;E#15
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(letrec {E#10} in C#16)),
             ((var X#3),(letrec {E#10} in C#16)),
             ((var X#8),(letrec {X#2=(var X#3);E#10;E#15;EE#14[X#9,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#2=(var X#3);E#15;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),(letrec {E#10} in C#16[[.]])),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#9)],
           E#11  |->  {X#2=(var X#3);E#15},
           X#1   |->  X#8,
           E#4   |->  {E#15;EE#14[X#9,(var X#8)]},
           C#7   |->  (letrec {E#10} in C#16),
           S#12  |->  C#16[(var X#3)]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(letrec {E#10} in C#16[(var X#3)]);E#15;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(letrec {E#10} in C#16[(var X#2)]);E#15;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(letrec {E#10} in C#16[(var X#3)]);E#15;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#2=(var X#3);X#8=C#16[(var X#3)];E#10;E#15;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (letrec {X#17=C#16[(var X#2)];E#19} in S#12)
       ;E#15
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#17= C#16[(var X#3)]
       ;X#2= (var X#3)
       ;X#8= S#12
       ;E#15
       ;E#19
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(letrec {X#17=C#16;E#19} in S#12)),
             ((var X#3),(letrec {X#17=C#16;E#19} in S#12)),
             ((var X#8),(letrec {X#17=C#16[(var X#3)];X#2=(var X#3);E#15;E#19;EE#14[X#9,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {X#17=C#16[(var X#3)];E#19} in [.])),
             [{X#2=(var X#3);E#15;EE#14[X#9,(var X#8)]},(letrec {X#17=C#16[(var X#3)];E#19} in [.])],
             ((var X#2),(letrec {X#17=C#16[[.]];E#19} in S#12)),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#9)],
           E#11  |->  {X#2=(var X#3);E#15},
           X#1   |->  X#8,
           E#4   |->  {E#15;EE#14[X#9,(var X#8)]},
           C#7   |->  (letrec {X#17=C#16;E#19} in S#12),
           E#10  |->  {X#17=C#16[(var X#3)];E#19},
           E#18  |->  {E#19}}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(letrec {X#17=C#16[(var X#3)];E#19} in S#12);E#15;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(letrec {X#17=C#16[(var X#2)];E#19} in S#12);E#15;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(letrec {X#17=C#16[(var X#3)];E#19} in S#12);E#15;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#17=C#16[(var X#3)];X#2=(var X#3);X#8=S#12;E#15;E#19;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#2)]
       ;X#2= (var X#3)
       ;X#8= (letrec {E#10} in S#12)
       ;E#16
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#2= (var X#3)
       ;X#8= S#12
       ;E#10
       ;E#16
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             ((var X#8),(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#10;E#16;EE#14[X#9,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#1=C#7[(var X#3)];X#2=(var X#3);E#16;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#9)],
           E#11  |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#16},
           E#15  |->  {X#1=C#7[(var X#3)];E#16},
           E#4   |->  {X#8=(letrec {E#10} in S#12);E#16;EE#14[X#9,(var X#8)]}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(letrec {E#10} in S#12);E#16;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);X#8=(letrec {E#10} in S#12);E#16;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=(letrec {E#10} in S#12);E#16;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);X#8=S#12;E#10;E#16;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#8)
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= A#17[(var X#2)]
       ;E#15
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#2= (var X#8)
       ;X#8= S#12
       ;X#9= A#17[(var X#8)]
       ;E#10
       ;E#15
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#16,C#7,A#17}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#17[[.]]),
             ((var X#8),A#17[[.]]),
             ((var X#8),(letrec {X#2=(var X#8);X#9=A#17[(var X#8)];E#10;E#15} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#2=(var X#8);X#9=A#17[(var X#8)];E#15},(letrec {E#10} in [.])],
             ((var X#2),A#17[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#8);E#15},
           EE#14[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#1          |->  X#9,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#15},
           A#16         |->  A#17,
           C#7          |->  A#17[[.]],
           C#18         |->  [.],
           X#3          |->  X#8}

and instantiated rules:

                                  (letrec {X#2=(var X#8);X#8=(letrec {E#10} in S#12);X#9=A#17[(var X#8)];E#15} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#2=(var X#8);X#8=(letrec {E#10} in S#12);X#9=A#17[(var X#2)];E#15} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(var X#8);X#8=(letrec {E#10} in S#12);X#9=A#17[(var X#8)];E#15} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#2=(var X#8);X#8=S#12;X#9=A#17[(var X#8)];E#10;E#15} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#3= (letrec {E#10} in S#12)
       ;X#9= A#17[(var X#2)]
       ;E#15
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#3= S#12
       ;X#9= A#17[(var X#3)]
       ;E#10
       ;E#15
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#16,C#7,A#17}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#17),
             ((var X#3),A#17),
             ((var X#3),(letrec {X#2=(var X#3);X#9=A#17[(var X#3)];E#10;E#15} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#2=(var X#3);X#9=A#17[(var X#3)];E#15},(letrec {E#10} in [.])],
             ((var X#2),A#17[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#1          |->  X#9,
           E#4          |->  {X#3=(letrec {E#10} in S#12);E#15},
           A#16         |->  A#17[[.]],
           C#7          |->  A#17,
           A#18         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#3=(letrec {E#10} in S#12);X#9=A#17[(var X#3)];E#15} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#3=(letrec {E#10} in S#12);X#9=A#17[(var X#2)];E#15} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#3=(letrec {E#10} in S#12);X#9=A#17[(var X#3)];E#15} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#2=(var X#3);X#3=S#12;X#9=A#17[(var X#3)];E#10;E#15} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= A#17[(app A#18[(var X#8)] C#19[(var X#2)])]
       ;E#15
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= S#12
       ;X#9= A#17[(app A#18[(var X#8)] C#19[(var X#3)])]
       ;E#10
       ;E#15
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#16,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#17[(app A#18[(var X#8)] C#19)]),
             ((var X#3),A#17[(app A#18[(var X#8)] C#19)]),
             ((var X#8),(letrec {X#2=(var X#3);X#9=A#17[(app A#18[(var X#8)] C#19[(var X#3)])];E#10;E#15} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#2=(var X#3);X#9=A#17[(app A#18[(var X#8)] C#19[(var X#3)])];E#15},(letrec {E#10} in [.])],
             ((var X#2),A#17[(app A#18[(var X#8)] C#19[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] C#19[(var X#3)])]},
           X#1          |->  X#9,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#15},
           C#7          |->  A#17[(app A#18[(var X#8)] C#19)],
           A#16         |->  A#17[(app A#18 C#19[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(letrec {E#10} in S#12);X#9=A#17[(app A#18[(var X#8)] C#19[(var X#3)])];E#15} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(letrec {E#10} in S#12);X#9=A#17[(app A#18[(var X#8)] C#19[(var X#2)])];E#15} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(letrec {E#10} in S#12);X#9=A#17[(app A#18[(var X#8)] C#19[(var X#3)])];E#15} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#2=(var X#3);X#8=S#12;X#9=A#17[(app A#18[(var X#8)] C#19[(var X#3)])];E#10;E#15} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#3= (letrec {E#10} in S#12)
       ;X#9= (var X#2)
       ;E#15
     in
        A#13[(var X#9)]
     )
    ,
     (letrec {X#2=(var X#3);X#3=S#12;X#9=(var X#3);E#10;E#15} in A#13[(var X#9)])
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),[.]),
             ((var X#3),[.]),
             ((var X#3),(letrec {X#2=(var X#3);X#9=(var X#3);E#10;E#15} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#2=(var X#3);X#9=(var X#3);E#15},(letrec {E#10} in [.])],
             ((var X#2),[.]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#9,
           E#4          |->  {X#3=(letrec {E#10} in S#12);E#15},
           C#7          |->  [.],
           A#16         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#3=(letrec {E#10} in S#12);X#9=(var X#3);E#15} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#3=(letrec {E#10} in S#12);X#9=(var X#2);E#15} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#3=(letrec {E#10} in S#12);X#9=(var X#3);E#15} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#2=(var X#3);X#3=S#12;X#9=(var X#3);E#10;E#15} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#17)
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= A#19[(var X#2)]
       ;E#15
       ;EE#18[X#17,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#2= (var X#17)
       ;X#8= S#12
       ;X#9= A#19[(var X#17)]
       ;E#10
       ;E#15
       ;EE#18[X#17,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#16,C#7,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#19[[.]]),
             ((var X#17),A#19[[.]]),
             ((var X#8),(letrec {X#2=(var X#17);X#9=A#19[(var X#17)];E#10;E#15;EE#18[X#17,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#2=(var X#17);X#9=A#19[(var X#17)];E#15;EE#18[X#17,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),A#19[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#17);E#15},
           EE#14[.1,.2] |-> {[.1]=A#19[(var X#17)];EE#18[X#17,[.2]]},
           X#1          |->  X#9,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#15;EE#18[X#17,(var X#8)]},
           A#16         |->  A#19,
           C#7          |->  A#19[[.]],
           C#20         |->  [.],
           X#3          |->  X#17}

and instantiated rules:

                                  (letrec {X#2=(var X#17);X#8=(letrec {E#10} in S#12);X#9=A#19[(var X#17)];E#15;EE#18[X#17,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#2=(var X#17);X#8=(letrec {E#10} in S#12);X#9=A#19[(var X#2)];E#15;EE#18[X#17,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(var X#17);X#8=(letrec {E#10} in S#12);X#9=A#19[(var X#17)];E#15;EE#18[X#17,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#2=(var X#17);X#8=S#12;X#9=A#19[(var X#17)];E#10;E#15;EE#18[X#17,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= A#19[(var X#2)]
       ;E#15
       ;EE#18[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= S#12
       ;X#9= A#19[(var X#3)]
       ;E#10
       ;E#15
       ;EE#18[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#16,C#7,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#19),
             ((var X#3),A#19),
             ((var X#8),(letrec {X#2=(var X#3);X#9=A#19[(var X#3)];E#10;E#15;EE#18[X#3,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#2=(var X#3);X#9=A#19[(var X#3)];E#15;EE#18[X#3,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),A#19[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=A#19[(var X#3)];EE#18[X#3,[.2]]},
           X#1          |->  X#9,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#15;EE#18[X#3,(var X#8)]},
           A#16         |->  A#19[[.]],
           C#7          |->  A#19,
           A#20         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(letrec {E#10} in S#12);X#9=A#19[(var X#3)];E#15;EE#18[X#3,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(letrec {E#10} in S#12);X#9=A#19[(var X#2)];E#15;EE#18[X#3,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(letrec {E#10} in S#12);X#9=A#19[(var X#3)];E#15;EE#18[X#3,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#2=(var X#3);X#8=S#12;X#9=A#19[(var X#3)];E#10;E#15;EE#18[X#3,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= A#19[(app A#20[(var X#17)] C#21[(var X#2)])]
       ;E#15
       ;EE#18[X#17,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= S#12
       ;X#9= A#19[(app A#20[(var X#17)] C#21[(var X#3)])]
       ;E#10
       ;E#15
       ;EE#18[X#17,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#16,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#19[(app A#20[(var X#17)] C#21)]),
             ((var X#3),A#19[(app A#20[(var X#17)] C#21)]),
             ((var X#8),(letrec {X#2=(var X#3);X#9=A#19[(app A#20[(var X#17)] C#21[(var X#3)])];E#10;E#15;EE#18[X#17,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#2=(var X#3);X#9=A#19[(app A#20[(var X#17)] C#21[(var X#3)])];E#15;EE#18[X#17,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),A#19[(app A#20[(var X#17)] C#21[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] C#21[(var X#3)])];EE#18[X#17,[.2]]},
           X#1          |->  X#9,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#15;EE#18[X#17,(var X#8)]},
           C#7          |->  A#19[(app A#20[(var X#17)] C#21)],
           A#16         |->  A#19[(app A#20 C#21[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(letrec {E#10} in S#12);X#9=A#19[(app A#20[(var X#17)] C#21[(var X#3)])];E#15;EE#18[X#17,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(letrec {E#10} in S#12);X#9=A#19[(app A#20[(var X#17)] C#21[(var X#2)])];E#15;EE#18[X#17,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(letrec {E#10} in S#12);X#9=A#19[(app A#20[(var X#17)] C#21[(var X#3)])];E#15;EE#18[X#17,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#2=(var X#3);X#8=S#12;X#9=A#19[(app A#20[(var X#17)] C#21[(var X#3)])];E#10;E#15;EE#18[X#17,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= (var X#2)
       ;E#15
       ;EE#18[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= S#12
       ;X#9= (var X#3)
       ;E#10
       ;E#15
       ;EE#18[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),[.]),
             ((var X#3),[.]),
             ((var X#8),(letrec {X#2=(var X#3);X#9=(var X#3);E#10;E#15;EE#18[X#3,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#2=(var X#3);X#9=(var X#3);E#15;EE#18[X#3,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=(var X#3);EE#18[X#3,[.2]]},
           X#1          |->  X#9,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#15;EE#18[X#3,(var X#8)]},
           C#7          |->  [.],
           A#16         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#15;EE#18[X#3,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(letrec {E#10} in S#12);X#9=(var X#2);E#15;EE#18[X#3,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#15;EE#18[X#3,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#2=(var X#3);X#8=S#12;X#9=(var X#3);E#10;E#15;EE#18[X#3,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(var X#2)]
       ;X#2= (var X#18)
       ;X#8= (letrec {E#10} in S#12)
       ;E#15
       ;EE#19[X#9,(var X#17)]
       ;EE#20[X#18,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#17= A#21[(var X#18)]
       ;X#2= (var X#18)
       ;X#8= S#12
       ;E#10
       ;E#15
       ;EE#19[X#9,(var X#17)]
       ;EE#20[X#18,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#16,C#7,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#21[[.]]),
             ((var X#18),A#21[[.]]),
             ((var X#8),(letrec {X#17=A#21[(var X#18)];X#2=(var X#18);E#10;E#15;EE#19[X#9,(var X#17)];EE#20[X#18,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#17=A#21[(var X#18)];X#2=(var X#18);E#15;EE#19[X#9,(var X#17)];EE#20[X#18,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),A#21[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#18);E#15},
           EE#14[.1,.2] |-> {X#17=A#21[(var X#18)];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#1          |->  X#17,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#18,(var X#8)]},
           A#16         |->  A#21,
           C#7          |->  A#21[[.]],
           C#22         |->  [.],
           X#3          |->  X#18}

and instantiated rules:

                                  (letrec {X#17=A#21[(var X#18)];X#2=(var X#18);X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#18,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#17=A#21[(var X#2)];X#2=(var X#18);X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#18,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#17=A#21[(var X#18)];X#2=(var X#18);X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#18,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#17=A#21[(var X#18)];X#2=(var X#18);X#8=S#12;E#10;E#15;EE#19[X#9,(var X#17)];EE#20[X#18,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(var X#2)]
       ;X#2= (var X#3)
       ;X#8= (letrec {E#10} in S#12)
       ;E#15
       ;EE#19[X#9,(var X#17)]
       ;EE#20[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#17= A#21[(var X#3)]
       ;X#2= (var X#3)
       ;X#8= S#12
       ;E#10
       ;E#15
       ;EE#19[X#9,(var X#17)]
       ;EE#20[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#16,C#7,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#21),
             ((var X#3),A#21),
             ((var X#8),(letrec {X#17=A#21[(var X#3)];X#2=(var X#3);E#10;E#15;EE#19[X#9,(var X#17)];EE#20[X#3,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#17=A#21[(var X#3)];X#2=(var X#3);E#15;EE#19[X#9,(var X#17)];EE#20[X#3,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),A#21[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=A#21[(var X#3)];EE#19[[.1],(var X#17)];EE#20[X#3,[.2]]},
           X#1          |->  X#17,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#3,(var X#8)]},
           A#16         |->  A#21[[.]],
           C#7          |->  A#21,
           A#22         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#17=A#21[(var X#3)];X#2=(var X#3);X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#3,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#17=A#21[(var X#2)];X#2=(var X#3);X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#3,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#17=A#21[(var X#3)];X#2=(var X#3);X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#3,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#17=A#21[(var X#3)];X#2=(var X#3);X#8=S#12;E#10;E#15;EE#19[X#9,(var X#17)];EE#20[X#3,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(app A#22[(var X#18)] C#23[(var X#2)])]
       ;X#2= (var X#3)
       ;X#8= (letrec {E#10} in S#12)
       ;E#15
       ;EE#19[X#9,(var X#17)]
       ;EE#20[X#18,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] C#23[(var X#3)])]
       ;X#2= (var X#3)
       ;X#8= S#12
       ;E#10
       ;E#15
       ;EE#19[X#9,(var X#17)]
       ;EE#20[X#18,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#16,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#21[(app A#22[(var X#18)] C#23)]),
             ((var X#3),A#21[(app A#22[(var X#18)] C#23)]),
             ((var X#8),(letrec {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#3)])];X#2=(var X#3);E#10;E#15;EE#19[X#9,(var X#17)];EE#20[X#18,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#17=A#21[(app A#22[(var X#18)] C#23[(var X#3)])];X#2=(var X#3);E#15;EE#19[X#9,(var X#17)];EE#20[X#18,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),A#21[(app A#22[(var X#18)] C#23[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#3)])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#1          |->  X#17,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#18,(var X#8)]},
           C#7          |->  A#21[(app A#22[(var X#18)] C#23)],
           A#16         |->  A#21[(app A#22 C#23[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#3)])];X#2=(var X#3);X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#18,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#2)])];X#2=(var X#3);X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#18,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#3)])];X#2=(var X#3);X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#18,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#3)])];X#2=(var X#3);X#8=S#12;E#10;E#15;EE#19[X#9,(var X#17)];EE#20[X#18,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#2)
       ;X#2= (var X#3)
       ;X#8= (letrec {E#10} in S#12)
       ;E#15
       ;EE#19[X#9,(var X#17)]
       ;EE#20[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#17= (var X#3)
       ;X#2= (var X#3)
       ;X#8= S#12
       ;E#10
       ;E#15
       ;EE#19[X#9,(var X#17)]
       ;EE#20[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),[.]),
             ((var X#3),[.]),
             ((var X#8),(letrec {X#17=(var X#3);X#2=(var X#3);E#10;E#15;EE#19[X#9,(var X#17)];EE#20[X#3,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#17=(var X#3);X#2=(var X#3);E#15;EE#19[X#9,(var X#17)];EE#20[X#3,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=(var X#3);EE#19[[.1],(var X#17)];EE#20[X#3,[.2]]},
           X#1          |->  X#17,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#3,(var X#8)]},
           C#7          |->  [.],
           A#16         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#17=(var X#3);X#2=(var X#3);X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#3,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#17=(var X#2);X#2=(var X#3);X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#3,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#17=(var X#3);X#2=(var X#3);X#8=(letrec {E#10} in S#12);E#15;EE#19[X#9,(var X#17)];EE#20[X#3,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#17=(var X#3);X#2=(var X#3);X#8=S#12;E#10;E#15;EE#19[X#9,(var X#17)];EE#20[X#3,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(var X#2)]
       ;X#2= (var X#8)
       ;X#8= (letrec {E#10} in S#12)
       ;E#15
       ;EE#18[X#9,(var X#17)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#17= A#19[(var X#8)]
       ;X#2= (var X#8)
       ;X#8= S#12
       ;E#10
       ;E#15
       ;EE#18[X#9,(var X#17)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#16,C#7,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#19[[.]]),
             ((var X#8),A#19[[.]]),
             ((var X#8),(letrec {X#17=A#19[(var X#8)];X#2=(var X#8);E#10;E#15;EE#18[X#9,(var X#17)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#17=A#19[(var X#8)];X#2=(var X#8);E#15;EE#18[X#9,(var X#17)]},(letrec {E#10} in [.])],
             ((var X#2),A#19[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#8);E#15},
           EE#14[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]},
           A#16         |->  A#19,
           C#7          |->  A#19[[.]],
           C#20         |->  [.],
           X#3          |->  X#8}

and instantiated rules:

                                  (letrec {X#17=A#19[(var X#8)];X#2=(var X#8);X#8=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#17=A#19[(var X#2)];X#2=(var X#8);X#8=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#17=A#19[(var X#8)];X#2=(var X#8);X#8=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#17=A#19[(var X#8)];X#2=(var X#8);X#8=S#12;E#10;E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(var X#2)]
       ;X#2= (var X#3)
       ;X#3= (letrec {E#10} in S#12)
       ;E#15
       ;EE#18[X#9,(var X#17)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#17= A#19[(var X#3)]
       ;X#2= (var X#3)
       ;X#3= S#12
       ;E#10
       ;E#15
       ;EE#18[X#9,(var X#17)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#16,C#7,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#19),
             ((var X#3),A#19),
             ((var X#3),(letrec {X#17=A#19[(var X#3)];X#2=(var X#3);E#10;E#15;EE#18[X#9,(var X#17)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#17=A#19[(var X#3)];X#2=(var X#3);E#15;EE#18[X#9,(var X#17)]},(letrec {E#10} in [.])],
             ((var X#2),A#19[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {X#3=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]},
           A#16         |->  A#19[[.]],
           C#7          |->  A#19,
           A#20         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#17=A#19[(var X#3)];X#2=(var X#3);X#3=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#17=A#19[(var X#2)];X#2=(var X#3);X#3=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#17=A#19[(var X#3)];X#2=(var X#3);X#3=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#17=A#19[(var X#3)];X#2=(var X#3);X#3=S#12;E#10;E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[(var X#8)] C#21[(var X#2)])]
       ;X#2= (var X#3)
       ;X#8= (letrec {E#10} in S#12)
       ;E#15
       ;EE#18[X#9,(var X#17)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(var X#8)] C#21[(var X#3)])]
       ;X#2= (var X#3)
       ;X#8= S#12
       ;E#10
       ;E#15
       ;EE#18[X#9,(var X#17)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#16,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#19[(app A#20[(var X#8)] C#21)]),
             ((var X#3),A#19[(app A#20[(var X#8)] C#21)]),
             ((var X#8),(letrec {X#17=A#19[(app A#20[(var X#8)] C#21[(var X#3)])];X#2=(var X#3);E#10;E#15;EE#18[X#9,(var X#17)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#17=A#19[(app A#20[(var X#8)] C#21[(var X#3)])];X#2=(var X#3);E#15;EE#18[X#9,(var X#17)]},(letrec {E#10} in [.])],
             ((var X#2),A#19[(app A#20[(var X#8)] C#21[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] C#21[(var X#3)])];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]},
           C#7          |->  A#19[(app A#20[(var X#8)] C#21)],
           A#16         |->  A#19[(app A#20 C#21[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(var X#8)] C#21[(var X#3)])];X#2=(var X#3);X#8=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#17=A#19[(app A#20[(var X#8)] C#21[(var X#2)])];X#2=(var X#3);X#8=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(var X#8)] C#21[(var X#3)])];X#2=(var X#3);X#8=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#17=A#19[(app A#20[(var X#8)] C#21[(var X#3)])];X#2=(var X#3);X#8=S#12;E#10;E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#2)
       ;X#2= (var X#3)
       ;X#3= (letrec {E#10} in S#12)
       ;E#15
       ;EE#18[X#9,(var X#17)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#17= (var X#3)
       ;X#2= (var X#3)
       ;X#3= S#12
       ;E#10
       ;E#15
       ;EE#18[X#9,(var X#17)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),[.]),
             ((var X#3),[.]),
             ((var X#3),(letrec {X#17=(var X#3);X#2=(var X#3);E#10;E#15;EE#18[X#9,(var X#17)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#17=(var X#3);X#2=(var X#3);E#15;EE#18[X#9,(var X#17)]},(letrec {E#10} in [.])],
             ((var X#2),[.]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           E#11         |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {X#3=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]},
           C#7          |->  [.],
           A#16         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#17=(var X#3);X#2=(var X#3);X#3=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#17=(var X#2);X#2=(var X#3);X#3=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#17=(var X#3);X#2=(var X#3);X#3=(letrec {E#10} in S#12);E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#17=(var X#3);X#2=(var X#3);X#3=S#12;E#10;E#15;EE#18[X#9,(var X#17)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= (letrec {E#10} in C#16[(var X#9)])
       ;X#9= (var X#3)
       ;E#11
     in
        A#13[(var X#9)]
     )
    ,
     (letrec {X#3=C#16[(var X#3)];X#9=(var X#3);E#10;E#11} in A#13[(var X#9)])
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#9),(letrec {E#10} in C#16)),
             ((var X#3),(letrec {E#10} in C#16)),
             ((var X#3),(letrec {X#9=(var X#3);E#10;E#11} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#9=(var X#3);E#11},(letrec {E#10} in [.])],
             ((var X#9),(letrec {E#10} in C#16[[.]])),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#2          |->  X#9,
           X#1          |->  X#3,
           E#4          |->  {E#11},
           C#7          |->  (letrec {E#10} in C#16),
           S#12         |->  C#16[(var X#3)],
           A#15         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#3=(letrec {E#10} in C#16[(var X#3)]);X#9=(var X#3);E#11} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#3=(letrec {E#10} in C#16[(var X#9)]);X#9=(var X#3);E#11} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#3=(letrec {E#10} in C#16[(var X#3)]);X#9=(var X#3);E#11} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#3=C#16[(var X#3)];X#9=(var X#3);E#10;E#11} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= (letrec {X#17=C#16[(var X#9)];E#19} in S#12)
       ;X#9= (var X#3)
       ;E#11
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#17= C#16[(var X#3)]
       ;X#3= S#12
       ;X#9= (var X#3)
       ;E#11
       ;E#19
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#9),(letrec {X#17=C#16;E#19} in S#12)),
             ((var X#3),(letrec {X#17=C#16;E#19} in S#12)),
             ((var X#3),(letrec {X#17=C#16[(var X#3)];X#9=(var X#3);E#11;E#19} in [.])),
             (A#13[(var X#9)],(letrec {X#17=C#16[(var X#3)];E#19} in [.])),
             [{X#9=(var X#3);E#11},(letrec {X#17=C#16[(var X#3)];E#19} in [.])],
             ((var X#9),(letrec {X#17=C#16[[.]];E#19} in S#12)),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#2          |->  X#9,
           X#1          |->  X#3,
           E#4          |->  {E#11},
           C#7          |->  (letrec {X#17=C#16;E#19} in S#12),
           E#10         |->  {X#17=C#16[(var X#3)];E#19},
           E#18         |->  {E#19},
           A#15         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#3=(letrec {X#17=C#16[(var X#3)];E#19} in S#12);X#9=(var X#3);E#11} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#3=(letrec {X#17=C#16[(var X#9)];E#19} in S#12);X#9=(var X#3);E#11} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#3=(letrec {X#17=C#16[(var X#3)];E#19} in S#12);X#9=(var X#3);E#11} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#17=C#16[(var X#3)];X#3=S#12;X#9=(var X#3);E#11;E#19} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#9)]
       ;X#3= (letrec {E#10} in S#12)
       ;X#9= (var X#3)
       ;E#16
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#3= S#12
       ;X#9= (var X#3)
       ;E#10
       ;E#16
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#9),C#7),
             ((var X#3),C#7),
             ((var X#3),(letrec {X#1=C#7[(var X#3)];X#9=(var X#3);E#10;E#16} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#1=C#7[(var X#3)];X#9=(var X#3);E#16},(letrec {E#10} in [.])],
             ((var X#9),C#7[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#2          |->  X#9,
           E#11         |->  {X#1=C#7[(var X#3)];E#16},
           E#4          |->  {X#3=(letrec {E#10} in S#12);E#16},
           A#15         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#3=(letrec {E#10} in S#12);X#9=(var X#3);E#16} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#9)];X#3=(letrec {E#10} in S#12);X#9=(var X#3);E#16} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#3=(letrec {E#10} in S#12);X#9=(var X#3);E#16} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#1=C#7[(var X#3)];X#3=S#12;X#9=(var X#3);E#10;E#16} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {E#10} in C#18[(var X#9)])
       ;X#9= (var X#3)
       ;E#11
       ;EE#17[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#8= C#18[(var X#3)]
       ;X#9= (var X#3)
       ;E#10
       ;E#11
       ;EE#17[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#9),(letrec {E#10} in C#18)),
             ((var X#3),(letrec {E#10} in C#18)),
             ((var X#8),(letrec {X#9=(var X#3);E#10;E#11;EE#17[X#3,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#9=(var X#3);E#11;EE#17[X#3,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#9),(letrec {E#10} in C#18[[.]])),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=(var X#3);EE#17[X#3,[.2]]},
           X#2          |->  X#9,
           X#1          |->  X#8,
           E#4          |->  {E#11;EE#17[X#3,(var X#8)]},
           C#7          |->  (letrec {E#10} in C#18),
           S#12         |->  C#18[(var X#3)],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in C#18[(var X#3)]);X#9=(var X#3);E#11;EE#17[X#3,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#8=(letrec {E#10} in C#18[(var X#9)]);X#9=(var X#3);E#11;EE#17[X#3,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in C#18[(var X#3)]);X#9=(var X#3);E#11;EE#17[X#3,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=C#18[(var X#3)];X#9=(var X#3);E#10;E#11;EE#17[X#3,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {X#19=C#18[(var X#9)];E#21} in S#12)
       ;X#9= (var X#3)
       ;E#11
       ;EE#17[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= C#18[(var X#3)]
       ;X#8= S#12
       ;X#9= (var X#3)
       ;E#11
       ;E#21
       ;EE#17[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#9),(letrec {X#19=C#18;E#21} in S#12)),
             ((var X#3),(letrec {X#19=C#18;E#21} in S#12)),
             ((var X#8),(letrec {X#19=C#18[(var X#3)];X#9=(var X#3);E#11;E#21;EE#17[X#3,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {X#19=C#18[(var X#3)];E#21} in [.])),
             [{X#9=(var X#3);E#11;EE#17[X#3,(var X#8)]},(letrec {X#19=C#18[(var X#3)];E#21} in [.])],
             ((var X#9),(letrec {X#19=C#18[[.]];E#21} in S#12)),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=(var X#3);EE#17[X#3,[.2]]},
           X#2          |->  X#9,
           X#1          |->  X#8,
           E#4          |->  {E#11;EE#17[X#3,(var X#8)]},
           C#7          |->  (letrec {X#19=C#18;E#21} in S#12),
           E#10         |->  {X#19=C#18[(var X#3)];E#21},
           E#20         |->  {E#21},
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#8=(letrec {X#19=C#18[(var X#3)];E#21} in S#12);X#9=(var X#3);E#11;EE#17[X#3,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#8=(letrec {X#19=C#18[(var X#9)];E#21} in S#12);X#9=(var X#3);E#11;EE#17[X#3,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {X#19=C#18[(var X#3)];E#21} in S#12);X#9=(var X#3);E#11;EE#17[X#3,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#19=C#18[(var X#3)];X#8=S#12;X#9=(var X#3);E#11;E#21;EE#17[X#3,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#9)]
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= (var X#3)
       ;E#18
       ;EE#17[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#8= S#12
       ;X#9= (var X#3)
       ;E#10
       ;E#18
       ;EE#17[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#9),C#7),
             ((var X#3),C#7),
             ((var X#8),(letrec {X#1=C#7[(var X#3)];X#9=(var X#3);E#10;E#18;EE#17[X#3,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#1=C#7[(var X#3)];X#9=(var X#3);E#18;EE#17[X#3,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#9),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=(var X#3);EE#17[X#3,[.2]]},
           X#2          |->  X#9,
           E#11         |->  {X#1=C#7[(var X#3)];E#18},
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#18;EE#17[X#3,(var X#8)]},
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#18;EE#17[X#3,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#9)];X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#18;EE#17[X#3,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#18;EE#17[X#3,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#1=C#7[(var X#3)];X#8=S#12;X#9=(var X#3);E#10;E#18;EE#17[X#3,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= A#19[(app A#20[(var X#8)] C#21[(var X#9)])]
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= (var X#3)
       ;E#11
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#3= A#19[(app A#20[(var X#8)] C#21[(var X#3)])]
       ;X#8= S#12
       ;X#9= (var X#3)
       ;E#10
       ;E#11
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#9),A#19[(app A#20[(var X#8)] C#21)]),
             ((var X#3),A#19[(app A#20[(var X#8)] C#21)]),
             ((var X#8),(letrec {X#3=A#19[(app A#20[(var X#8)] C#21[(var X#3)])];X#9=(var X#3);E#10;E#11} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#3=A#19[(app A#20[(var X#8)] C#21[(var X#3)])];X#9=(var X#3);E#11},(letrec {E#10} in [.])],
             ((var X#9),A#19[(app A#20[(var X#8)] C#21[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#3=A#19[(app A#20[[.2]] C#21[(var X#3)])];[.1]=(var X#3)},
           X#2          |->  X#9,
           EE#17[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] C#21[(var X#3)])]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#11},
           C#7          |->  A#19[(app A#20[(var X#8)] C#21)],
           A#18         |->  A#19[(app A#20 C#21[(var X#3)])],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#3=A#19[(app A#20[(var X#8)] C#21[(var X#3)])];X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#11} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#3=A#19[(app A#20[(var X#8)] C#21[(var X#9)])];X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#11} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#3=A#19[(app A#20[(var X#8)] C#21[(var X#3)])];X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#11} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#3=A#19[(app A#20[(var X#8)] C#21[(var X#3)])];X#8=S#12;X#9=(var X#3);E#10;E#11} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= A#21[(app A#22[(var X#19)] C#23[(var X#9)])]
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= (var X#3)
       ;E#11
       ;EE#20[X#19,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#3= A#21[(app A#22[(var X#19)] C#23[(var X#3)])]
       ;X#8= S#12
       ;X#9= (var X#3)
       ;E#10
       ;E#11
       ;EE#20[X#19,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#9),A#21[(app A#22[(var X#19)] C#23)]),
             ((var X#3),A#21[(app A#22[(var X#19)] C#23)]),
             ((var X#8),(letrec {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];X#9=(var X#3);E#10;E#11;EE#20[X#19,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#3=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];X#9=(var X#3);E#11;EE#20[X#19,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#9),A#21[(app A#22[(var X#19)] C#23[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];[.1]=(var X#3);EE#20[X#19,[.2]]},
           X#2          |->  X#9,
           EE#17[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];EE#20[X#19,[.2]]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#20[X#19,(var X#8)]},
           C#7          |->  A#21[(app A#22[(var X#19)] C#23)],
           A#18         |->  A#21[(app A#22 C#23[(var X#3)])],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#11;EE#20[X#19,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#9)])];X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#11;EE#20[X#19,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#11;EE#20[X#19,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];X#8=S#12;X#9=(var X#3);E#10;E#11;EE#20[X#19,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] C#25[(var X#9)])]
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= (var X#3)
       ;E#11
       ;EE#21[X#3,(var X#19)]
       ;EE#22[X#20,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] C#25[(var X#3)])]
       ;X#8= S#12
       ;X#9= (var X#3)
       ;E#10
       ;E#11
       ;EE#21[X#3,(var X#19)]
       ;EE#22[X#20,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#9),A#23[(app A#24[(var X#20)] C#25)]),
             ((var X#3),A#23[(app A#24[(var X#20)] C#25)]),
             ((var X#8),(letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];X#9=(var X#3);E#10;E#11;EE#21[X#3,(var X#19)];EE#22[X#20,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];X#9=(var X#3);E#11;EE#21[X#3,(var X#19)];EE#22[X#20,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#9),A#23[(app A#24[(var X#20)] C#25[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];[.1]=(var X#3);EE#21[X#3,(var X#19)];EE#22[X#20,[.2]]},
           X#2          |->  X#9,
           EE#17[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#1          |->  X#19,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#21[X#3,(var X#19)];EE#22[X#20,(var X#8)]},
           C#7          |->  A#23[(app A#24[(var X#20)] C#25)],
           A#18         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#11;EE#21[X#3,(var X#19)];EE#22[X#20,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#9)])];X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#11;EE#21[X#3,(var X#19)];EE#22[X#20,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#11;EE#21[X#3,(var X#19)];EE#22[X#20,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];X#8=S#12;X#9=(var X#3);E#10;E#11;EE#21[X#3,(var X#19)];EE#22[X#20,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(var X#8)] C#23[(var X#9)])]
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= (var X#3)
       ;E#11
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(var X#8)] C#23[(var X#3)])]
       ;X#8= S#12
       ;X#9= (var X#3)
       ;E#10
       ;E#11
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#9),A#21[(app A#22[(var X#8)] C#23)]),
             ((var X#3),A#21[(app A#22[(var X#8)] C#23)]),
             ((var X#8),(letrec {X#19=A#21[(app A#22[(var X#8)] C#23[(var X#3)])];X#9=(var X#3);E#10;E#11;EE#20[X#3,(var X#19)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#19=A#21[(app A#22[(var X#8)] C#23[(var X#3)])];X#9=(var X#3);E#11;EE#20[X#3,(var X#19)]},(letrec {E#10} in [.])],
             ((var X#9),A#21[(app A#22[(var X#8)] C#23[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] C#23[(var X#3)])];[.1]=(var X#3);EE#20[X#3,(var X#19)]},
           X#2          |->  X#9,
           EE#17[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] C#23[(var X#3)])];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#20[X#3,(var X#19)]},
           C#7          |->  A#21[(app A#22[(var X#8)] C#23)],
           A#18         |->  A#21[(app A#22 C#23[(var X#3)])],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(var X#8)] C#23[(var X#3)])];X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#11;EE#20[X#3,(var X#19)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#19=A#21[(app A#22[(var X#8)] C#23[(var X#9)])];X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#11;EE#20[X#3,(var X#19)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(var X#8)] C#23[(var X#3)])];X#8=(letrec {E#10} in S#12);X#9=(var X#3);E#11;EE#20[X#3,(var X#19)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#19=A#21[(app A#22[(var X#8)] C#23[(var X#3)])];X#8=S#12;X#9=(var X#3);E#10;E#11;EE#20[X#3,(var X#19)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#8= (letrec {E#10} in C#20[(var X#16)])
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#8= C#20[(var X#3)]
       ;E#10
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),(letrec {E#10} in C#20)),
             ((var X#3),(letrec {E#10} in C#20)),
             ((var X#8),(letrec {X#16=(var X#3);E#10;E#11;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=(var X#3);E#11;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#16),(letrec {E#10} in C#20[[.]])),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=(var X#3);EE#18[[.1],(var X#16)];EE#19[X#3,[.2]]},
           X#2          |->  X#16,
           X#1          |->  X#8,
           E#4          |->  {E#11;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]},
           C#7          |->  (letrec {E#10} in C#20),
           S#12         |->  C#20[(var X#3)],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#8=(letrec {E#10} in C#20[(var X#3)]);E#11;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#8=(letrec {E#10} in C#20[(var X#16)]);E#11;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#8=(letrec {E#10} in C#20[(var X#3)]);E#11;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#8=C#20[(var X#3)];E#10;E#11;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#8= (letrec {X#21=C#20[(var X#16)];E#23} in S#12)
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= C#20[(var X#3)]
       ;X#8= S#12
       ;E#11
       ;E#23
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),(letrec {X#21=C#20;E#23} in S#12)),
             ((var X#3),(letrec {X#21=C#20;E#23} in S#12)),
             ((var X#8),(letrec {X#16=(var X#3);X#21=C#20[(var X#3)];E#11;E#23;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {X#21=C#20[(var X#3)];E#23} in [.])),
             [{X#16=(var X#3);E#11;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]},(letrec {X#21=C#20[(var X#3)];E#23} in [.])],
             ((var X#16),(letrec {X#21=C#20[[.]];E#23} in S#12)),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=(var X#3);EE#18[[.1],(var X#16)];EE#19[X#3,[.2]]},
           X#2          |->  X#16,
           X#1          |->  X#8,
           E#4          |->  {E#11;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]},
           C#7          |->  (letrec {X#21=C#20;E#23} in S#12),
           E#10         |->  {X#21=C#20[(var X#3)];E#23},
           E#22         |->  {E#23},
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#8=(letrec {X#21=C#20[(var X#3)];E#23} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#8=(letrec {X#21=C#20[(var X#16)];E#23} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#8=(letrec {X#21=C#20[(var X#3)];E#23} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#21=C#20[(var X#3)];X#8=S#12;E#11;E#23;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#16)]
       ;X#16= (var X#3)
       ;X#8= (letrec {E#10} in S#12)
       ;E#20
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#16= (var X#3)
       ;X#8= S#12
       ;E#10
       ;E#20
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#16),C#7),
             ((var X#3),C#7),
             ((var X#8),(letrec {X#1=C#7[(var X#3)];X#16=(var X#3);E#10;E#20;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#1=C#7[(var X#3)];X#16=(var X#3);E#20;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#16),C#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=(var X#3);EE#18[[.1],(var X#16)];EE#19[X#3,[.2]]},
           X#2          |->  X#16,
           E#11         |->  {X#1=C#7[(var X#3)];E#20},
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#20;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]},
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#16=(var X#3);X#8=(letrec {E#10} in S#12);E#20;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#16)];X#16=(var X#3);X#8=(letrec {E#10} in S#12);E#20;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#16=(var X#3);X#8=(letrec {E#10} in S#12);E#20;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#1=C#7[(var X#3)];X#16=(var X#3);X#8=S#12;E#10;E#20;EE#18[X#9,(var X#16)];EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= A#21[(app A#22[(var X#16)] C#23[(var X#16)])]
       ;E#11
       ;EE#19[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#8= S#12
       ;X#9= A#21[(app A#22[(var X#16)] C#23[(var X#3)])]
       ;E#10
       ;E#11
       ;EE#19[X#3,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#21[(app A#22[(var X#16)] C#23)]),
             ((var X#3),A#21[(app A#22[(var X#16)] C#23)]),
             ((var X#8),(letrec {X#16=(var X#3);X#9=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];E#10;E#11;EE#19[X#3,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=(var X#3);X#9=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];E#11;EE#19[X#3,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#16),A#21[(app A#22[(var X#16)] C#23[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=(var X#3);[.1]=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];EE#19[X#3,[.2]]},
           X#2          |->  X#16,
           EE#18[.1,.2] |-> {[.1]=A#21[(app A#22[[.2]] C#23[(var X#3)])]},
           X#1          |->  X#9,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#19[X#3,(var X#8)]},
           C#7          |->  A#21[(app A#22[(var X#16)] C#23)],
           A#20         |->  A#21[(app A#22 C#23[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#8=(letrec {E#10} in S#12);X#9=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];E#11;EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#8=(letrec {E#10} in S#12);X#9=A#21[(app A#22[(var X#16)] C#23[(var X#16)])];E#11;EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#8=(letrec {E#10} in S#12);X#9=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];E#11;EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#8=S#12;X#9=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];E#10;E#11;EE#19[X#3,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= A#23[(app A#24[(var X#21)] C#25[(var X#16)])]
       ;E#11
       ;EE#19[X#3,(var X#8)]
       ;EE#22[X#21,(var X#16)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#8= S#12
       ;X#9= A#23[(app A#24[(var X#21)] C#25[(var X#3)])]
       ;E#10
       ;E#11
       ;EE#19[X#3,(var X#8)]
       ;EE#22[X#21,(var X#16)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#23[(app A#24[(var X#21)] C#25)]),
             ((var X#3),A#23[(app A#24[(var X#21)] C#25)]),
             ((var X#8),(letrec {X#16=(var X#3);X#9=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#10;E#11;EE#19[X#3,(var X#8)];EE#22[X#21,(var X#16)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=(var X#3);X#9=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#11;EE#19[X#3,(var X#8)];EE#22[X#21,(var X#16)]},(letrec {E#10} in [.])],
             ((var X#16),A#23[(app A#24[(var X#21)] C#25[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=(var X#3);[.1]=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];EE#19[X#3,[.2]];EE#22[X#21,(var X#16)]},
           X#2          |->  X#16,
           EE#18[.1,.2] |-> {[.1]=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];EE#22[X#21,[.2]]},
           X#1          |->  X#9,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#19[X#3,(var X#8)];EE#22[X#21,(var X#16)]},
           C#7          |->  A#23[(app A#24[(var X#21)] C#25)],
           A#20         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#8=(letrec {E#10} in S#12);X#9=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#11;EE#19[X#3,(var X#8)];EE#22[X#21,(var X#16)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#8=(letrec {E#10} in S#12);X#9=A#23[(app A#24[(var X#21)] C#25[(var X#16)])];E#11;EE#19[X#3,(var X#8)];EE#22[X#21,(var X#16)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#8=(letrec {E#10} in S#12);X#9=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#11;EE#19[X#3,(var X#8)];EE#22[X#21,(var X#16)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#8=S#12;X#9=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#10;E#11;EE#19[X#3,(var X#8)];EE#22[X#21,(var X#16)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#25[(app A#26[(var X#22)] C#27[(var X#16)])]
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#19[X#3,(var X#8)]
       ;EE#23[X#9,(var X#21)]
       ;EE#24[X#22,(var X#16)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#25[(app A#26[(var X#22)] C#27[(var X#3)])]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#19[X#3,(var X#8)]
       ;EE#23[X#9,(var X#21)]
       ;EE#24[X#22,(var X#16)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#25[(app A#26[(var X#22)] C#27)]),
             ((var X#3),A#25[(app A#26[(var X#22)] C#27)]),
             ((var X#8),(letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#10;E#11;EE#19[X#3,(var X#8)];EE#23[X#9,(var X#21)];EE#24[X#22,(var X#16)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#11;EE#19[X#3,(var X#8)];EE#23[X#9,(var X#21)];EE#24[X#22,(var X#16)]},(letrec {E#10} in [.])],
             ((var X#16),A#25[(app A#26[(var X#22)] C#27[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];EE#19[X#3,[.2]];EE#23[[.1],(var X#21)];EE#24[X#22,(var X#16)]},
           X#2          |->  X#16,
           EE#18[.1,.2] |-> {X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];EE#23[[.1],(var X#21)];EE#24[X#22,[.2]]},
           X#1          |->  X#21,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#19[X#3,(var X#8)];EE#23[X#9,(var X#21)];EE#24[X#22,(var X#16)]},
           C#7          |->  A#25[(app A#26[(var X#22)] C#27)],
           A#20         |->  A#25[(app A#26 C#27[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];X#8=(letrec {E#10} in S#12);E#11;EE#19[X#3,(var X#8)];EE#23[X#9,(var X#21)];EE#24[X#22,(var X#16)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#16)])];X#8=(letrec {E#10} in S#12);E#11;EE#19[X#3,(var X#8)];EE#23[X#9,(var X#21)];EE#24[X#22,(var X#16)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];X#8=(letrec {E#10} in S#12);E#11;EE#19[X#3,(var X#8)];EE#23[X#9,(var X#21)];EE#24[X#22,(var X#16)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];X#8=S#12;E#10;E#11;EE#19[X#3,(var X#8)];EE#23[X#9,(var X#21)];EE#24[X#22,(var X#16)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app A#24[(var X#16)] C#25[(var X#16)])]
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#19[X#3,(var X#8)]
       ;EE#22[X#9,(var X#21)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app A#24[(var X#16)] C#25[(var X#3)])]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#19[X#3,(var X#8)]
       ;EE#22[X#9,(var X#21)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#23[(app A#24[(var X#16)] C#25)]),
             ((var X#3),A#23[(app A#24[(var X#16)] C#25)]),
             ((var X#8),(letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#3)])];E#10;E#11;EE#19[X#3,(var X#8)];EE#22[X#9,(var X#21)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#3)])];E#11;EE#19[X#3,(var X#8)];EE#22[X#9,(var X#21)]},(letrec {E#10} in [.])],
             ((var X#16),A#23[(app A#24[(var X#16)] C#25[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#3)])];EE#19[X#3,[.2]];EE#22[[.1],(var X#21)]},
           X#2          |->  X#16,
           EE#18[.1,.2] |-> {X#21=A#23[(app A#24[[.2]] C#25[(var X#3)])];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#19[X#3,(var X#8)];EE#22[X#9,(var X#21)]},
           C#7          |->  A#23[(app A#24[(var X#16)] C#25)],
           A#20         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#3)])];X#8=(letrec {E#10} in S#12);E#11;EE#19[X#3,(var X#8)];EE#22[X#9,(var X#21)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#16)])];X#8=(letrec {E#10} in S#12);E#11;EE#19[X#3,(var X#8)];EE#22[X#9,(var X#21)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#3)])];X#8=(letrec {E#10} in S#12);E#11;EE#19[X#3,(var X#8)];EE#22[X#9,(var X#21)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#3)])];X#8=S#12;E#10;E#11;EE#19[X#3,(var X#8)];EE#22[X#9,(var X#21)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(app A#22[(var X#8)] C#23[(var X#16)])]
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#18[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(app A#22[(var X#8)] C#23[(var X#3)])]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#18[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#21[(app A#22[(var X#8)] C#23)]),
             ((var X#3),A#21[(app A#22[(var X#8)] C#23)]),
             ((var X#8),(letrec {X#16=(var X#3);X#3=A#21[(app A#22[(var X#8)] C#23[(var X#3)])];E#10;E#11;EE#18[X#9,(var X#16)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=(var X#3);X#3=A#21[(app A#22[(var X#8)] C#23[(var X#3)])];E#11;EE#18[X#9,(var X#16)]},(letrec {E#10} in [.])],
             ((var X#16),A#21[(app A#22[(var X#8)] C#23[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=A#21[(app A#22[[.2]] C#23[(var X#3)])];EE#18[[.1],(var X#16)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=A#21[(app A#22[[.2]] C#23[(var X#3)])]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)]},
           C#7          |->  A#21[(app A#22[(var X#8)] C#23)],
           A#20         |->  A#21[(app A#22 C#23[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=A#21[(app A#22[(var X#8)] C#23[(var X#3)])];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=A#21[(app A#22[(var X#8)] C#23[(var X#16)])];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=A#21[(app A#22[(var X#8)] C#23[(var X#3)])];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#3=A#21[(app A#22[(var X#8)] C#23[(var X#3)])];X#8=S#12;E#10;E#11;EE#18[X#9,(var X#16)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= A#23[(app A#24[(var X#21)] C#25[(var X#16)])]
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#22[X#21,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= A#23[(app A#24[(var X#21)] C#25[(var X#3)])]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#22[X#21,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#23[(app A#24[(var X#21)] C#25)]),
             ((var X#3),A#23[(app A#24[(var X#21)] C#25)]),
             ((var X#8),(letrec {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#10;E#11;EE#18[X#9,(var X#16)];EE#22[X#21,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#11;EE#18[X#9,(var X#16)];EE#22[X#21,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#16),A#23[(app A#24[(var X#21)] C#25[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];EE#18[[.1],(var X#16)];EE#22[X#21,[.2]]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];EE#22[X#21,[.2]]},
           X#1          |->  X#3,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#22[X#21,(var X#8)]},
           C#7          |->  A#23[(app A#24[(var X#21)] C#25)],
           A#20         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#22[X#21,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#16)])];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#22[X#21,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#22[X#21,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];X#8=S#12;E#10;E#11;EE#18[X#9,(var X#16)];EE#22[X#21,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#25[(app A#26[(var X#22)] C#27[(var X#16)])]
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#23[X#3,(var X#21)]
       ;EE#24[X#22,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#25[(app A#26[(var X#22)] C#27[(var X#3)])]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#23[X#3,(var X#21)]
       ;EE#24[X#22,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#25[(app A#26[(var X#22)] C#27)]),
             ((var X#3),A#25[(app A#26[(var X#22)] C#27)]),
             ((var X#8),(letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#10;E#11;EE#18[X#9,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#11;EE#18[X#9,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#16),A#25[(app A#26[(var X#22)] C#27[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];EE#18[[.1],(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,[.2]]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];EE#23[[.1],(var X#21)];EE#24[X#22,[.2]]},
           X#1          |->  X#21,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(var X#8)]},
           C#7          |->  A#25[(app A#26[(var X#22)] C#27)],
           A#20         |->  A#25[(app A#26 C#27[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(var X#8)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#16)])];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];X#8=S#12;E#10;E#11;EE#18[X#9,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app A#24[(var X#8)] C#25[(var X#16)])]
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app A#24[(var X#8)] C#25[(var X#3)])]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#23[(app A#24[(var X#8)] C#25)]),
             ((var X#3),A#23[(app A#24[(var X#8)] C#25)]),
             ((var X#8),(letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#8)] C#25[(var X#3)])];E#10;E#11;EE#18[X#9,(var X#16)];EE#22[X#3,(var X#21)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=(var X#3);X#21=A#23[(app A#24[(var X#8)] C#25[(var X#3)])];E#11;EE#18[X#9,(var X#16)];EE#22[X#3,(var X#21)]},(letrec {E#10} in [.])],
             ((var X#16),A#23[(app A#24[(var X#8)] C#25[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#23[(app A#24[[.2]] C#25[(var X#3)])];EE#18[[.1],(var X#16)];EE#22[X#3,(var X#21)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=A#23[(app A#24[[.2]] C#25[(var X#3)])];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#22[X#3,(var X#21)]},
           C#7          |->  A#23[(app A#24[(var X#8)] C#25)],
           A#20         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#8)] C#25[(var X#3)])];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#8)] C#25[(var X#16)])];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#8)] C#25[(var X#3)])];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#8)] C#25[(var X#3)])];X#8=S#12;E#10;E#11;EE#18[X#9,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= (letrec {E#10} in C#18[(var X#16)])
       ;E#11
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= C#18[(var X#3)]
       ;E#10
       ;E#11
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),(letrec {E#10} in C#18)),
             ((var X#3),(letrec {E#10} in C#18)),
             ((var X#3),(letrec {X#16=(var X#3);E#10;E#11;EE#17[X#9,(var X#16)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=(var X#3);E#11;EE#17[X#9,(var X#16)]},(letrec {E#10} in [.])],
             ((var X#16),(letrec {E#10} in C#18[[.]])),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#2          |->  X#16,
           X#1          |->  X#3,
           E#4          |->  {E#11;EE#17[X#9,(var X#16)]},
           C#7          |->  (letrec {E#10} in C#18),
           S#12         |->  C#18[(var X#3)],
           A#15         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=(letrec {E#10} in C#18[(var X#3)]);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=(letrec {E#10} in C#18[(var X#16)]);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=(letrec {E#10} in C#18[(var X#3)]);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#3=C#18[(var X#3)];E#10;E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= (letrec {X#19=C#18[(var X#16)];E#21} in S#12)
       ;E#11
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#19= C#18[(var X#3)]
       ;X#3= S#12
       ;E#11
       ;E#21
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),(letrec {X#19=C#18;E#21} in S#12)),
             ((var X#3),(letrec {X#19=C#18;E#21} in S#12)),
             ((var X#3),(letrec {X#16=(var X#3);X#19=C#18[(var X#3)];E#11;E#21;EE#17[X#9,(var X#16)]} in [.])),
             (A#13[(var X#9)],(letrec {X#19=C#18[(var X#3)];E#21} in [.])),
             [{X#16=(var X#3);E#11;EE#17[X#9,(var X#16)]},(letrec {X#19=C#18[(var X#3)];E#21} in [.])],
             ((var X#16),(letrec {X#19=C#18[[.]];E#21} in S#12)),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#2          |->  X#16,
           X#1          |->  X#3,
           E#4          |->  {E#11;EE#17[X#9,(var X#16)]},
           C#7          |->  (letrec {X#19=C#18;E#21} in S#12),
           E#10         |->  {X#19=C#18[(var X#3)];E#21},
           E#20         |->  {E#21},
           A#15         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=(letrec {X#19=C#18[(var X#3)];E#21} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=(letrec {X#19=C#18[(var X#16)];E#21} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=(letrec {X#19=C#18[(var X#3)];E#21} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#19=C#18[(var X#3)];X#3=S#12;E#11;E#21;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#16)]
       ;X#16= (var X#3)
       ;X#3= (letrec {E#10} in S#12)
       ;E#18
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#16= (var X#3)
       ;X#3= S#12
       ;E#10
       ;E#18
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#16),C#7),
             ((var X#3),C#7),
             ((var X#3),(letrec {X#1=C#7[(var X#3)];X#16=(var X#3);E#10;E#18;EE#17[X#9,(var X#16)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#1=C#7[(var X#3)];X#16=(var X#3);E#18;EE#17[X#9,(var X#16)]},(letrec {E#10} in [.])],
             ((var X#16),C#7[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#2          |->  X#16,
           E#11         |->  {X#1=C#7[(var X#3)];E#18},
           E#4          |->  {X#3=(letrec {E#10} in S#12);E#18;EE#17[X#9,(var X#16)]},
           A#15         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#16=(var X#3);X#3=(letrec {E#10} in S#12);E#18;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#16)];X#16=(var X#3);X#3=(letrec {E#10} in S#12);E#18;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#16=(var X#3);X#3=(letrec {E#10} in S#12);E#18;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#1=C#7[(var X#3)];X#16=(var X#3);X#3=S#12;E#10;E#18;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= (letrec {E#10} in S#12)
       ;X#9= A#19[(app A#20[(var X#16)] C#21[(var X#16)])]
       ;E#11
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= S#12
       ;X#9= A#19[(app A#20[(var X#16)] C#21[(var X#3)])]
       ;E#10
       ;E#11
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#19[(app A#20[(var X#16)] C#21)]),
             ((var X#3),A#19[(app A#20[(var X#16)] C#21)]),
             ((var X#3),(letrec {X#16=(var X#3);X#9=A#19[(app A#20[(var X#16)] C#21[(var X#3)])];E#10;E#11} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=(var X#3);X#9=A#19[(app A#20[(var X#16)] C#21[(var X#3)])];E#11},(letrec {E#10} in [.])],
             ((var X#16),A#19[(app A#20[(var X#16)] C#21[[.]])]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=[.2];[.1]=A#19[(app A#20[(var X#16)] C#21[(var X#3)])]},
           X#2          |->  X#16,
           EE#17[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] C#21[(var X#3)])]},
           X#1          |->  X#9,
           E#4          |->  {X#3=(letrec {E#10} in S#12);E#11},
           C#7          |->  A#19[(app A#20[(var X#16)] C#21)],
           A#18         |->  A#19[(app A#20 C#21[(var X#3)])],
           A#15         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=(letrec {E#10} in S#12);X#9=A#19[(app A#20[(var X#16)] C#21[(var X#3)])];E#11} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=(letrec {E#10} in S#12);X#9=A#19[(app A#20[(var X#16)] C#21[(var X#16)])];E#11} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=(letrec {E#10} in S#12);X#9=A#19[(app A#20[(var X#16)] C#21[(var X#3)])];E#11} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#3=S#12;X#9=A#19[(app A#20[(var X#16)] C#21[(var X#3)])];E#10;E#11} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= (letrec {E#10} in S#12)
       ;X#9= A#21[(app A#22[(var X#19)] C#23[(var X#16)])]
       ;E#11
       ;EE#20[X#19,(var X#16)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= S#12
       ;X#9= A#21[(app A#22[(var X#19)] C#23[(var X#3)])]
       ;E#10
       ;E#11
       ;EE#20[X#19,(var X#16)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#21[(app A#22[(var X#19)] C#23)]),
             ((var X#3),A#21[(app A#22[(var X#19)] C#23)]),
             ((var X#3),(letrec {X#16=(var X#3);X#9=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];E#10;E#11;EE#20[X#19,(var X#16)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=(var X#3);X#9=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];E#11;EE#20[X#19,(var X#16)]},(letrec {E#10} in [.])],
             ((var X#16),A#21[(app A#22[(var X#19)] C#23[[.]])]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=[.2];[.1]=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];EE#20[X#19,(var X#16)]},
           X#2          |->  X#16,
           EE#17[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];EE#20[X#19,[.2]]},
           X#1          |->  X#9,
           E#4          |->  {X#3=(letrec {E#10} in S#12);E#11;EE#20[X#19,(var X#16)]},
           C#7          |->  A#21[(app A#22[(var X#19)] C#23)],
           A#18         |->  A#21[(app A#22 C#23[(var X#3)])],
           A#15         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=(letrec {E#10} in S#12);X#9=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];E#11;EE#20[X#19,(var X#16)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=(letrec {E#10} in S#12);X#9=A#21[(app A#22[(var X#19)] C#23[(var X#16)])];E#11;EE#20[X#19,(var X#16)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=(letrec {E#10} in S#12);X#9=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];E#11;EE#20[X#19,(var X#16)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#3=S#12;X#9=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];E#10;E#11;EE#20[X#19,(var X#16)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#19= A#23[(app A#24[(var X#20)] C#25[(var X#16)])]
       ;X#3= (letrec {E#10} in S#12)
       ;E#11
       ;EE#21[X#9,(var X#19)]
       ;EE#22[X#20,(var X#16)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#19= A#23[(app A#24[(var X#20)] C#25[(var X#3)])]
       ;X#3= S#12
       ;E#10
       ;E#11
       ;EE#21[X#9,(var X#19)]
       ;EE#22[X#20,(var X#16)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#23[(app A#24[(var X#20)] C#25)]),
             ((var X#3),A#23[(app A#24[(var X#20)] C#25)]),
             ((var X#3),(letrec {X#16=(var X#3);X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];E#10;E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#16)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=(var X#3);X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#16)]},(letrec {E#10} in [.])],
             ((var X#16),A#23[(app A#24[(var X#20)] C#25[[.]])]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=[.2];X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];EE#21[[.1],(var X#19)];EE#22[X#20,(var X#16)]},
           X#2          |->  X#16,
           EE#17[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#1          |->  X#19,
           E#4          |->  {X#3=(letrec {E#10} in S#12);E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#16)]},
           C#7          |->  A#23[(app A#24[(var X#20)] C#25)],
           A#18         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];X#3=(letrec {E#10} in S#12);E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#16)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#19=A#23[(app A#24[(var X#20)] C#25[(var X#16)])];X#3=(letrec {E#10} in S#12);E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#16)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];X#3=(letrec {E#10} in S#12);E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#16)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];X#3=S#12;E#10;E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#16)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#19= A#21[(app A#22[(var X#16)] C#23[(var X#16)])]
       ;X#3= (letrec {E#10} in S#12)
       ;E#11
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#19= A#21[(app A#22[(var X#16)] C#23[(var X#3)])]
       ;X#3= S#12
       ;E#10
       ;E#11
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#21[(app A#22[(var X#16)] C#23)]),
             ((var X#3),A#21[(app A#22[(var X#16)] C#23)]),
             ((var X#3),(letrec {X#16=(var X#3);X#19=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];E#10;E#11;EE#20[X#9,(var X#19)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=(var X#3);X#19=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];E#11;EE#20[X#9,(var X#19)]},(letrec {E#10} in [.])],
             ((var X#16),A#21[(app A#22[(var X#16)] C#23[[.]])]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#3),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),C#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=[.2];X#19=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];EE#20[[.1],(var X#19)]},
           X#2          |->  X#16,
           EE#17[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] C#23[(var X#3)])];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {X#3=(letrec {E#10} in S#12);E#11;EE#20[X#9,(var X#19)]},
           C#7          |->  A#21[(app A#22[(var X#16)] C#23)],
           A#18         |->  A#21[(app A#22 C#23[(var X#3)])],
           A#15         |->  [.],
           X#8          |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#19=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];X#3=(letrec {E#10} in S#12);E#11;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#19=A#21[(app A#22[(var X#16)] C#23[(var X#16)])];X#3=(letrec {E#10} in S#12);E#11;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#19=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];X#3=(letrec {E#10} in S#12);E#11;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=(var X#3);X#19=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];X#3=S#12;E#10;E#11;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     A#12[(app (letrec {E#8} in T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#9)]
    ,
     A#12[(letrec
              E#8
           in
              (app T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#9)
           )]
  )

where

   Delta1 = {T#14,T#13,A#11,T#6,A#12}
   Delta2 = {E#8}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#9,(letrec {E#8} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#9,(letrec {E#8} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {A#11  |->  A#12,
           T#6   |->  A#12[(app (letrec {E#8} in T#15) S#9)],
           T#13  |->  (app (letrec {E#8} in T#15) S#9),
           T#14  |->  (letrec {E#8} in T#15),
           S#10  |->  T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  A#12[(app (letrec {E#8} in T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#9)]
    -cpx-e1->                     A#12[(app (letrec {E#8} in T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#9)]
    ................................................................................
                                  A#12[(app (letrec {E#8} in T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#9)]
    -SR,lapp1->                   A#12[(letrec {E#8} in (app T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#9))]
    

================================================================================
Critical Pair:

  (
     A#12[(app (letrec
                   X#16= T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
                  ;E#18
                in
                   S#10
                ) S#9)]
    ,
     A#12[(letrec
              X#16= T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
             ;E#18
           in
              (app S#10 S#9)
           )]
  )

where

   Delta1 = {T#14,T#13,A#11,T#6,A#12}
   Delta2 = {E#8}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#9,(letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#9,(letrec {E#8} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {A#11  |->  A#12,
           T#6   |->  A#12[(app (letrec {X#16=T#15;E#18} in S#10) S#9)],
           T#13  |->  (app (letrec {X#16=T#15;E#18} in S#10) S#9),
           T#14  |->  (letrec {X#16=T#15;E#18} in S#10),
           E#8   |->  {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  A#12[(app (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18} in S#10) S#9)]
    -cpx-e1->                     A#12[(app (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#18} in S#10) S#9)]
    ................................................................................
                                  A#12[(app (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18} in S#10) S#9)]
    -SR,lapp1->                   A#12[(letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18} in (app S#10 S#9))]
    

================================================================================
Critical Pair:

  (
     A#12[(app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#16} in S#10) S#9)]
    ,
     A#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16} in (app S#10 S#9))]
  )

where

   Delta1 = {T#13,A#11,T#6,A#12}
   Delta2 = {E#8}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#9,(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#9,(letrec {E#8} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {A#11  |->  A#12,
           T#6   |->  A#12[(app [.] S#9)],
           T#13  |->  (app [.] S#9),
           T#14  |->  [.],
           S#5   |->  S#10,
           E#8   |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#16},
           E#15  |->  {X#1=C#7[(var X#3)];E#16},
           E#4   |->  {E#16}}

and instantiated rules:

                                  A#12[(app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16} in S#10) S#9)]
    -cpx-e1->                     A#12[(app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#16} in S#10) S#9)]
    ................................................................................
                                  A#12[(app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16} in S#10) S#9)]
    -SR,lapp1->                   A#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16} in (app S#10 S#9))]
    

================================================================================
Critical Pair:

  (
     A#12[(app (letrec {E#8} in S#10) T#14[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
    ,
     A#12[(letrec
              E#8
           in
              (app S#10 T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])
           )]
  )

where

   Delta1 = {T#13,A#11,T#6,A#12}
   Delta2 = {E#8}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {E#8} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#9,(letrec {E#8} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {A#11  |->  A#12,
           T#6   |->  A#12[(app (letrec {E#8} in S#10) T#14)],
           T#13  |->  (app (letrec {E#8} in S#10) T#14),
           S#9   |->  T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  A#12[(app (letrec {E#8} in S#10) T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
    -cpx-e1->                     A#12[(app (letrec {E#8} in S#10) T#14[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
    ................................................................................
                                  A#12[(app (letrec {E#8} in S#10) T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
    -SR,lapp1->                   A#12[(letrec {E#8} in (app S#10 T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]))]
    

================================================================================
Critical Pair:

  (
     A#12[(app A#13[(app (letrec {E#8} in S#10) S#9)] T#14[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
    ,
     A#12[(app A#13[(letrec {E#8} in (app S#10 S#9))] T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
  )

where

   Delta1 = {A#11,T#6}
   Delta2 = {E#8}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#9,(letrec {E#8} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#9,(letrec {E#8} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  A#12[(app A#13[(app (letrec {E#8} in S#10) S#9)] T#14)],
           A#11  |->  A#12[(app A#13 T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  A#12[(app A#13[(app (letrec {E#8} in S#10) S#9)] T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
    -cpx-e1->                     A#12[(app A#13[(app (letrec {E#8} in S#10) S#9)] T#14[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
    ................................................................................
                                  A#12[(app A#13[(app (letrec {E#8} in S#10) S#9)] T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
    -SR,lapp1->                   A#12[(app A#13[(letrec {E#8} in (app S#10 S#9))] T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#8} in T#13[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#9)
    ,
     (letrec
        E#8
     in
        (app T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#9)
     )
  )

where

   Delta1 = {T#12,T#6}
   Delta2 = {E#8}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#9,(letrec {E#8} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#9,(letrec {E#8} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {A#11  |->  [.],
           T#6   |->  (app (letrec {E#8} in T#13) S#9),
           T#12  |->  (letrec {E#8} in T#13),
           S#10  |->  T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (app (letrec {E#8} in T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#9)
    -cpx-e1->                     (app (letrec {E#8} in T#13[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#9)
    ................................................................................
                                  (app (letrec {E#8} in T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#9)
    -SR,lapp1->                   (letrec {E#8} in (app T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#9))
    

================================================================================
Critical Pair:

  (
     (app (letrec
             X#14= T#13[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
            ;E#16
          in
             S#10
          ) S#9)
    ,
     (letrec
        X#14= T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;E#16
     in
        (app S#10 S#9)
     )
  )

where

   Delta1 = {T#12,T#6}
   Delta2 = {E#8}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#9,(letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#9,(letrec {E#8} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {A#11  |->  [.],
           T#6   |->  (app (letrec {X#14=T#13;E#16} in S#10) S#9),
           T#12  |->  (letrec {X#14=T#13;E#16} in S#10),
           E#8   |->  {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (app (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16} in S#10) S#9)
    -cpx-e1->                     (app (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#16} in S#10) S#9)
    ................................................................................
                                  (app (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16} in S#10) S#9)
    -SR,lapp1->                   (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16} in (app S#10 S#9))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#14} in S#10) S#9)
    ,
     (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#14} in (app S#10 S#9))
  )

where

   Delta1 = {T#6}
   Delta2 = {E#8}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#9,(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#14} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#9,(letrec {E#8} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {A#11  |->  [.],
           T#6   |->  (app [.] S#9),
           T#12  |->  [.],
           S#5   |->  S#10,
           E#8   |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#14},
           E#13  |->  {X#1=C#7[(var X#3)];E#14},
           E#4   |->  {E#14}}

and instantiated rules:

                                  (app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#14} in S#10) S#9)
    -cpx-e1->                     (app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#14} in S#10) S#9)
    ................................................................................
                                  (app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#14} in S#10) S#9)
    -SR,lapp1->                   (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#14} in (app S#10 S#9))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#8} in S#10) T#12[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])
    ,
     (letrec
        E#8
     in
        (app S#10 T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#8}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {E#8} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#9,(letrec {E#8} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {A#11  |->  [.],
           T#6   |->  (app (letrec {E#8} in S#10) T#12),
           S#9   |->  T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (app (letrec {E#8} in S#10) T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])
    -cpx-e1->                     (app (letrec {E#8} in S#10) T#12[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])
    ................................................................................
                                  (app (letrec {E#8} in S#10) T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])
    -SR,lapp1->                   (letrec {E#8} in (app S#10 T#12[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#14[(app (letrec {E#9} in T#17[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#10)]
     )
    ,
     (letrec
        E#8
     in
        A#14[(letrec
                 E#9
              in
                 (app T#17[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#10)
              )]
     )
  )

where

   Delta1 = {T#16,T#15,A#12,T#13,T#6,A#14}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#10,(letrec {E#9} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(letrec {E#9} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in A#14[(app (letrec {E#9} in T#17) S#10)]),
           A#12  |->  A#14,
           T#13  |->  A#14[(app (letrec {E#9} in T#17) S#10)],
           T#15  |->  (app (letrec {E#9} in T#17) S#10),
           T#16  |->  (letrec {E#9} in T#17),
           S#11  |->  T#17[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {E#8} in A#14[(app (letrec {E#9} in T#17[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#10)])
    -cpx-e1->                     (letrec {E#8} in A#14[(app (letrec {E#9} in T#17[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#10)])
    ................................................................................
                                  (letrec {E#8} in A#14[(app (letrec {E#9} in T#17[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#14[(letrec {E#9} in (app T#17[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#10))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#14[(app (letrec
                      X#18= T#17[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
                     ;E#20
                   in
                      S#11
                   ) S#10)]
     )
    ,
     (letrec
        E#8
     in
        A#14[(letrec
                 X#18= T#17[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
                ;E#20
              in
                 (app S#11 S#10)
              )]
     )
  )

where

   Delta1 = {T#16,T#15,A#12,T#13,T#6,A#14}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#10,(letrec {X#18=T#17[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#20} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(letrec {E#9} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in A#14[(app (letrec {X#18=T#17;E#20} in S#11) S#10)]),
           A#12  |->  A#14,
           T#13  |->  A#14[(app (letrec {X#18=T#17;E#20} in S#11) S#10)],
           T#15  |->  (app (letrec {X#18=T#17;E#20} in S#11) S#10),
           T#16  |->  (letrec {X#18=T#17;E#20} in S#11),
           E#9   |->  {X#18=T#17[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#20},
           E#19  |->  {E#20}}

and instantiated rules:

                                  (letrec {E#8} in A#14[(app (letrec {X#18=T#17[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#20} in S#11) S#10)])
    -cpx-e1->                     (letrec {E#8} in A#14[(app (letrec {X#18=T#17[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#20} in S#11) S#10)])
    ................................................................................
                                  (letrec {E#8} in A#14[(app (letrec {X#18=T#17[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#20} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#14[(letrec {X#18=T#17[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#20} in (app S#11 S#10))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#14[(app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#18} in S#11) S#10)]
     )
    ,
     (letrec
        E#8
     in
        A#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#18} in (app S#11 S#10))]
     )
  )

where

   Delta1 = {T#15,A#12,T#13,T#6,A#14}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#10,(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#18} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(letrec {E#9} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in A#14[(app [.] S#10)]),
           A#12  |->  A#14,
           T#13  |->  A#14[(app [.] S#10)],
           T#15  |->  (app [.] S#10),
           T#16  |->  [.],
           S#5   |->  S#11,
           E#9   |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#18},
           E#17  |->  {X#1=C#7[(var X#3)];E#18},
           E#4   |->  {E#18}}

and instantiated rules:

                                  (letrec {E#8} in A#14[(app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#18} in S#11) S#10)])
    -cpx-e1->                     (letrec {E#8} in A#14[(app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#18} in S#11) S#10)])
    ................................................................................
                                  (letrec {E#8} in A#14[(app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#18} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#18} in (app S#11 S#10))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#14[(app (letrec {E#9} in S#11) T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
     )
    ,
     (letrec
        E#8
     in
        A#14[(letrec
                 E#9
              in
                 (app S#11 T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])
              )]
     )
  )

where

   Delta1 = {T#15,A#12,T#13,T#6,A#14}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {E#9} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(letrec {E#9} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in A#14[(app (letrec {E#9} in S#11) T#16)]),
           A#12  |->  A#14,
           T#13  |->  A#14[(app (letrec {E#9} in S#11) T#16)],
           T#15  |->  (app (letrec {E#9} in S#11) T#16),
           S#10  |->  T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {E#8} in A#14[(app (letrec {E#9} in S#11) T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -cpx-e1->                     (letrec {E#8} in A#14[(app (letrec {E#9} in S#11) T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])])
    ................................................................................
                                  (letrec {E#8} in A#14[(app (letrec {E#9} in S#11) T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -SR,lapp2->                   (letrec {E#8} in A#14[(letrec {E#9} in (app S#11 T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#14[(app A#15[(app (letrec {E#9} in S#11) S#10)] T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
     )
    ,
     (letrec
        E#8
     in
        A#14[(app A#15[(letrec {E#9} in (app S#11 S#10))] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#13,T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#10,(letrec {E#9} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(letrec {E#9} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in A#14[(app A#15[(app (letrec {E#9} in S#11) S#10)] T#16)]),
           T#13  |->  A#14[(app A#15[(app (letrec {E#9} in S#11) S#10)] T#16)],
           A#12  |->  A#14[(app A#15 T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {E#8} in A#14[(app A#15[(app (letrec {E#9} in S#11) S#10)] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -cpx-e1->                     (letrec {E#8} in A#14[(app A#15[(app (letrec {E#9} in S#11) S#10)] T#16[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])])
    ................................................................................
                                  (letrec {E#8} in A#14[(app A#15[(app (letrec {E#9} in S#11) S#10)] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -SR,lapp2->                   (letrec {E#8} in A#14[(app A#15[(letrec {E#9} in (app S#11 S#10))] T#16[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        (app (letrec {E#9} in T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#10)
     )
    ,
     (letrec
        E#8
     in
        (letrec
           E#9
        in
           (app T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#10)
        )
     )
  )

where

   Delta1 = {T#14,T#13,T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#10,(letrec {E#9} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(letrec {E#9} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in (app (letrec {E#9} in T#15) S#10)),
           A#12  |->  [.],
           T#13  |->  (app (letrec {E#9} in T#15) S#10),
           T#14  |->  (letrec {E#9} in T#15),
           S#11  |->  T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {E#8} in (app (letrec {E#9} in T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#10))
    -cpx-e1->                     (letrec {E#8} in (app (letrec {E#9} in T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#10))
    ................................................................................
                                  (letrec {E#8} in (app (letrec {E#9} in T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#10))
    -SR,lapp2->                   (letrec {E#8} in (letrec {E#9} in (app T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#10)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        (app (letrec
                X#16= T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
               ;E#18
             in
                S#11
             ) S#10)
     )
    ,
     (letrec
        E#8
     in
        (letrec
           X#16= T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
          ;E#18
        in
           (app S#11 S#10)
        )
     )
  )

where

   Delta1 = {T#14,T#13,T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#10,(letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(letrec {E#9} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in (app (letrec {X#16=T#15;E#18} in S#11) S#10)),
           A#12  |->  [.],
           T#13  |->  (app (letrec {X#16=T#15;E#18} in S#11) S#10),
           T#14  |->  (letrec {X#16=T#15;E#18} in S#11),
           E#9   |->  {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {E#8} in (app (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18} in S#11) S#10))
    -cpx-e1->                     (letrec {E#8} in (app (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#18} in S#11) S#10))
    ................................................................................
                                  (letrec {E#8} in (app (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18} in S#11) S#10))
    -SR,lapp2->                   (letrec {E#8} in (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18} in (app S#11 S#10)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        (app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#16} in S#11) S#10)
     )
    ,
     (letrec
        E#8
     in
        (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16} in (app S#11 S#10))
     )
  )

where

   Delta1 = {T#13,T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#10,(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(letrec {E#9} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in (app [.] S#10)),
           A#12  |->  [.],
           T#13  |->  (app [.] S#10),
           T#14  |->  [.],
           S#5   |->  S#11,
           E#9   |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#16},
           E#15  |->  {X#1=C#7[(var X#3)];E#16},
           E#4   |->  {E#16}}

and instantiated rules:

                                  (letrec {E#8} in (app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16} in S#11) S#10))
    -cpx-e1->                     (letrec {E#8} in (app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#16} in S#11) S#10))
    ................................................................................
                                  (letrec {E#8} in (app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16} in S#11) S#10))
    -SR,lapp2->                   (letrec {E#8} in (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16} in (app S#11 S#10)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        (app (letrec {E#9} in S#11) T#14[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])
     )
    ,
     (letrec
        E#8
     in
        (letrec
           E#9
        in
           (app S#11 T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])
        )
     )
  )

where

   Delta1 = {T#13,T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {E#9} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(letrec {E#9} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in (app (letrec {E#9} in S#11) T#14)),
           A#12  |->  [.],
           T#13  |->  (app (letrec {E#9} in S#11) T#14),
           S#10  |->  T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {E#8} in (app (letrec {E#9} in S#11) T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]))
    -cpx-e1->                     (letrec {E#8} in (app (letrec {E#9} in S#11) T#14[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]))
    ................................................................................
                                  (letrec {E#8} in (app (letrec {E#9} in S#11) T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]))
    -SR,lapp2->                   (letrec {E#8} in (letrec {E#9} in (app S#11 T#14[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
       ;E#16
     in
        A#12[(app (letrec {E#9} in S#11) S#10)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;E#16
     in
        A#12[(letrec {E#9} in (app S#11 S#10))]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#10,(letrec {E#9} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(letrec {E#9} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#14=T#13;E#16} in A#12[(app (letrec {E#9} in S#11) S#10)]),
           E#8   |->  {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -cpx-e1->                     (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#16} in A#12[(app (letrec {E#9} in S#11) S#10)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {X#14=T#13[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#16} in A#12[(letrec {E#9} in (app S#11 S#10))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#2)]
       ;X#2= (var X#3)
       ;E#14
     in
        A#12[(app (letrec {E#9} in S#11) S#10)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#2= (var X#3)
       ;E#14
     in
        A#12[(letrec {E#9} in (app S#11 S#10))]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#10,(letrec {E#9} in [.])),
             ((var X#2),C#7[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#10,(letrec {E#9} in [.])),((var X#2),C#7[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(app (letrec {E#9} in S#11) S#10)],
           E#8   |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#14},
           E#13  |->  {X#1=C#7[(var X#3)];E#14},
           E#4   |->  {E#14}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#14} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#14} in A#12[(app (letrec {E#9} in S#11) S#10)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#14} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#14} in A#12[(letrec {E#9} in (app S#11 S#10))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
       ;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]
     in
        A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
     )
    ,
     (letrec
        E#9
       ;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]
     in
        A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
     )
  )

where

   Delta1 = {A#13,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#16[(app A#17[[.]] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]),
             ((var X#8),A#16[(app A#17[[.]] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#8)] T#18)],
           A#13  |->  A#16[(app A#17 T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -cpx-e1->                     (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])])
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
       ;E#18
       ;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
       ;E#18
       ;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#16=T#15;E#18;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)]),
           E#9   |->  {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18},
           E#17  |->  {E#18;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]}}

and instantiated rules:

                                  (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#18;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=T#15[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#18;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#19[(app (letrec {E#10} in T#22[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#11)]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#19[(letrec
                      E#10
                   in
                      (app T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#11)
                   )]
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#21,T#20,A#18,T#15,T#6,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#19[(app (letrec {E#10} in T#22) S#11)];E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  A#19,
           T#15         |->  A#19[(app (letrec {E#10} in T#22) S#11)],
           T#20         |->  (app (letrec {E#10} in T#22) S#11),
           T#21         |->  (letrec {E#10} in T#22),
           S#12         |->  T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=A#19[(app (letrec {E#10} in T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#11)];E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#8=A#19[(app (letrec {E#10} in T#22[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#11)];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#19[(app (letrec {E#10} in T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#11)];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#19[(letrec {E#10} in (app T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#11))];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#19[(app (letrec
                           X#23= T#22[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
                          ;E#25
                        in
                           S#12
                        ) S#11)]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#19[(letrec
                      X#23= T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
                     ;E#25
                   in
                      (app S#12 S#11)
                   )]
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#21,T#20,A#18,T#15,T#6,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {X#23=T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#25} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#19[(app (letrec {X#23=T#22;E#25} in S#12) S#11)];E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  A#19,
           T#15         |->  A#19[(app (letrec {X#23=T#22;E#25} in S#12) S#11)],
           T#20         |->  (app (letrec {X#23=T#22;E#25} in S#12) S#11),
           T#21         |->  (letrec {X#23=T#22;E#25} in S#12),
           E#10         |->  {X#23=T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#25},
           E#24         |->  {E#25}}

and instantiated rules:

                                  (letrec {X#8=A#19[(app (letrec {X#23=T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#25} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#8=A#19[(app (letrec {X#23=T#22[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#25} in S#12) S#11)];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#19[(app (letrec {X#23=T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#25} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#19[(letrec {X#23=T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#25} in (app S#12 S#11))];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#19[(app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#23} in S#12) S#11)]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#23} in (app S#12 S#11))]
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#6,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#23} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#19[(app [.] S#11)];E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  A#19,
           T#15         |->  A#19[(app [.] S#11)],
           T#20         |->  (app [.] S#11),
           T#21         |->  [.],
           S#5          |->  S#12,
           E#10         |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#23},
           E#22         |->  {X#1=C#7[(var X#3)];E#23},
           E#4          |->  {E#23}}

and instantiated rules:

                                  (letrec {X#8=A#19[(app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#23} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#8=A#19[(app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#23} in S#12) S#11)];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#19[(app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#23} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#23} in (app S#12 S#11))];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#19[(app (letrec {E#10} in S#12) T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#19[(letrec
                      E#10
                   in
                      (app S#12 T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])
                   )]
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#6,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {E#10} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#19[(app (letrec {E#10} in S#12) T#21)];E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  A#19,
           T#15         |->  A#19[(app (letrec {E#10} in S#12) T#21)],
           T#20         |->  (app (letrec {E#10} in S#12) T#21),
           S#11         |->  T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=A#19[(app (letrec {E#10} in S#12) T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#8=A#19[(app (letrec {E#10} in S#12) T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#19[(app (letrec {E#10} in S#12) T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#19[(letrec {E#10} in (app S#12 T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]))];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#19[(app A#20[(letrec {E#10} in (app S#12 S#11))] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] T#21)];E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           T#15         |->  A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] T#21)],
           A#18         |->  A#19[(app A#20 T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#8=A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#19[(app A#20[(letrec {E#10} in (app S#12 S#11))] T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (app (letrec {E#10} in T#20[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#11)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= (letrec
                E#10
             in
                (app T#20[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#11)
             )
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#19,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=(app (letrec {E#10} in T#20) S#11);E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  [.],
           T#15         |->  (app (letrec {E#10} in T#20) S#11),
           T#19         |->  (letrec {E#10} in T#20),
           S#12         |->  T#20[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=(app (letrec {E#10} in T#20[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#11);E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#8=(app (letrec {E#10} in T#20[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#11);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (letrec {E#10} in T#20[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#11);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=(letrec {E#10} in (app T#20[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#11));E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (app (letrec
                     X#21= T#20[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
                    ;E#23
                  in
                     S#12
                  ) S#11)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= (letrec
                X#21= T#20[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
               ;E#23
             in
                (app S#12 S#11)
             )
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#19,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {X#21=T#20[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#23} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=(app (letrec {X#21=T#20;E#23} in S#12) S#11);E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  [.],
           T#15         |->  (app (letrec {X#21=T#20;E#23} in S#12) S#11),
           T#19         |->  (letrec {X#21=T#20;E#23} in S#12),
           E#10         |->  {X#21=T#20[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#23},
           E#22         |->  {E#23}}

and instantiated rules:

                                  (letrec {X#8=(app (letrec {X#21=T#20[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#23} in S#12) S#11);E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#8=(app (letrec {X#21=T#20[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#23} in S#12) S#11);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (letrec {X#21=T#20[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#23} in S#12) S#11);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=(letrec {X#21=T#20[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#23} in (app S#12 S#11));E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#21} in S#12) S#11)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#21} in (app S#12 S#11))
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#21} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=(app [.] S#11);E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  [.],
           T#15         |->  (app [.] S#11),
           T#19         |->  [.],
           S#5          |->  S#12,
           E#10         |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#21},
           E#20         |->  {X#1=C#7[(var X#3)];E#21},
           E#4          |->  {E#21}}

and instantiated rules:

                                  (letrec {X#8=(app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#21} in S#12) S#11);E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#8=(app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#21} in S#12) S#11);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#21} in S#12) S#11);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#21} in (app S#12 S#11));E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (app (letrec {E#10} in S#12) T#19[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= (letrec
                E#10
             in
                (app S#12 T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])
             )
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {E#10} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=(app (letrec {E#10} in S#12) T#19);E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  [.],
           T#15         |->  (app (letrec {E#10} in S#12) T#19),
           S#11         |->  T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=(app (letrec {E#10} in S#12) T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]);E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#8=(app (letrec {E#10} in S#12) T#19[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (letrec {E#10} in S#12) T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=(letrec {E#10} in (app S#12 T#19[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]));E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;E#9
       ;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;E#9
       ;EE#20[X#19,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#21[(app A#22[(var X#19)] T#23)];E#9;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];EE#20[X#19,[.2]]},
           X#16         |->  X#8,
           E#17         |->  {E#9;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]},
           T#15         |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];E#9;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9;EE#20[X#19,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;E#9
       ;EE#21[X#8,(var X#19)]
       ;EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;E#9
       ;EE#21[X#8,(var X#19)]
       ;EE#22[X#20,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];E#9;EE#21[X#8,(var X#19)];EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#21[X#8,(var X#19)];EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]},
           T#15         |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9;EE#21[X#8,(var X#19)];EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];E#9;EE#21[X#8,(var X#19)];EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9;EE#21[X#8,(var X#19)];EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9;EE#21[X#8,(var X#19)];EE#22[X#20,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app (letrec {E#10} in T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#11)]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(letrec
                       E#10
                    in
                       (app T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#11)
                    )]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#23,T#22,A#18,T#15,T#6,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app (letrec {E#10} in T#24) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  A#21,
           T#15         |->  A#21[(app (letrec {E#10} in T#24) S#11)],
           T#22         |->  (app (letrec {E#10} in T#24) S#11),
           T#23         |->  (letrec {E#10} in T#24),
           S#12         |->  T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app (letrec {E#10} in T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#21[(app (letrec {E#10} in T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app (letrec {E#10} in T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#21[(letrec {E#10} in (app T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#11))];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app (letrec
                            X#25= T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
                           ;E#27
                         in
                            S#12
                         ) S#11)]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(letrec
                       X#25= T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
                      ;E#27
                    in
                       (app S#12 S#11)
                    )]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#23,T#22,A#18,T#15,T#6,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {X#25=T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#27} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app (letrec {X#25=T#24;E#27} in S#12) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  A#21,
           T#15         |->  A#21[(app (letrec {X#25=T#24;E#27} in S#12) S#11)],
           T#22         |->  (app (letrec {X#25=T#24;E#27} in S#12) S#11),
           T#23         |->  (letrec {X#25=T#24;E#27} in S#12),
           E#10         |->  {X#25=T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#27},
           E#26         |->  {E#27}}

and instantiated rules:

                                  (letrec {X#19=A#21[(app (letrec {X#25=T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#27} in S#12) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#21[(app (letrec {X#25=T#24[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#27} in S#12) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app (letrec {X#25=T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#27} in S#12) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#21[(letrec {X#25=T#24[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#27} in (app S#12 S#11))];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#25} in S#12) S#11)]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#25} in (app S#12 S#11))]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#6,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#25} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app [.] S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  A#21,
           T#15         |->  A#21[(app [.] S#11)],
           T#22         |->  (app [.] S#11),
           T#23         |->  [.],
           S#5          |->  S#12,
           E#10         |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#25},
           E#24         |->  {X#1=C#7[(var X#3)];E#25},
           E#4          |->  {E#25}}

and instantiated rules:

                                  (letrec {X#19=A#21[(app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#25} in S#12) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#21[(app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#25} in S#12) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#25} in S#12) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#25} in (app S#12 S#11))];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app (letrec {E#10} in S#12) T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(letrec
                       E#10
                    in
                       (app S#12 T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])
                    )]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#6,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {E#10} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app (letrec {E#10} in S#12) T#23)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  A#21,
           T#15         |->  A#21[(app (letrec {E#10} in S#12) T#23)],
           T#22         |->  (app (letrec {E#10} in S#12) T#23),
           S#11         |->  T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app (letrec {E#10} in S#12) T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#21[(app (letrec {E#10} in S#12) T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app (letrec {E#10} in S#12) T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#21[(letrec {E#10} in (app S#12 T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]))];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(letrec {E#10} in (app S#12 S#11))] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] T#23)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           T#15         |->  A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] T#23[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#21[(app A#22[(letrec {E#10} in (app S#12 S#11))] T#23[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (app (letrec {E#10} in T#22[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#11)
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= (letrec
                 E#10
              in
                 (app T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#11)
              )
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#21,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=(app (letrec {E#10} in T#22) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  [.],
           T#15         |->  (app (letrec {E#10} in T#22) S#11),
           T#21         |->  (letrec {E#10} in T#22),
           S#12         |->  T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {X#19=(app (letrec {E#10} in T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=(app (letrec {E#10} in T#22[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=(app (letrec {E#10} in T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=(letrec {E#10} in (app T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)] S#11));E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (app (letrec
                      X#23= T#22[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
                     ;E#25
                   in
                      S#12
                   ) S#11)
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= (letrec
                 X#23= T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
                ;E#25
              in
                 (app S#12 S#11)
              )
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#21,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {X#23=T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#25} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=(app (letrec {X#23=T#22;E#25} in S#12) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  [.],
           T#15         |->  (app (letrec {X#23=T#22;E#25} in S#12) S#11),
           T#21         |->  (letrec {X#23=T#22;E#25} in S#12),
           E#10         |->  {X#23=T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#25},
           E#24         |->  {E#25}}

and instantiated rules:

                                  (letrec {X#19=(app (letrec {X#23=T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#25} in S#12) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=(app (letrec {X#23=T#22[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)];E#25} in S#12) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=(app (letrec {X#23=T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#25} in S#12) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=(letrec {X#23=T#22[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)];E#25} in (app S#12 S#11));E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#23} in S#12) S#11)
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#23} in (app S#12 S#11))
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#23} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=(app [.] S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  [.],
           T#15         |->  (app [.] S#11),
           T#21         |->  [.],
           S#5          |->  S#12,
           E#10         |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#23},
           E#22         |->  {X#1=C#7[(var X#3)];E#23},
           E#4          |->  {E#23}}

and instantiated rules:

                                  (letrec {X#19=(app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#23} in S#12) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=(app (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#23} in S#12) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=(app (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#23} in S#12) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#23} in (app S#12 S#11));E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (app (letrec {E#10} in S#12) T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)])
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= (letrec
                 E#10
              in
                 (app S#12 T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)])
              )
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)],(letrec {E#10} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=(app (letrec {E#10} in S#12) T#21);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  [.],
           T#15         |->  (app (letrec {E#10} in S#12) T#21),
           S#11         |->  T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]}

and instantiated rules:

                                  (letrec {X#19=(app (letrec {E#10} in S#12) T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=(app (letrec {E#10} in S#12) T#21[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=(app (letrec {E#10} in S#12) T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=(letrec {E#10} in (app S#12 T#21[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]));E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#2)]
       ;X#2= (var X#3)
       ;E#16
       ;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#2= (var X#3)
       ;E#16
       ;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#8)],
           E#9   |->  {X#1=C#7[(var X#3)];X#2=(var X#3);E#16},
           E#15  |->  {X#1=C#7[(var X#3)];E#16},
           E#4   |->  {E#16;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]}}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#16;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#16;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= A#17[(app (letrec {E#10} in C#20[(var X#2)]) S#11)]
       ;E#15
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= A#17[(letrec {E#10} in (app C#20[(var X#3)] S#11))]
       ;E#15
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#19,C#18,A#16,C#7,A#17}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#17[(app (letrec {E#10} in C#20) S#11)]),
             ((var X#3),A#17[(app (letrec {E#10} in C#20) S#11)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#17[(app (letrec {E#10} in C#20[[.]]) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#1          |->  X#8,
           E#4          |->  {E#15},
           A#16         |->  A#17,
           C#7          |->  A#17[(app (letrec {E#10} in C#20) S#11)],
           C#18         |->  (app (letrec {E#10} in C#20) S#11),
           C#19         |->  (letrec {E#10} in C#20),
           S#12         |->  C#20[(var X#3)]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=A#17[(app (letrec {E#10} in C#20[(var X#3)]) S#11)];E#15} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=A#17[(app (letrec {E#10} in C#20[(var X#2)]) S#11)];E#15} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=A#17[(app (letrec {E#10} in C#20[(var X#3)]) S#11)];E#15} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#2=(var X#3);X#8=A#17[(letrec {E#10} in (app C#20[(var X#3)] S#11))];E#15} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= A#17[(app (letrec {X#21=C#20[(var X#2)];E#23} in S#12) S#11)]
       ;E#15
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= A#17[(letrec {X#21=C#20[(var X#3)];E#23} in (app S#12 S#11))]
       ;E#15
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#19,C#18,A#16,C#7,A#17}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#17[(app (letrec {X#21=C#20;E#23} in S#12) S#11)]),
             ((var X#3),A#17[(app (letrec {X#21=C#20;E#23} in S#12) S#11)]),
             (S#11,(letrec {X#21=C#20[(var X#3)];E#23} in [.])),
             ((var X#2),A#17[(app (letrec {X#21=C#20[[.]];E#23} in S#12) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#1          |->  X#8,
           E#4          |->  {E#15},
           A#16         |->  A#17,
           C#7          |->  A#17[(app (letrec {X#21=C#20;E#23} in S#12) S#11)],
           C#18         |->  (app (letrec {X#21=C#20;E#23} in S#12) S#11),
           C#19         |->  (letrec {X#21=C#20;E#23} in S#12),
           E#10         |->  {X#21=C#20[(var X#3)];E#23},
           E#22         |->  {E#23}}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=A#17[(app (letrec {X#21=C#20[(var X#3)];E#23} in S#12) S#11)];E#15} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=A#17[(app (letrec {X#21=C#20[(var X#2)];E#23} in S#12) S#11)];E#15} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=A#17[(app (letrec {X#21=C#20[(var X#3)];E#23} in S#12) S#11)];E#15} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#2=(var X#3);X#8=A#17[(letrec {X#21=C#20[(var X#3)];E#23} in (app S#12 S#11))];E#15} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= A#17[(app (letrec {E#10} in S#12) C#19[(var X#2)])]
       ;E#15
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= A#17[(letrec {E#10} in (app S#12 C#19[(var X#3)]))]
       ;E#15
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#18,A#16,C#7,A#17}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#17[(app (letrec {E#10} in S#12) C#19)]),
             ((var X#3),A#17[(app (letrec {E#10} in S#12) C#19)]),
             (C#19[(var X#3)],(letrec {E#10} in [.])),
             ((var X#2),A#17[(app (letrec {E#10} in S#12) C#19[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#1          |->  X#8,
           E#4          |->  {E#15},
           A#16         |->  A#17,
           C#7          |->  A#17[(app (letrec {E#10} in S#12) C#19)],
           C#18         |->  (app (letrec {E#10} in S#12) C#19),
           S#11         |->  C#19[(var X#3)]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=A#17[(app (letrec {E#10} in S#12) C#19[(var X#3)])];E#15} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=A#17[(app (letrec {E#10} in S#12) C#19[(var X#2)])];E#15} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=A#17[(app (letrec {E#10} in S#12) C#19[(var X#3)])];E#15} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#2=(var X#3);X#8=A#17[(letrec {E#10} in (app S#12 C#19[(var X#3)]))];E#15} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= A#17[(app A#18[(app (letrec {E#10} in S#12) S#11)] C#19[(var X#2)])]
       ;E#15
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= A#17[(app A#18[(letrec {E#10} in (app S#12 S#11))] C#19[(var X#3)])]
       ;E#15
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#17[(app A#18[(app (letrec {E#10} in S#12) S#11)] C#19)]),
             ((var X#3),A#17[(app A#18[(app (letrec {E#10} in S#12) S#11)] C#19)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#17[(app A#18[(app (letrec {E#10} in S#12) S#11)] C#19[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] C#19[(var X#3)])]},
           X#1          |->  X#8,
           E#4          |->  {E#15},
           C#7          |->  A#17[(app A#18[(app (letrec {E#10} in S#12) S#11)] C#19)],
           A#16         |->  A#17[(app A#18 C#19[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=A#17[(app A#18[(app (letrec {E#10} in S#12) S#11)] C#19[(var X#3)])];E#15} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=A#17[(app A#18[(app (letrec {E#10} in S#12) S#11)] C#19[(var X#2)])];E#15} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=A#17[(app A#18[(app (letrec {E#10} in S#12) S#11)] C#19[(var X#3)])];E#15} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#2=(var X#3);X#8=A#17[(app A#18[(letrec {E#10} in (app S#12 S#11))] C#19[(var X#3)])];E#15} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (app (letrec {E#10} in C#18[(var X#2)]) S#11)
       ;E#15
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= (letrec {E#10} in (app C#18[(var X#3)] S#11))
       ;E#15
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#17,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(app (letrec {E#10} in C#18) S#11)),
             ((var X#3),(app (letrec {E#10} in C#18) S#11)),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),(app (letrec {E#10} in C#18[[.]]) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#8,
           E#4          |->  {E#15},
           A#16         |->  [.],
           C#7          |->  (app (letrec {E#10} in C#18) S#11),
           C#17         |->  (letrec {E#10} in C#18),
           S#12         |->  C#18[(var X#3)]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(app (letrec {E#10} in C#18[(var X#3)]) S#11);E#15} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(app (letrec {E#10} in C#18[(var X#2)]) S#11);E#15} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(app (letrec {E#10} in C#18[(var X#3)]) S#11);E#15} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#2=(var X#3);X#8=(letrec {E#10} in (app C#18[(var X#3)] S#11));E#15} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (app (letrec {X#19=C#18[(var X#2)];E#21} in S#12) S#11)
       ;E#15
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= (letrec {X#19=C#18[(var X#3)];E#21} in (app S#12 S#11))
       ;E#15
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#17,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(app (letrec {X#19=C#18;E#21} in S#12) S#11)),
             ((var X#3),(app (letrec {X#19=C#18;E#21} in S#12) S#11)),
             (S#11,(letrec {X#19=C#18[(var X#3)];E#21} in [.])),
             ((var X#2),(app (letrec {X#19=C#18[[.]];E#21} in S#12) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#8,
           E#4          |->  {E#15},
           A#16         |->  [.],
           C#7          |->  (app (letrec {X#19=C#18;E#21} in S#12) S#11),
           C#17         |->  (letrec {X#19=C#18;E#21} in S#12),
           E#10         |->  {X#19=C#18[(var X#3)];E#21},
           E#20         |->  {E#21}}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(app (letrec {X#19=C#18[(var X#3)];E#21} in S#12) S#11);E#15} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(app (letrec {X#19=C#18[(var X#2)];E#21} in S#12) S#11);E#15} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(app (letrec {X#19=C#18[(var X#3)];E#21} in S#12) S#11);E#15} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#2=(var X#3);X#8=(letrec {X#19=C#18[(var X#3)];E#21} in (app S#12 S#11));E#15} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (app (letrec {E#10} in S#12) C#17[(var X#2)])
       ;E#15
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= (letrec {E#10} in (app S#12 C#17[(var X#3)]))
       ;E#15
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(app (letrec {E#10} in S#12) C#17)),
             ((var X#3),(app (letrec {E#10} in S#12) C#17)),
             (C#17[(var X#3)],(letrec {E#10} in [.])),
             ((var X#2),(app (letrec {E#10} in S#12) C#17[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#8,
           E#4          |->  {E#15},
           A#16         |->  [.],
           C#7          |->  (app (letrec {E#10} in S#12) C#17),
           S#11         |->  C#17[(var X#3)]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(app (letrec {E#10} in S#12) C#17[(var X#3)]);E#15} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(app (letrec {E#10} in S#12) C#17[(var X#2)]);E#15} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(app (letrec {E#10} in S#12) C#17[(var X#3)]);E#15} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#2=(var X#3);X#8=(letrec {E#10} in (app S#12 C#17[(var X#3)]));E#15} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#17)
       ;X#8= A#19[(var X#2)]
       ;E#15
       ;EE#18[X#17,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#17)
       ;X#8= A#19[(var X#17)]
       ;E#15
       ;EE#18[X#17,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#19[[.]]),
             ((var X#17),A#19[[.]]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#19[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#17);E#15},
           EE#14[.1,.2] |-> {[.1]=A#19[(var X#17)];EE#18[X#17,[.2]]},
           X#1          |->  X#8,
           E#4          |->  {E#15;EE#18[X#17,(app (letrec {E#10} in S#12) S#11)]},
           A#16         |->  A#19,
           C#7          |->  A#19[[.]],
           C#20         |->  [.],
           X#3          |->  X#17}

and instantiated rules:

                                  (letrec {X#2=(var X#17);X#8=A#19[(var X#17)];E#15;EE#18[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#17);X#8=A#19[(var X#2)];E#15;EE#18[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#17);X#8=A#19[(var X#17)];E#15;EE#18[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#2=(var X#17);X#8=A#19[(var X#17)];E#15;EE#18[X#17,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= A#19[(var X#2)]
       ;E#15
       ;EE#18[X#3,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= A#19[(var X#3)]
       ;E#15
       ;EE#18[X#3,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#19),
             ((var X#3),A#19),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#19[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=A#19[(var X#3)];EE#18[X#3,[.2]]},
           X#1          |->  X#8,
           E#4          |->  {E#15;EE#18[X#3,(app (letrec {E#10} in S#12) S#11)]},
           A#16         |->  A#19[[.]],
           C#7          |->  A#19,
           A#20         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=A#19[(var X#3)];E#15;EE#18[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=A#19[(var X#2)];E#15;EE#18[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=A#19[(var X#3)];E#15;EE#18[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#2=(var X#3);X#8=A#19[(var X#3)];E#15;EE#18[X#3,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= A#19[(app A#20[(var X#17)] C#21[(var X#2)])]
       ;E#15
       ;EE#18[X#17,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= A#19[(app A#20[(var X#17)] C#21[(var X#3)])]
       ;E#15
       ;EE#18[X#17,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#19[(app A#20[(var X#17)] C#21)]),
             ((var X#3),A#19[(app A#20[(var X#17)] C#21)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#19[(app A#20[(var X#17)] C#21[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] C#21[(var X#3)])];EE#18[X#17,[.2]]},
           X#1          |->  X#8,
           E#4          |->  {E#15;EE#18[X#17,(app (letrec {E#10} in S#12) S#11)]},
           C#7          |->  A#19[(app A#20[(var X#17)] C#21)],
           A#16         |->  A#19[(app A#20 C#21[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=A#19[(app A#20[(var X#17)] C#21[(var X#3)])];E#15;EE#18[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=A#19[(app A#20[(var X#17)] C#21[(var X#2)])];E#15;EE#18[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=A#19[(app A#20[(var X#17)] C#21[(var X#3)])];E#15;EE#18[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#2=(var X#3);X#8=A#19[(app A#20[(var X#17)] C#21[(var X#3)])];E#15;EE#18[X#17,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#3)
       ;X#8= (var X#2)
       ;E#15
       ;EE#18[X#3,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#2= (var X#3)
       ;X#8= (var X#3)
       ;E#15
       ;EE#18[X#3,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),[.]),
             ((var X#3),[.]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {[.1]=(var X#3);EE#18[X#3,[.2]]},
           X#1          |->  X#8,
           E#4          |->  {E#15;EE#18[X#3,(app (letrec {E#10} in S#12) S#11)]},
           C#7          |->  [.],
           A#16         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#2=(var X#3);X#8=(var X#3);E#15;EE#18[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#2=(var X#3);X#8=(var X#2);E#15;EE#18[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#2=(var X#3);X#8=(var X#3);E#15;EE#18[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#2=(var X#3);X#8=(var X#3);E#15;EE#18[X#3,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(var X#2)]
       ;X#2= (var X#18)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#18,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= A#21[(var X#18)]
       ;X#2= (var X#18)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#18,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#21[[.]]),
             ((var X#18),A#21[[.]]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#21[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#18);E#15},
           EE#14[.1,.2] |-> {X#17=A#21[(var X#18)];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (letrec {E#10} in S#12) S#11)]},
           A#16         |->  A#21,
           C#7          |->  A#21[[.]],
           C#22         |->  [.],
           X#3          |->  X#18}

and instantiated rules:

                                  (letrec {X#17=A#21[(var X#18)];X#2=(var X#18);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=A#21[(var X#2)];X#2=(var X#18);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=A#21[(var X#18)];X#2=(var X#18);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#17=A#21[(var X#18)];X#2=(var X#18);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(var X#2)]
       ;X#2= (var X#3)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#3,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= A#21[(var X#3)]
       ;X#2= (var X#3)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#3,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#21),
             ((var X#3),A#21),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#21[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=A#21[(var X#3)];EE#19[[.1],(var X#17)];EE#20[X#3,[.2]]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (letrec {E#10} in S#12) S#11)]},
           A#16         |->  A#21[[.]],
           C#7          |->  A#21,
           A#22         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#17=A#21[(var X#3)];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=A#21[(var X#2)];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=A#21[(var X#3)];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#17=A#21[(var X#3)];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(app A#22[(var X#18)] C#23[(var X#2)])]
       ;X#2= (var X#3)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#18,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] C#23[(var X#3)])]
       ;X#2= (var X#3)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#18,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#21[(app A#22[(var X#18)] C#23)]),
             ((var X#3),A#21[(app A#22[(var X#18)] C#23)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#21[(app A#22[(var X#18)] C#23[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#3)])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (letrec {E#10} in S#12) S#11)]},
           C#7          |->  A#21[(app A#22[(var X#18)] C#23)],
           A#16         |->  A#21[(app A#22 C#23[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#3)])];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#2)])];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#3)])];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#17=A#21[(app A#22[(var X#18)] C#23[(var X#3)])];X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#18,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#2)
       ;X#2= (var X#3)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#3,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= (var X#3)
       ;X#2= (var X#3)
       ;E#15
       ;EE#19[X#8,(var X#17)]
       ;EE#20[X#3,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),[.]),
             ((var X#3),[.]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=(var X#3);EE#19[[.1],(var X#17)];EE#20[X#3,[.2]]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (letrec {E#10} in S#12) S#11)]},
           C#7          |->  [.],
           A#16         |->  [.],
           X#18         |->  X#3}

and instantiated rules:

                                  (letrec {X#17=(var X#3);X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=(var X#2);X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=(var X#3);X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#17=(var X#3);X#2=(var X#3);E#15;EE#19[X#8,(var X#17)];EE#20[X#3,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app (letrec {E#10} in C#22[(var X#2)]) S#11)]
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= A#19[(letrec {E#10} in (app C#22[(var X#3)] S#11))]
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#21,C#20,A#16,C#7,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#19[(app (letrec {E#10} in C#22) S#11)]),
             ((var X#3),A#19[(app (letrec {E#10} in C#22) S#11)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#19[(app (letrec {E#10} in C#22[[.]]) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#18[X#8,(var X#17)]},
           A#16         |->  A#19,
           C#7          |->  A#19[(app (letrec {E#10} in C#22) S#11)],
           C#20         |->  (app (letrec {E#10} in C#22) S#11),
           C#21         |->  (letrec {E#10} in C#22),
           S#12         |->  C#22[(var X#3)]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app (letrec {E#10} in C#22[(var X#3)]) S#11)];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=A#19[(app (letrec {E#10} in C#22[(var X#2)]) S#11)];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=A#19[(app (letrec {E#10} in C#22[(var X#3)]) S#11)];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#17=A#19[(letrec {E#10} in (app C#22[(var X#3)] S#11))];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app (letrec {X#23=C#22[(var X#2)];E#25} in S#12) S#11)]
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= A#19[(letrec {X#23=C#22[(var X#3)];E#25} in (app S#12 S#11))]
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#21,C#20,A#16,C#7,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#19[(app (letrec {X#23=C#22;E#25} in S#12) S#11)]),
             ((var X#3),A#19[(app (letrec {X#23=C#22;E#25} in S#12) S#11)]),
             (S#11,(letrec {X#23=C#22[(var X#3)];E#25} in [.])),
             ((var X#2),A#19[(app (letrec {X#23=C#22[[.]];E#25} in S#12) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#18[X#8,(var X#17)]},
           A#16         |->  A#19,
           C#7          |->  A#19[(app (letrec {X#23=C#22;E#25} in S#12) S#11)],
           C#20         |->  (app (letrec {X#23=C#22;E#25} in S#12) S#11),
           C#21         |->  (letrec {X#23=C#22;E#25} in S#12),
           E#10         |->  {X#23=C#22[(var X#3)];E#25},
           E#24         |->  {E#25}}

and instantiated rules:

                                  (letrec {X#17=A#19[(app (letrec {X#23=C#22[(var X#3)];E#25} in S#12) S#11)];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=A#19[(app (letrec {X#23=C#22[(var X#2)];E#25} in S#12) S#11)];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=A#19[(app (letrec {X#23=C#22[(var X#3)];E#25} in S#12) S#11)];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#17=A#19[(letrec {X#23=C#22[(var X#3)];E#25} in (app S#12 S#11))];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app (letrec {E#10} in S#12) C#21[(var X#2)])]
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= A#19[(letrec {E#10} in (app S#12 C#21[(var X#3)]))]
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#20,A#16,C#7,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#19[(app (letrec {E#10} in S#12) C#21)]),
             ((var X#3),A#19[(app (letrec {E#10} in S#12) C#21)]),
             (C#21[(var X#3)],(letrec {E#10} in [.])),
             ((var X#2),A#19[(app (letrec {E#10} in S#12) C#21[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#18[X#8,(var X#17)]},
           A#16         |->  A#19,
           C#7          |->  A#19[(app (letrec {E#10} in S#12) C#21)],
           C#20         |->  (app (letrec {E#10} in S#12) C#21),
           S#11         |->  C#21[(var X#3)]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app (letrec {E#10} in S#12) C#21[(var X#3)])];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=A#19[(app (letrec {E#10} in S#12) C#21[(var X#2)])];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=A#19[(app (letrec {E#10} in S#12) C#21[(var X#3)])];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#17=A#19[(letrec {E#10} in (app S#12 C#21[(var X#3)]))];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21[(var X#2)])]
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(letrec {E#10} in (app S#12 S#11))] C#21[(var X#3)])]
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#16,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21)]),
             ((var X#3),A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] C#21[(var X#3)])];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#18[X#8,(var X#17)]},
           C#7          |->  A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21)],
           A#16         |->  A#19[(app A#20 C#21[(var X#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21[(var X#3)])];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21[(var X#2)])];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21[(var X#3)])];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#17=A#19[(app A#20[(letrec {E#10} in (app S#12 S#11))] C#21[(var X#3)])];X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (app (letrec {E#10} in C#20[(var X#2)]) S#11)
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= (letrec {E#10} in (app C#20[(var X#3)] S#11))
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#19,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(app (letrec {E#10} in C#20) S#11)),
             ((var X#3),(app (letrec {E#10} in C#20) S#11)),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),(app (letrec {E#10} in C#20[[.]]) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#18[X#8,(var X#17)]},
           A#16         |->  [.],
           C#7          |->  (app (letrec {E#10} in C#20) S#11),
           C#19         |->  (letrec {E#10} in C#20),
           S#12         |->  C#20[(var X#3)]}

and instantiated rules:

                                  (letrec {X#17=(app (letrec {E#10} in C#20[(var X#3)]) S#11);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=(app (letrec {E#10} in C#20[(var X#2)]) S#11);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=(app (letrec {E#10} in C#20[(var X#3)]) S#11);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#17=(letrec {E#10} in (app C#20[(var X#3)] S#11));X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (app (letrec {X#21=C#20[(var X#2)];E#23} in S#12) S#11)
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= (letrec {X#21=C#20[(var X#3)];E#23} in (app S#12 S#11))
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#19,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(app (letrec {X#21=C#20;E#23} in S#12) S#11)),
             ((var X#3),(app (letrec {X#21=C#20;E#23} in S#12) S#11)),
             (S#11,(letrec {X#21=C#20[(var X#3)];E#23} in [.])),
             ((var X#2),(app (letrec {X#21=C#20[[.]];E#23} in S#12) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#18[X#8,(var X#17)]},
           A#16         |->  [.],
           C#7          |->  (app (letrec {X#21=C#20;E#23} in S#12) S#11),
           C#19         |->  (letrec {X#21=C#20;E#23} in S#12),
           E#10         |->  {X#21=C#20[(var X#3)];E#23},
           E#22         |->  {E#23}}

and instantiated rules:

                                  (letrec {X#17=(app (letrec {X#21=C#20[(var X#3)];E#23} in S#12) S#11);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=(app (letrec {X#21=C#20[(var X#2)];E#23} in S#12) S#11);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=(app (letrec {X#21=C#20[(var X#3)];E#23} in S#12) S#11);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#17=(letrec {X#21=C#20[(var X#3)];E#23} in (app S#12 S#11));X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (app (letrec {E#10} in S#12) C#19[(var X#2)])
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= (letrec {E#10} in (app S#12 C#19[(var X#3)]))
       ;X#2= (var X#3)
       ;E#15
       ;EE#18[X#8,(var X#17)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(app (letrec {E#10} in S#12) C#19)),
             ((var X#3),(app (letrec {E#10} in S#12) C#19)),
             (C#19[(var X#3)],(letrec {E#10} in [.])),
             ((var X#2),(app (letrec {E#10} in S#12) C#19[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           E#9          |->  {X#2=(var X#3);E#15},
           EE#14[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#4          |->  {E#15;EE#18[X#8,(var X#17)]},
           A#16         |->  [.],
           C#7          |->  (app (letrec {E#10} in S#12) C#19),
           S#11         |->  C#19[(var X#3)]}

and instantiated rules:

                                  (letrec {X#17=(app (letrec {E#10} in S#12) C#19[(var X#3)]);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#17=(app (letrec {E#10} in S#12) C#19[(var X#2)]);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=(app (letrec {E#10} in S#12) C#19[(var X#3)]);X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#17=(letrec {E#10} in (app S#12 C#19[(var X#3)]));X#2=(var X#3);E#15;EE#18[X#8,(var X#17)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#8)]
       ;X#8= (var X#3)
       ;E#18
       ;EE#17[X#3,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#8= (var X#3)
       ;E#18
       ;EE#17[X#3,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#8),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {E#10} in [.])),
             ((var X#8),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=(var X#3);EE#17[X#3,[.2]]},
           X#2          |->  X#8,
           E#9          |->  {X#1=C#7[(var X#3)];E#18},
           E#4          |->  {E#18;EE#17[X#3,(app (letrec {E#10} in S#12) S#11)]},
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#8=(var X#3);E#18;EE#17[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#8)];X#8=(var X#3);E#18;EE#17[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#8=(var X#3);E#18;EE#17[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#1=C#7[(var X#3)];X#8=(var X#3);E#18;EE#17[X#3,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= A#19[(app (letrec {E#10} in C#22[(var X#8)]) S#11)]
       ;X#8= (var X#3)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#3= A#19[(letrec {E#10} in (app C#22[(var X#3)] S#11))]
       ;X#8= (var X#3)
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#21,C#20,A#18,C#7,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#8),A#19[(app (letrec {E#10} in C#22) S#11)]),
             ((var X#3),A#19[(app (letrec {E#10} in C#22) S#11)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#8),A#19[(app (letrec {E#10} in C#22[[.]]) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#3=A#19[[.2]];[.1]=(var X#3)},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#1          |->  X#3,
           E#4          |->  {E#9},
           A#18         |->  A#19,
           C#7          |->  A#19[(app (letrec {E#10} in C#22) S#11)],
           A#15         |->  [.],
           X#16         |->  X#3,
           C#20         |->  (app (letrec {E#10} in C#22) S#11),
           C#21         |->  (letrec {E#10} in C#22),
           S#12         |->  C#22[(var X#3)]}

and instantiated rules:

                                  (letrec {X#3=A#19[(app (letrec {E#10} in C#22[(var X#3)]) S#11)];X#8=(var X#3);E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#3=A#19[(app (letrec {E#10} in C#22[(var X#8)]) S#11)];X#8=(var X#3);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#3=A#19[(app (letrec {E#10} in C#22[(var X#3)]) S#11)];X#8=(var X#3);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#3=A#19[(letrec {E#10} in (app C#22[(var X#3)] S#11))];X#8=(var X#3);E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= A#19[(app (letrec {X#23=C#22[(var X#8)];E#25} in S#12) S#11)]
       ;X#8= (var X#3)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#3= A#19[(letrec {X#23=C#22[(var X#3)];E#25} in (app S#12 S#11))]
       ;X#8= (var X#3)
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#21,C#20,A#18,C#7,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#8),A#19[(app (letrec {X#23=C#22;E#25} in S#12) S#11)]),
             ((var X#3),A#19[(app (letrec {X#23=C#22;E#25} in S#12) S#11)]),
             (S#11,(letrec {X#23=C#22[(var X#3)];E#25} in [.])),
             ((var X#8),A#19[(app (letrec {X#23=C#22[[.]];E#25} in S#12) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#3=A#19[[.2]];[.1]=(var X#3)},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#1          |->  X#3,
           E#4          |->  {E#9},
           A#18         |->  A#19,
           C#7          |->  A#19[(app (letrec {X#23=C#22;E#25} in S#12) S#11)],
           A#15         |->  [.],
           X#16         |->  X#3,
           C#20         |->  (app (letrec {X#23=C#22;E#25} in S#12) S#11),
           C#21         |->  (letrec {X#23=C#22;E#25} in S#12),
           E#10         |->  {X#23=C#22[(var X#3)];E#25},
           E#24         |->  {E#25}}

and instantiated rules:

                                  (letrec {X#3=A#19[(app (letrec {X#23=C#22[(var X#3)];E#25} in S#12) S#11)];X#8=(var X#3);E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#3=A#19[(app (letrec {X#23=C#22[(var X#8)];E#25} in S#12) S#11)];X#8=(var X#3);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#3=A#19[(app (letrec {X#23=C#22[(var X#3)];E#25} in S#12) S#11)];X#8=(var X#3);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#3=A#19[(letrec {X#23=C#22[(var X#3)];E#25} in (app S#12 S#11))];X#8=(var X#3);E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= A#19[(app (letrec {E#10} in S#12) C#21[(var X#8)])]
       ;X#8= (var X#3)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#3= A#19[(letrec {E#10} in (app S#12 C#21[(var X#3)]))]
       ;X#8= (var X#3)
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#20,A#18,C#7,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#8),A#19[(app (letrec {E#10} in S#12) C#21)]),
             ((var X#3),A#19[(app (letrec {E#10} in S#12) C#21)]),
             (C#21[(var X#3)],(letrec {E#10} in [.])),
             ((var X#8),A#19[(app (letrec {E#10} in S#12) C#21[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#3=A#19[[.2]];[.1]=(var X#3)},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#1          |->  X#3,
           E#4          |->  {E#9},
           A#18         |->  A#19,
           C#7          |->  A#19[(app (letrec {E#10} in S#12) C#21)],
           A#15         |->  [.],
           X#16         |->  X#3,
           C#20         |->  (app (letrec {E#10} in S#12) C#21),
           S#11         |->  C#21[(var X#3)]}

and instantiated rules:

                                  (letrec {X#3=A#19[(app (letrec {E#10} in S#12) C#21[(var X#3)])];X#8=(var X#3);E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#3=A#19[(app (letrec {E#10} in S#12) C#21[(var X#8)])];X#8=(var X#3);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#3=A#19[(app (letrec {E#10} in S#12) C#21[(var X#3)])];X#8=(var X#3);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#3=A#19[(letrec {E#10} in (app S#12 C#21[(var X#3)]))];X#8=(var X#3);E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21[(var X#8)])]
       ;X#8= (var X#3)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#3= A#19[(app A#20[(letrec {E#10} in (app S#12 S#11))] C#21[(var X#3)])]
       ;X#8= (var X#3)
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#8),A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21)]),
             ((var X#3),A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#8),A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#3=A#19[(app A#20[[.2]] C#21[(var X#3)])];[.1]=(var X#3)},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] C#21[(var X#3)])]},
           X#1          |->  X#3,
           E#4          |->  {E#9},
           C#7          |->  A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21)],
           A#18         |->  A#19[(app A#20 C#21[(var X#3)])],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#3=A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21[(var X#3)])];X#8=(var X#3);E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#3=A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21[(var X#8)])];X#8=(var X#3);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#3=A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] C#21[(var X#3)])];X#8=(var X#3);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#3=A#19[(app A#20[(letrec {E#10} in (app S#12 S#11))] C#21[(var X#3)])];X#8=(var X#3);E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= (app (letrec {E#10} in C#20[(var X#8)]) S#11)
       ;X#8= (var X#3)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#3= (letrec {E#10} in (app C#20[(var X#3)] S#11))
       ;X#8= (var X#3)
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#19,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#8),(app (letrec {E#10} in C#20) S#11)),
             ((var X#3),(app (letrec {E#10} in C#20) S#11)),
             (S#11,(letrec {E#10} in [.])),
             ((var X#8),(app (letrec {E#10} in C#20[[.]]) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#3=[.2];[.1]=(var X#3)},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#3,
           E#4          |->  {E#9},
           A#18         |->  [.],
           C#7          |->  (app (letrec {E#10} in C#20) S#11),
           C#19         |->  (letrec {E#10} in C#20),
           S#12         |->  C#20[(var X#3)],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#3=(app (letrec {E#10} in C#20[(var X#3)]) S#11);X#8=(var X#3);E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#3=(app (letrec {E#10} in C#20[(var X#8)]) S#11);X#8=(var X#3);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#3=(app (letrec {E#10} in C#20[(var X#3)]) S#11);X#8=(var X#3);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#3=(letrec {E#10} in (app C#20[(var X#3)] S#11));X#8=(var X#3);E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= (app (letrec {X#21=C#20[(var X#8)];E#23} in S#12) S#11)
       ;X#8= (var X#3)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#3= (letrec {X#21=C#20[(var X#3)];E#23} in (app S#12 S#11))
       ;X#8= (var X#3)
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#19,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#8),(app (letrec {X#21=C#20;E#23} in S#12) S#11)),
             ((var X#3),(app (letrec {X#21=C#20;E#23} in S#12) S#11)),
             (S#11,(letrec {X#21=C#20[(var X#3)];E#23} in [.])),
             ((var X#8),(app (letrec {X#21=C#20[[.]];E#23} in S#12) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#3=[.2];[.1]=(var X#3)},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#3,
           E#4          |->  {E#9},
           A#18         |->  [.],
           C#7          |->  (app (letrec {X#21=C#20;E#23} in S#12) S#11),
           C#19         |->  (letrec {X#21=C#20;E#23} in S#12),
           E#10         |->  {X#21=C#20[(var X#3)];E#23},
           E#22         |->  {E#23},
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#3=(app (letrec {X#21=C#20[(var X#3)];E#23} in S#12) S#11);X#8=(var X#3);E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#3=(app (letrec {X#21=C#20[(var X#8)];E#23} in S#12) S#11);X#8=(var X#3);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#3=(app (letrec {X#21=C#20[(var X#3)];E#23} in S#12) S#11);X#8=(var X#3);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#3=(letrec {X#21=C#20[(var X#3)];E#23} in (app S#12 S#11));X#8=(var X#3);E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= (app (letrec {E#10} in S#12) C#19[(var X#8)])
       ;X#8= (var X#3)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#3= (letrec {E#10} in (app S#12 C#19[(var X#3)]))
       ;X#8= (var X#3)
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#8),(app (letrec {E#10} in S#12) C#19)),
             ((var X#3),(app (letrec {E#10} in S#12) C#19)),
             (C#19[(var X#3)],(letrec {E#10} in [.])),
             ((var X#8),(app (letrec {E#10} in S#12) C#19[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#3=[.2];[.1]=(var X#3)},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#3,
           E#4          |->  {E#9},
           A#18         |->  [.],
           C#7          |->  (app (letrec {E#10} in S#12) C#19),
           S#11         |->  C#19[(var X#3)],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#3=(app (letrec {E#10} in S#12) C#19[(var X#3)]);X#8=(var X#3);E#9} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#3=(app (letrec {E#10} in S#12) C#19[(var X#8)]);X#8=(var X#3);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#3=(app (letrec {E#10} in S#12) C#19[(var X#3)]);X#8=(var X#3);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#3=(letrec {E#10} in (app S#12 C#19[(var X#3)]));X#8=(var X#3);E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#3= A#21[(app A#22[(var X#19)] C#23[(var X#8)])]
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#3= A#21[(app A#22[(var X#19)] C#23[(var X#3)])]
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#19,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#8),A#21[(app A#22[(var X#19)] C#23)]),
             ((var X#3),A#21[(app A#22[(var X#19)] C#23)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#8),A#21[(app A#22[(var X#19)] C#23[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];[.1]=(var X#3);EE#20[X#19,[.2]]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];EE#20[X#19,[.2]]},
           X#1          |->  X#3,
           E#4          |->  {E#9;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]},
           C#7          |->  A#21[(app A#22[(var X#19)] C#23)],
           A#18         |->  A#21[(app A#22 C#23[(var X#3)])],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];X#8=(var X#3);E#9;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#8)])];X#8=(var X#3);E#9;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];X#8=(var X#3);E#9;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#3=A#21[(app A#22[(var X#19)] C#23[(var X#3)])];X#8=(var X#3);E#9;EE#20[X#19,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] C#25[(var X#8)])]
       ;X#8= (var X#3)
       ;E#9
       ;EE#21[X#3,(var X#19)]
       ;EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] C#25[(var X#3)])]
       ;X#8= (var X#3)
       ;E#9
       ;EE#21[X#3,(var X#19)]
       ;EE#22[X#20,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#8),A#23[(app A#24[(var X#20)] C#25)]),
             ((var X#3),A#23[(app A#24[(var X#20)] C#25)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#8),A#23[(app A#24[(var X#20)] C#25[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];[.1]=(var X#3);EE#21[X#3,(var X#19)];EE#22[X#20,[.2]]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#1          |->  X#19,
           E#4          |->  {E#9;EE#21[X#3,(var X#19)];EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]},
           C#7          |->  A#23[(app A#24[(var X#20)] C#25)],
           A#18         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];X#8=(var X#3);E#9;EE#21[X#3,(var X#19)];EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#8)])];X#8=(var X#3);E#9;EE#21[X#3,(var X#19)];EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];X#8=(var X#3);E#9;EE#21[X#3,(var X#19)];EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#23[(app A#24[(var X#20)] C#25[(var X#3)])];X#8=(var X#3);E#9;EE#21[X#3,(var X#19)];EE#22[X#20,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app (letrec {E#10} in C#24[(var X#8)]) S#11)]
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(letrec {E#10} in (app C#24[(var X#3)] S#11))]
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#23,C#22,A#18,C#7,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#8),A#21[(app (letrec {E#10} in C#24) S#11)]),
             ((var X#3),A#21[(app (letrec {E#10} in C#24) S#11)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#8),A#21[(app (letrec {E#10} in C#24[[.]]) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];[.1]=(var X#3);EE#20[X#3,(var X#19)]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {E#9;EE#20[X#3,(var X#19)]},
           A#18         |->  A#21,
           C#7          |->  A#21[(app (letrec {E#10} in C#24) S#11)],
           A#15         |->  [.],
           X#16         |->  X#3,
           C#22         |->  (app (letrec {E#10} in C#24) S#11),
           C#23         |->  (letrec {E#10} in C#24),
           S#12         |->  C#24[(var X#3)]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app (letrec {E#10} in C#24[(var X#3)]) S#11)];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#21[(app (letrec {E#10} in C#24[(var X#8)]) S#11)];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app (letrec {E#10} in C#24[(var X#3)]) S#11)];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#21[(letrec {E#10} in (app C#24[(var X#3)] S#11))];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app (letrec {X#25=C#24[(var X#8)];E#27} in S#12) S#11)]
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(letrec {X#25=C#24[(var X#3)];E#27} in (app S#12 S#11))]
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#23,C#22,A#18,C#7,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#8),A#21[(app (letrec {X#25=C#24;E#27} in S#12) S#11)]),
             ((var X#3),A#21[(app (letrec {X#25=C#24;E#27} in S#12) S#11)]),
             (S#11,(letrec {X#25=C#24[(var X#3)];E#27} in [.])),
             ((var X#8),A#21[(app (letrec {X#25=C#24[[.]];E#27} in S#12) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];[.1]=(var X#3);EE#20[X#3,(var X#19)]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {E#9;EE#20[X#3,(var X#19)]},
           A#18         |->  A#21,
           C#7          |->  A#21[(app (letrec {X#25=C#24;E#27} in S#12) S#11)],
           A#15         |->  [.],
           X#16         |->  X#3,
           C#22         |->  (app (letrec {X#25=C#24;E#27} in S#12) S#11),
           C#23         |->  (letrec {X#25=C#24;E#27} in S#12),
           E#10         |->  {X#25=C#24[(var X#3)];E#27},
           E#26         |->  {E#27}}

and instantiated rules:

                                  (letrec {X#19=A#21[(app (letrec {X#25=C#24[(var X#3)];E#27} in S#12) S#11)];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#21[(app (letrec {X#25=C#24[(var X#8)];E#27} in S#12) S#11)];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app (letrec {X#25=C#24[(var X#3)];E#27} in S#12) S#11)];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#21[(letrec {X#25=C#24[(var X#3)];E#27} in (app S#12 S#11))];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app (letrec {E#10} in S#12) C#23[(var X#8)])]
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(letrec {E#10} in (app S#12 C#23[(var X#3)]))]
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#22,A#18,C#7,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#8),A#21[(app (letrec {E#10} in S#12) C#23)]),
             ((var X#3),A#21[(app (letrec {E#10} in S#12) C#23)]),
             (C#23[(var X#3)],(letrec {E#10} in [.])),
             ((var X#8),A#21[(app (letrec {E#10} in S#12) C#23[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];[.1]=(var X#3);EE#20[X#3,(var X#19)]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {E#9;EE#20[X#3,(var X#19)]},
           A#18         |->  A#21,
           C#7          |->  A#21[(app (letrec {E#10} in S#12) C#23)],
           A#15         |->  [.],
           X#16         |->  X#3,
           C#22         |->  (app (letrec {E#10} in S#12) C#23),
           S#11         |->  C#23[(var X#3)]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app (letrec {E#10} in S#12) C#23[(var X#3)])];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#21[(app (letrec {E#10} in S#12) C#23[(var X#8)])];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app (letrec {E#10} in S#12) C#23[(var X#3)])];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#21[(letrec {E#10} in (app S#12 C#23[(var X#3)]))];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23[(var X#8)])]
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(letrec {E#10} in (app S#12 S#11))] C#23[(var X#3)])]
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#8),A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23)]),
             ((var X#3),A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#8),A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] C#23[(var X#3)])];[.1]=(var X#3);EE#20[X#3,(var X#19)]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] C#23[(var X#3)])];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {E#9;EE#20[X#3,(var X#19)]},
           C#7          |->  A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23)],
           A#18         |->  A#21[(app A#22 C#23[(var X#3)])],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23[(var X#3)])];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23[(var X#8)])];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23[(var X#3)])];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#21[(app A#22[(letrec {E#10} in (app S#12 S#11))] C#23[(var X#3)])];X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (app (letrec {E#10} in C#22[(var X#8)]) S#11)
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= (letrec {E#10} in (app C#22[(var X#3)] S#11))
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#21,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#8),(app (letrec {E#10} in C#22) S#11)),
             ((var X#3),(app (letrec {E#10} in C#22) S#11)),
             (S#11,(letrec {E#10} in [.])),
             ((var X#8),(app (letrec {E#10} in C#22[[.]]) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#19=[.2];[.1]=(var X#3);EE#20[X#3,(var X#19)]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {E#9;EE#20[X#3,(var X#19)]},
           A#18         |->  [.],
           C#7          |->  (app (letrec {E#10} in C#22) S#11),
           C#21         |->  (letrec {E#10} in C#22),
           S#12         |->  C#22[(var X#3)],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=(app (letrec {E#10} in C#22[(var X#3)]) S#11);X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=(app (letrec {E#10} in C#22[(var X#8)]) S#11);X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=(app (letrec {E#10} in C#22[(var X#3)]) S#11);X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=(letrec {E#10} in (app C#22[(var X#3)] S#11));X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (app (letrec {X#23=C#22[(var X#8)];E#25} in S#12) S#11)
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= (letrec {X#23=C#22[(var X#3)];E#25} in (app S#12 S#11))
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#21,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#8),(app (letrec {X#23=C#22;E#25} in S#12) S#11)),
             ((var X#3),(app (letrec {X#23=C#22;E#25} in S#12) S#11)),
             (S#11,(letrec {X#23=C#22[(var X#3)];E#25} in [.])),
             ((var X#8),(app (letrec {X#23=C#22[[.]];E#25} in S#12) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#19=[.2];[.1]=(var X#3);EE#20[X#3,(var X#19)]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {E#9;EE#20[X#3,(var X#19)]},
           A#18         |->  [.],
           C#7          |->  (app (letrec {X#23=C#22;E#25} in S#12) S#11),
           C#21         |->  (letrec {X#23=C#22;E#25} in S#12),
           E#10         |->  {X#23=C#22[(var X#3)];E#25},
           E#24         |->  {E#25},
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=(app (letrec {X#23=C#22[(var X#3)];E#25} in S#12) S#11);X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=(app (letrec {X#23=C#22[(var X#8)];E#25} in S#12) S#11);X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=(app (letrec {X#23=C#22[(var X#3)];E#25} in S#12) S#11);X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=(letrec {X#23=C#22[(var X#3)];E#25} in (app S#12 S#11));X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (app (letrec {E#10} in S#12) C#21[(var X#8)])
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= (letrec {E#10} in (app S#12 C#21[(var X#3)]))
       ;X#8= (var X#3)
       ;E#9
       ;EE#20[X#3,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#8),(app (letrec {E#10} in S#12) C#21)),
             ((var X#3),(app (letrec {E#10} in S#12) C#21)),
             (C#21[(var X#3)],(letrec {E#10} in [.])),
             ((var X#8),(app (letrec {E#10} in S#12) C#21[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#19=[.2];[.1]=(var X#3);EE#20[X#3,(var X#19)]},
           X#2          |->  X#8,
           EE#17[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#4          |->  {E#9;EE#20[X#3,(var X#19)]},
           A#18         |->  [.],
           C#7          |->  (app (letrec {E#10} in S#12) C#21),
           S#11         |->  C#21[(var X#3)],
           A#15         |->  [.],
           X#16         |->  X#3}

and instantiated rules:

                                  (letrec {X#19=(app (letrec {E#10} in S#12) C#21[(var X#3)]);X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#19=(app (letrec {E#10} in S#12) C#21[(var X#8)]);X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=(app (letrec {E#10} in S#12) C#21[(var X#3)]);X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=(letrec {E#10} in (app S#12 C#21[(var X#3)]));X#8=(var X#3);E#9;EE#20[X#3,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= C#7[(var X#16)]
       ;X#16= (var X#3)
       ;E#20
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#1= C#7[(var X#3)]
       ;X#16= (var X#3)
       ;E#20
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#3,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#16),C#7),
             ((var X#3),C#7),
             (S#11,(letrec {E#10} in [.])),
             ((var X#16),C#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);EE#18[[.1],(var X#16)];EE#19[X#3,[.2]]},
           X#2          |->  X#16,
           E#9          |->  {X#1=C#7[(var X#3)];E#20},
           E#4          |->  {E#20;EE#18[X#8,(var X#16)];EE#19[X#3,(app (letrec {E#10} in S#12) S#11)]},
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#1=C#7[(var X#3)];X#16=(var X#3);E#20;EE#18[X#8,(var X#16)];EE#19[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#1=C#7[(var X#16)];X#16=(var X#3);E#20;EE#18[X#8,(var X#16)];EE#19[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#1=C#7[(var X#3)];X#16=(var X#3);E#20;EE#18[X#8,(var X#16)];EE#19[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#1=C#7[(var X#3)];X#16=(var X#3);E#20;EE#18[X#8,(var X#16)];EE#19[X#3,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#8= A#21[(app A#22[(var X#16)] C#23[(var X#16)])]
       ;E#9
       ;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#8= A#21[(app A#22[(var X#16)] C#23[(var X#3)])]
       ;E#9
       ;EE#19[X#3,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#21[(app A#22[(var X#16)] C#23)]),
             ((var X#3),A#21[(app A#22[(var X#16)] C#23)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#16),A#21[(app A#22[(var X#16)] C#23[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);[.1]=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];EE#19[X#3,[.2]]},
           X#2          |->  X#16,
           EE#18[.1,.2] |-> {[.1]=A#21[(app A#22[[.2]] C#23[(var X#3)])]},
           X#1          |->  X#8,
           E#4          |->  {E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)]},
           C#7          |->  A#21[(app A#22[(var X#16)] C#23)],
           A#20         |->  A#21[(app A#22 C#23[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#8=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#8=A#21[(app A#22[(var X#16)] C#23[(var X#16)])];E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#8=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#8=A#21[(app A#22[(var X#16)] C#23[(var X#3)])];E#9;EE#19[X#3,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#8= A#23[(app A#24[(var X#21)] C#25[(var X#16)])]
       ;E#9
       ;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)]
       ;EE#22[X#21,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#8= A#23[(app A#24[(var X#21)] C#25[(var X#3)])]
       ;E#9
       ;EE#19[X#3,(letrec {E#10} in (app S#12 S#11))]
       ;EE#22[X#21,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#23[(app A#24[(var X#21)] C#25)]),
             ((var X#3),A#23[(app A#24[(var X#21)] C#25)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#16),A#23[(app A#24[(var X#21)] C#25[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);[.1]=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];EE#19[X#3,[.2]];EE#22[X#21,(var X#16)]},
           X#2          |->  X#16,
           EE#18[.1,.2] |-> {[.1]=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];EE#22[X#21,[.2]]},
           X#1          |->  X#8,
           E#4          |->  {E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)];EE#22[X#21,(var X#16)]},
           C#7          |->  A#23[(app A#24[(var X#21)] C#25)],
           A#20         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#8=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)];EE#22[X#21,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#8=A#23[(app A#24[(var X#21)] C#25[(var X#16)])];E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)];EE#22[X#21,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#8=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)];EE#22[X#21,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#8=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#9;EE#19[X#3,(letrec {E#10} in (app S#12 S#11))];EE#22[X#21,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#25[(app A#26[(var X#22)] C#27[(var X#16)])]
       ;E#9
       ;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)]
       ;EE#23[X#8,(var X#21)]
       ;EE#24[X#22,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#25[(app A#26[(var X#22)] C#27[(var X#3)])]
       ;E#9
       ;EE#19[X#3,(letrec {E#10} in (app S#12 S#11))]
       ;EE#23[X#8,(var X#21)]
       ;EE#24[X#22,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#25[(app A#26[(var X#22)] C#27)]),
             ((var X#3),A#25[(app A#26[(var X#22)] C#27)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#16),A#25[(app A#26[(var X#22)] C#27[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];EE#19[X#3,[.2]];EE#23[[.1],(var X#21)];EE#24[X#22,(var X#16)]},
           X#2          |->  X#16,
           EE#18[.1,.2] |-> {X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];EE#23[[.1],(var X#21)];EE#24[X#22,[.2]]},
           X#1          |->  X#21,
           E#4          |->  {E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)];EE#23[X#8,(var X#21)];EE#24[X#22,(var X#16)]},
           C#7          |->  A#25[(app A#26[(var X#22)] C#27)],
           A#20         |->  A#25[(app A#26 C#27[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)];EE#23[X#8,(var X#21)];EE#24[X#22,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#16)])];E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)];EE#23[X#8,(var X#21)];EE#24[X#22,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)];EE#23[X#8,(var X#21)];EE#24[X#22,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#9;EE#19[X#3,(letrec {E#10} in (app S#12 S#11))];EE#23[X#8,(var X#21)];EE#24[X#22,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app A#24[(var X#16)] C#25[(var X#16)])]
       ;E#9
       ;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)]
       ;EE#22[X#8,(var X#21)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app A#24[(var X#16)] C#25[(var X#3)])]
       ;E#9
       ;EE#19[X#3,(letrec {E#10} in (app S#12 S#11))]
       ;EE#22[X#8,(var X#21)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#23[(app A#24[(var X#16)] C#25)]),
             ((var X#3),A#23[(app A#24[(var X#16)] C#25)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#16),A#23[(app A#24[(var X#16)] C#25[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#3)])];EE#19[X#3,[.2]];EE#22[[.1],(var X#21)]},
           X#2          |->  X#16,
           EE#18[.1,.2] |-> {X#21=A#23[(app A#24[[.2]] C#25[(var X#3)])];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)];EE#22[X#8,(var X#21)]},
           C#7          |->  A#23[(app A#24[(var X#16)] C#25)],
           A#20         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#3)])];E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)];EE#22[X#8,(var X#21)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#16)])];E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)];EE#22[X#8,(var X#21)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#3)])];E#9;EE#19[X#3,(app (letrec {E#10} in S#12) S#11)];EE#22[X#8,(var X#21)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(var X#16)] C#25[(var X#3)])];E#9;EE#19[X#3,(letrec {E#10} in (app S#12 S#11))];EE#22[X#8,(var X#21)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(app (letrec {E#10} in C#24[(var X#16)]) S#11)]
       ;E#9
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(letrec {E#10} in (app C#24[(var X#3)] S#11))]
       ;E#9
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#23,C#22,A#20,C#7,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#21[(app (letrec {E#10} in C#24) S#11)]),
             ((var X#3),A#21[(app (letrec {E#10} in C#24) S#11)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#16),A#21[(app (letrec {E#10} in C#24[[.]]) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=A#21[[.2]];EE#18[[.1],(var X#16)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=A#21[[.2]]},
           X#1          |->  X#3,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)]},
           A#20         |->  A#21,
           C#7          |->  A#21[(app (letrec {E#10} in C#24) S#11)],
           A#15         |->  [.],
           X#17         |->  X#3,
           C#22         |->  (app (letrec {E#10} in C#24) S#11),
           C#23         |->  (letrec {E#10} in C#24),
           S#12         |->  C#24[(var X#3)]}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=A#21[(app (letrec {E#10} in C#24[(var X#3)]) S#11)];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=A#21[(app (letrec {E#10} in C#24[(var X#16)]) S#11)];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=A#21[(app (letrec {E#10} in C#24[(var X#3)]) S#11)];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#3=A#21[(letrec {E#10} in (app C#24[(var X#3)] S#11))];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(app (letrec {X#25=C#24[(var X#16)];E#27} in S#12) S#11)]
       ;E#9
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(letrec {X#25=C#24[(var X#3)];E#27} in (app S#12 S#11))]
       ;E#9
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#23,C#22,A#20,C#7,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#21[(app (letrec {X#25=C#24;E#27} in S#12) S#11)]),
             ((var X#3),A#21[(app (letrec {X#25=C#24;E#27} in S#12) S#11)]),
             (S#11,(letrec {X#25=C#24[(var X#3)];E#27} in [.])),
             ((var X#16),A#21[(app (letrec {X#25=C#24[[.]];E#27} in S#12) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=A#21[[.2]];EE#18[[.1],(var X#16)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=A#21[[.2]]},
           X#1          |->  X#3,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)]},
           A#20         |->  A#21,
           C#7          |->  A#21[(app (letrec {X#25=C#24;E#27} in S#12) S#11)],
           A#15         |->  [.],
           X#17         |->  X#3,
           C#22         |->  (app (letrec {X#25=C#24;E#27} in S#12) S#11),
           C#23         |->  (letrec {X#25=C#24;E#27} in S#12),
           E#10         |->  {X#25=C#24[(var X#3)];E#27},
           E#26         |->  {E#27}}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=A#21[(app (letrec {X#25=C#24[(var X#3)];E#27} in S#12) S#11)];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=A#21[(app (letrec {X#25=C#24[(var X#16)];E#27} in S#12) S#11)];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=A#21[(app (letrec {X#25=C#24[(var X#3)];E#27} in S#12) S#11)];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#3=A#21[(letrec {X#25=C#24[(var X#3)];E#27} in (app S#12 S#11))];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(app (letrec {E#10} in S#12) C#23[(var X#16)])]
       ;E#9
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(letrec {E#10} in (app S#12 C#23[(var X#3)]))]
       ;E#9
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#22,A#20,C#7,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#21[(app (letrec {E#10} in S#12) C#23)]),
             ((var X#3),A#21[(app (letrec {E#10} in S#12) C#23)]),
             (C#23[(var X#3)],(letrec {E#10} in [.])),
             ((var X#16),A#21[(app (letrec {E#10} in S#12) C#23[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=A#21[[.2]];EE#18[[.1],(var X#16)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=A#21[[.2]]},
           X#1          |->  X#3,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)]},
           A#20         |->  A#21,
           C#7          |->  A#21[(app (letrec {E#10} in S#12) C#23)],
           A#15         |->  [.],
           X#17         |->  X#3,
           C#22         |->  (app (letrec {E#10} in S#12) C#23),
           S#11         |->  C#23[(var X#3)]}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=A#21[(app (letrec {E#10} in S#12) C#23[(var X#3)])];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=A#21[(app (letrec {E#10} in S#12) C#23[(var X#16)])];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=A#21[(app (letrec {E#10} in S#12) C#23[(var X#3)])];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#3=A#21[(letrec {E#10} in (app S#12 C#23[(var X#3)]))];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23[(var X#16)])]
       ;E#9
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= A#21[(app A#22[(letrec {E#10} in (app S#12 S#11))] C#23[(var X#3)])]
       ;E#9
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23)]),
             ((var X#3),A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#16),A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=A#21[(app A#22[[.2]] C#23[(var X#3)])];EE#18[[.1],(var X#16)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=A#21[(app A#22[[.2]] C#23[(var X#3)])]},
           X#1          |->  X#3,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)]},
           C#7          |->  A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23)],
           A#20         |->  A#21[(app A#22 C#23[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23[(var X#3)])];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23[(var X#16)])];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] C#23[(var X#3)])];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#3=A#21[(app A#22[(letrec {E#10} in (app S#12 S#11))] C#23[(var X#3)])];E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= (app (letrec {E#10} in C#22[(var X#16)]) S#11)
       ;E#9
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= (letrec {E#10} in (app C#22[(var X#3)] S#11))
       ;E#9
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#21,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),(app (letrec {E#10} in C#22) S#11)),
             ((var X#3),(app (letrec {E#10} in C#22) S#11)),
             (S#11,(letrec {E#10} in [.])),
             ((var X#16),(app (letrec {E#10} in C#22[[.]]) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=[.2];EE#18[[.1],(var X#16)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#3,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)]},
           A#20         |->  [.],
           C#7          |->  (app (letrec {E#10} in C#22) S#11),
           C#21         |->  (letrec {E#10} in C#22),
           S#12         |->  C#22[(var X#3)],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=(app (letrec {E#10} in C#22[(var X#3)]) S#11);E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=(app (letrec {E#10} in C#22[(var X#16)]) S#11);E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=(app (letrec {E#10} in C#22[(var X#3)]) S#11);E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#3=(letrec {E#10} in (app C#22[(var X#3)] S#11));E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= (app (letrec {X#23=C#22[(var X#16)];E#25} in S#12) S#11)
       ;E#9
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= (letrec {X#23=C#22[(var X#3)];E#25} in (app S#12 S#11))
       ;E#9
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#21,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),(app (letrec {X#23=C#22;E#25} in S#12) S#11)),
             ((var X#3),(app (letrec {X#23=C#22;E#25} in S#12) S#11)),
             (S#11,(letrec {X#23=C#22[(var X#3)];E#25} in [.])),
             ((var X#16),(app (letrec {X#23=C#22[[.]];E#25} in S#12) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=[.2];EE#18[[.1],(var X#16)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#3,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)]},
           A#20         |->  [.],
           C#7          |->  (app (letrec {X#23=C#22;E#25} in S#12) S#11),
           C#21         |->  (letrec {X#23=C#22;E#25} in S#12),
           E#10         |->  {X#23=C#22[(var X#3)];E#25},
           E#24         |->  {E#25},
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=(app (letrec {X#23=C#22[(var X#3)];E#25} in S#12) S#11);E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=(app (letrec {X#23=C#22[(var X#16)];E#25} in S#12) S#11);E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=(app (letrec {X#23=C#22[(var X#3)];E#25} in S#12) S#11);E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#3=(letrec {X#23=C#22[(var X#3)];E#25} in (app S#12 S#11));E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= (app (letrec {E#10} in S#12) C#21[(var X#16)])
       ;E#9
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= (letrec {E#10} in (app S#12 C#21[(var X#3)]))
       ;E#9
       ;EE#18[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),(app (letrec {E#10} in S#12) C#21)),
             ((var X#3),(app (letrec {E#10} in S#12) C#21)),
             (C#21[(var X#3)],(letrec {E#10} in [.])),
             ((var X#16),(app (letrec {E#10} in S#12) C#21[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=[.2];EE#18[[.1],(var X#16)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#3,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)]},
           A#20         |->  [.],
           C#7          |->  (app (letrec {E#10} in S#12) C#21),
           S#11         |->  C#21[(var X#3)],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=(app (letrec {E#10} in S#12) C#21[(var X#3)]);E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=(app (letrec {E#10} in S#12) C#21[(var X#16)]);E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=(app (letrec {E#10} in S#12) C#21[(var X#3)]);E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#3=(letrec {E#10} in (app S#12 C#21[(var X#3)]));E#9;EE#18[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#3= A#23[(app A#24[(var X#21)] C#25[(var X#16)])]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#21,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#3= A#23[(app A#24[(var X#21)] C#25[(var X#3)])]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#21,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#23[(app A#24[(var X#21)] C#25)]),
             ((var X#3),A#23[(app A#24[(var X#21)] C#25)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#16),A#23[(app A#24[(var X#21)] C#25[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];EE#18[[.1],(var X#16)];EE#22[X#21,[.2]]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {[.1]=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];EE#22[X#21,[.2]]},
           X#1          |->  X#3,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)];EE#22[X#21,(app (letrec {E#10} in S#12) S#11)]},
           C#7          |->  A#23[(app A#24[(var X#21)] C#25)],
           A#20         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#9;EE#18[X#8,(var X#16)];EE#22[X#21,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#16)])];E#9;EE#18[X#8,(var X#16)];EE#22[X#21,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#9;EE#18[X#8,(var X#16)];EE#22[X#21,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#3=A#23[(app A#24[(var X#21)] C#25[(var X#3)])];E#9;EE#18[X#8,(var X#16)];EE#22[X#21,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#25[(app A#26[(var X#22)] C#27[(var X#16)])]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#23[X#3,(var X#21)]
       ;EE#24[X#22,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#25[(app A#26[(var X#22)] C#27[(var X#3)])]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#23[X#3,(var X#21)]
       ;EE#24[X#22,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#25[(app A#26[(var X#22)] C#27)]),
             ((var X#3),A#25[(app A#26[(var X#22)] C#27)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#16),A#25[(app A#26[(var X#22)] C#27[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];EE#18[[.1],(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,[.2]]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];EE#23[[.1],(var X#21)];EE#24[X#22,[.2]]},
           X#1          |->  X#21,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(app (letrec {E#10} in S#12) S#11)]},
           C#7          |->  A#25[(app A#26[(var X#22)] C#27)],
           A#20         |->  A#25[(app A#26 C#27[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#9;EE#18[X#8,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#16)])];E#9;EE#18[X#8,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#9;EE#18[X#8,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#21=A#25[(app A#26[(var X#22)] C#27[(var X#3)])];E#9;EE#18[X#8,(var X#16)];EE#23[X#3,(var X#21)];EE#24[X#22,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app (letrec {E#10} in C#26[(var X#16)]) S#11)]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(letrec {E#10} in (app C#26[(var X#3)] S#11))]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#25,C#24,A#20,C#7,A#23}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#23[(app (letrec {E#10} in C#26) S#11)]),
             ((var X#3),A#23[(app (letrec {E#10} in C#26) S#11)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#16),A#23[(app (letrec {E#10} in C#26[[.]]) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#23[[.2]];EE#18[[.1],(var X#16)];EE#22[X#3,(var X#21)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=A#23[[.2]];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]},
           A#20         |->  A#23,
           C#7          |->  A#23[(app (letrec {E#10} in C#26) S#11)],
           A#15         |->  [.],
           X#17         |->  X#3,
           C#24         |->  (app (letrec {E#10} in C#26) S#11),
           C#25         |->  (letrec {E#10} in C#26),
           S#12         |->  C#26[(var X#3)]}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#23[(app (letrec {E#10} in C#26[(var X#3)]) S#11)];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#23[(app (letrec {E#10} in C#26[(var X#16)]) S#11)];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#23[(app (letrec {E#10} in C#26[(var X#3)]) S#11)];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#21=A#23[(letrec {E#10} in (app C#26[(var X#3)] S#11))];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app (letrec {X#27=C#26[(var X#16)];E#29} in S#12) S#11)]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(letrec {X#27=C#26[(var X#3)];E#29} in (app S#12 S#11))]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#25,C#24,A#20,C#7,A#23}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#23[(app (letrec {X#27=C#26;E#29} in S#12) S#11)]),
             ((var X#3),A#23[(app (letrec {X#27=C#26;E#29} in S#12) S#11)]),
             (S#11,(letrec {X#27=C#26[(var X#3)];E#29} in [.])),
             ((var X#16),A#23[(app (letrec {X#27=C#26[[.]];E#29} in S#12) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#23[[.2]];EE#18[[.1],(var X#16)];EE#22[X#3,(var X#21)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=A#23[[.2]];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]},
           A#20         |->  A#23,
           C#7          |->  A#23[(app (letrec {X#27=C#26;E#29} in S#12) S#11)],
           A#15         |->  [.],
           X#17         |->  X#3,
           C#24         |->  (app (letrec {X#27=C#26;E#29} in S#12) S#11),
           C#25         |->  (letrec {X#27=C#26;E#29} in S#12),
           E#10         |->  {X#27=C#26[(var X#3)];E#29},
           E#28         |->  {E#29}}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#23[(app (letrec {X#27=C#26[(var X#3)];E#29} in S#12) S#11)];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#23[(app (letrec {X#27=C#26[(var X#16)];E#29} in S#12) S#11)];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#23[(app (letrec {X#27=C#26[(var X#3)];E#29} in S#12) S#11)];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#21=A#23[(letrec {X#27=C#26[(var X#3)];E#29} in (app S#12 S#11))];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app (letrec {E#10} in S#12) C#25[(var X#16)])]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(letrec {E#10} in (app S#12 C#25[(var X#3)]))]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#24,A#20,C#7,A#23}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#23[(app (letrec {E#10} in S#12) C#25)]),
             ((var X#3),A#23[(app (letrec {E#10} in S#12) C#25)]),
             (C#25[(var X#3)],(letrec {E#10} in [.])),
             ((var X#16),A#23[(app (letrec {E#10} in S#12) C#25[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#23[[.2]];EE#18[[.1],(var X#16)];EE#22[X#3,(var X#21)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=A#23[[.2]];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]},
           A#20         |->  A#23,
           C#7          |->  A#23[(app (letrec {E#10} in S#12) C#25)],
           A#15         |->  [.],
           X#17         |->  X#3,
           C#24         |->  (app (letrec {E#10} in S#12) C#25),
           S#11         |->  C#25[(var X#3)]}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#23[(app (letrec {E#10} in S#12) C#25[(var X#3)])];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#23[(app (letrec {E#10} in S#12) C#25[(var X#16)])];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#23[(app (letrec {E#10} in S#12) C#25[(var X#3)])];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#21=A#23[(letrec {E#10} in (app S#12 C#25[(var X#3)]))];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app A#24[(app (letrec {E#10} in S#12) S#11)] C#25[(var X#16)])]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= A#23[(app A#24[(letrec {E#10} in (app S#12 S#11))] C#25[(var X#3)])]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#20,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),A#23[(app A#24[(app (letrec {E#10} in S#12) S#11)] C#25)]),
             ((var X#3),A#23[(app A#24[(app (letrec {E#10} in S#12) S#11)] C#25)]),
             (S#11,(letrec {E#10} in [.])),
             ((var X#16),A#23[(app A#24[(app (letrec {E#10} in S#12) S#11)] C#25[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=A#23[(app A#24[[.2]] C#25[(var X#3)])];EE#18[[.1],(var X#16)];EE#22[X#3,(var X#21)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=A#23[(app A#24[[.2]] C#25[(var X#3)])];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]},
           C#7          |->  A#23[(app A#24[(app (letrec {E#10} in S#12) S#11)] C#25)],
           A#20         |->  A#23[(app A#24 C#25[(var X#3)])],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(app (letrec {E#10} in S#12) S#11)] C#25[(var X#3)])];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(app (letrec {E#10} in S#12) S#11)] C#25[(var X#16)])];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(app (letrec {E#10} in S#12) S#11)] C#25[(var X#3)])];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#21=A#23[(app A#24[(letrec {E#10} in (app S#12 S#11))] C#25[(var X#3)])];E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= (app (letrec {E#10} in C#24[(var X#16)]) S#11)
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= (letrec {E#10} in (app C#24[(var X#3)] S#11))
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#23,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),(app (letrec {E#10} in C#24) S#11)),
             ((var X#3),(app (letrec {E#10} in C#24) S#11)),
             (S#11,(letrec {E#10} in [.])),
             ((var X#16),(app (letrec {E#10} in C#24[[.]]) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=[.2];EE#18[[.1],(var X#16)];EE#22[X#3,(var X#21)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=[.2];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]},
           A#20         |->  [.],
           C#7          |->  (app (letrec {E#10} in C#24) S#11),
           C#23         |->  (letrec {E#10} in C#24),
           S#12         |->  C#24[(var X#3)],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=(app (letrec {E#10} in C#24[(var X#3)]) S#11);E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=(app (letrec {E#10} in C#24[(var X#16)]) S#11);E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=(app (letrec {E#10} in C#24[(var X#3)]) S#11);E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#21=(letrec {E#10} in (app C#24[(var X#3)] S#11));E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= (app (letrec {X#25=C#24[(var X#16)];E#27} in S#12) S#11)
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= (letrec {X#25=C#24[(var X#3)];E#27} in (app S#12 S#11))
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#23,C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),(app (letrec {X#25=C#24;E#27} in S#12) S#11)),
             ((var X#3),(app (letrec {X#25=C#24;E#27} in S#12) S#11)),
             (S#11,(letrec {X#25=C#24[(var X#3)];E#27} in [.])),
             ((var X#16),(app (letrec {X#25=C#24[[.]];E#27} in S#12) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=[.2];EE#18[[.1],(var X#16)];EE#22[X#3,(var X#21)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=[.2];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]},
           A#20         |->  [.],
           C#7          |->  (app (letrec {X#25=C#24;E#27} in S#12) S#11),
           C#23         |->  (letrec {X#25=C#24;E#27} in S#12),
           E#10         |->  {X#25=C#24[(var X#3)];E#27},
           E#26         |->  {E#27},
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=(app (letrec {X#25=C#24[(var X#3)];E#27} in S#12) S#11);E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=(app (letrec {X#25=C#24[(var X#16)];E#27} in S#12) S#11);E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=(app (letrec {X#25=C#24[(var X#3)];E#27} in S#12) S#11);E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#21=(letrec {X#25=C#24[(var X#3)];E#27} in (app S#12 S#11));E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#3)
       ;X#21= (app (letrec {E#10} in S#12) C#23[(var X#16)])
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (var X#3)
       ;X#21= (letrec {E#10} in (app S#12 C#23[(var X#3)]))
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#22[X#3,(var X#21)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {C#7}
   Delta2 = {E#10}
   Delta3 = {((var X#16),(app (letrec {E#10} in S#12) C#23)),
             ((var X#3),(app (letrec {E#10} in S#12) C#23)),
             (C#23[(var X#3)],(letrec {E#10} in [.])),
             ((var X#16),(app (letrec {E#10} in S#12) C#23[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -cpx-e1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
    -cpx-e1->                     T#6[(letrec {X#1=C#7[(var X#2)];X#2=(var X#3);E#4} in S#5)]
    and constraints: ((var X#2),C#7), ((var X#3),C#7)
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=C#7[(var X#3)];X#2=(var X#3);E#4} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),C#7),((var X#3),C#7),(S#11,(letrec {E#10} in [.])),((var X#2),C#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=(var X#3);X#21=[.2];EE#18[[.1],(var X#16)];EE#22[X#3,(var X#21)]},
           X#2          |->  X#16,
           EE#19[.1,.2] |-> {X#21=[.2];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#4          |->  {E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]},
           A#20         |->  [.],
           C#7          |->  (app (letrec {E#10} in S#12) C#23),
           S#11         |->  C#23[(var X#3)],
           A#15         |->  [.],
           X#17         |->  X#3}

and instantiated rules:

                                  (letrec {X#16=(var X#3);X#21=(app (letrec {E#10} in S#12) C#23[(var X#3)]);E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -cpx-e1->                     (letrec {X#16=(var X#3);X#21=(app (letrec {E#10} in S#12) C#23[(var X#16)]);E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(var X#3);X#21=(app (letrec {E#10} in S#12) C#23[(var X#3)]);E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(var X#3);X#21=(letrec {E#10} in (app S#12 C#23[(var X#3)]));E#9;EE#18[X#8,(var X#16)];EE#22[X#3,(var X#21)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     A#11[(app (\ X#7.S#9) T#13[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
    ,
     A#11[(letrec {X#7=T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#9)]
  )

where

   Delta1 = {T#12,A#10,T#6,A#11}
   Delta2 = {}
   Delta3 = {(T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(\ X#7.[.])),
             (T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {X#7=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  A#10[(app (\ X#7.S#9) S#8)]
    -SR,lbeta1->                  A#10[(letrec {X#7=S#8} in S#9)]
    and constraints: (S#8,(\ X#7.[.])), (S#8,(letrec {X#7=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        A#10[(app (\ X#7.S#9) S#8)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#8,(\ X#7.[.])),(S#8,(letrec {X#7=[.]} in S#9)),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {A#10  |->  A#11,
           T#6   |->  A#11[(app (\ X#7.S#9) T#13)],
           T#12  |->  (app (\ X#7.S#9) T#13),
           S#8   |->  T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  A#11[(app (\ X#7.S#9) T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
    -xch1->                       A#11[(app (\ X#7.S#9) T#13[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
    ................................................................................
                                  A#11[(app (\ X#7.S#9) T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
    -SR,lbeta1->                  A#11[(letrec {X#7=T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#9)]
    

================================================================================
Critical Pair:

  (
     A#11[(app A#12[(app (\ X#7.S#9) S#8)] T#13[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
    ,
     A#11[(app A#12[(letrec {X#7=S#8} in S#9)] T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
  )

where

   Delta1 = {A#10,T#6}
   Delta2 = {}
   Delta3 = {(S#8,(\ X#7.[.])),
             (S#8,(letrec {X#7=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  A#10[(app (\ X#7.S#9) S#8)]
    -SR,lbeta1->                  A#10[(letrec {X#7=S#8} in S#9)]
    and constraints: (S#8,(\ X#7.[.])), (S#8,(letrec {X#7=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        A#10[(app (\ X#7.S#9) S#8)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#8,(\ X#7.[.])),(S#8,(letrec {X#7=[.]} in S#9)),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  A#11[(app A#12[(app (\ X#7.S#9) S#8)] T#13)],
           A#10  |->  A#11[(app A#12 T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  A#11[(app A#12[(app (\ X#7.S#9) S#8)] T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
    -xch1->                       A#11[(app A#12[(app (\ X#7.S#9) S#8)] T#13[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
    ................................................................................
                                  A#11[(app A#12[(app (\ X#7.S#9) S#8)] T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
    -SR,lbeta1->                  A#11[(app A#12[(letrec {X#7=S#8} in S#9)] T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
    

================================================================================
Critical Pair:

  (
     (app (\ X#7.S#9) T#11[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])
    ,
     (letrec {X#7=T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#9)
  )

where

   Delta1 = {T#6}
   Delta2 = {}
   Delta3 = {(T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(\ X#7.[.])),
             (T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {X#7=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  A#10[(app (\ X#7.S#9) S#8)]
    -SR,lbeta1->                  A#10[(letrec {X#7=S#8} in S#9)]
    and constraints: (S#8,(\ X#7.[.])), (S#8,(letrec {X#7=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        A#10[(app (\ X#7.S#9) S#8)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#8,(\ X#7.[.])),(S#8,(letrec {X#7=[.]} in S#9)),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {A#10  |->  [.],
           T#6   |->  (app (\ X#7.S#9) T#11),
           S#8   |->  T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (app (\ X#7.S#9) T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])
    -xch1->                       (app (\ X#7.S#9) T#11[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])
    ................................................................................
                                  (app (\ X#7.S#9) T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])
    -SR,lbeta1->                  (letrec {X#7=T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#9)
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#13[(app (\ X#7.S#10) T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
     )
    ,
     (letrec
        E#8
     in
        A#13[(letrec {X#7=T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#10)]
     )
  )

where

   Delta1 = {T#14,A#11,T#12,T#6,A#13}
   Delta2 = {E#8}
   Delta3 = {(T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(\ X#7.[.])),
             (T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {X#7=[.]} in S#10)),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in A#13[(app (\ X#7.S#10) T#15)]),
           A#11  |->  A#13,
           T#12  |->  A#13[(app (\ X#7.S#10) T#15)],
           T#14  |->  (app (\ X#7.S#10) T#15),
           S#9   |->  T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#8} in A#13[(app (\ X#7.S#10) T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -xch1->                       (letrec {E#8} in A#13[(app (\ X#7.S#10) T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#8} in A#13[(app (\ X#7.S#10) T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -SR,lbeta2->                  (letrec {E#8} in A#13[(letrec {X#7=T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
     )
    ,
     (letrec
        E#8
     in
        A#13[(app A#14[(letrec {X#7=S#9} in S#10)] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#11,T#12,T#6}
   Delta2 = {E#8}
   Delta3 = {(S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15)]),
           T#12  |->  A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {E#8} in A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -xch1->                       (letrec {E#8} in A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#8} in A#13[(app A#14[(app (\ X#7.S#10) S#9)] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -SR,lbeta2->                  (letrec {E#8} in A#13[(app A#14[(letrec {X#7=S#9} in S#10)] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        (app (\ X#7.S#10) T#13[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])
     )
    ,
     (letrec
        E#8
     in
        (letrec {X#7=T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#10)
     )
  )

where

   Delta1 = {T#12,T#6}
   Delta2 = {E#8}
   Delta3 = {(T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(\ X#7.[.])),
             (T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {X#7=[.]} in S#10)),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in (app (\ X#7.S#10) T#13)),
           A#11  |->  [.],
           T#12  |->  (app (\ X#7.S#10) T#13),
           S#9   |->  T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#8} in (app (\ X#7.S#10) T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))
    -xch1->                       (letrec {E#8} in (app (\ X#7.S#10) T#13[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]))
    ................................................................................
                                  (letrec {E#8} in (app (\ X#7.S#10) T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))
    -SR,lbeta2->                  (letrec {E#8} in (letrec {X#7=T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#10))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
       ;E#15
     in
        A#11[(app (\ X#7.S#10) S#9)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;E#15
     in
        A#11[(letrec {X#7=S#9} in S#10)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#8}
   Delta3 = {(S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {X#13=T#12;E#15} in A#11[(app (\ X#7.S#10) S#9)]),
           E#8   |->  {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15} in A#11[(app (\ X#7.S#10) S#9)])
    -xch1->                       (letrec {X#13=T#12[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#15} in A#11[(app (\ X#7.S#10) S#9)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15} in A#11[(letrec {X#7=S#9} in S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#4;X#2=(var X#1);E#13} in A#11[(app (\ X#7.S#10) S#9)])
    ,
     (letrec {X#1=(var X#2);X#2=S#4;E#13} in A#11[(letrec {X#7=S#9} in S#10)])
  )

where

   Delta1 = {}
   Delta2 = {E#8}
   Delta3 = {(S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {E#8} in A#11[(letrec {X#7=S#9} in S#10)])
    and constraints: E#8/= {}, (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8} in A#11[(app (\ X#7.S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#11[(app (\ X#7.S#10) S#9)],
           E#8   |->  {X#1=(var X#2);X#2=S#4;E#13},
           E#12  |->  {X#1=(var X#2);E#13},
           E#3   |->  {E#13}}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#2=S#4;E#13} in A#11[(app (\ X#7.S#10) S#9)])
    -xch1->                       (letrec {X#1=S#4;X#2=(var X#1);E#13} in A#11[(app (\ X#7.S#10) S#9)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#2=S#4;E#13} in A#11[(app (\ X#7.S#10) S#9)])
    -SR,lbeta2->                  (letrec {X#1=(var X#2);X#2=S#4;E#13} in A#11[(letrec {X#7=S#9} in S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
       ;EE#13[X#7,(app (\ X#8.S#11) S#10)]
     in
        A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
     )
    ,
     (letrec
        E#9
       ;EE#13[X#7,(letrec {X#8=S#10} in S#11)]
     in
        A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#14,T#6}
   Delta2 = {}
   Delta3 = {(S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#15[(app A#16[[.]] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]),
             ((var X#7),A#15[(app A#16[[.]] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#7)] T#17)],
           A#12  |->  A#15[(app A#16 T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -xch1->                       (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
       ;E#17
       ;EE#13[X#7,(app (\ X#8.S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;E#17
       ;EE#13[X#7,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {}
   Delta3 = {(S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#15=T#14;E#17;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)]),
           E#9   |->  {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17},
           E#16  |->  {E#17;EE#13[X#7,(app (\ X#8.S#11) S#10)]}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#15=T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#17;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app (\ X#8.S#11) T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#9
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(letrec {X#8=T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#11)]
       ;E#9
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#19,A#17,T#14,T#6,A#18}
   Delta2 = {}
   Delta3 = {(T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(\ X#8.[.])),
             (T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {X#8=[.]} in S#11)),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#18[(app (\ X#8.S#11) T#20)];E#9} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#9},
           A#17         |->  A#18,
           T#14         |->  A#18[(app (\ X#8.S#11) T#20)],
           T#19         |->  (app (\ X#8.S#11) T#20),
           S#10         |->  T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=A#18[(app (\ X#8.S#11) T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9} in A#12[(var X#7)])
    -xch1->                       (letrec {X#7=A#18[(app (\ X#8.S#11) T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#9} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app (\ X#8.S#11) T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#7=A#18[(letrec {X#8=T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#11)];E#9} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#9
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(app A#19[(letrec {X#8=S#10} in S#11)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#9
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {}
   Delta3 = {(S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20)];E#9} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]},
           X#15         |->  X#7,
           E#16         |->  {E#9},
           T#14         |->  A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20)],
           A#17         |->  A#18[(app A#19 T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9} in A#12[(var X#7)])
    -xch1->                       (letrec {X#7=A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#9} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app A#19[(app (\ X#8.S#11) S#10)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#7=A#18[(app A#19[(letrec {X#8=S#10} in S#11)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (app (\ X#8.S#11) T#18[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])
       ;E#9
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= (letrec {X#8=T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#11)
       ;E#9
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {}
   Delta3 = {(T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(\ X#8.[.])),
             (T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {X#8=[.]} in S#11)),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(app (\ X#8.S#11) T#18);E#9} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {E#9},
           A#17         |->  [.],
           T#14         |->  (app (\ X#8.S#11) T#18),
           S#10         |->  T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=(app (\ X#8.S#11) T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]);E#9} in A#12[(var X#7)])
    -xch1->                       (letrec {X#7=(app (\ X#8.S#11) T#18[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]);E#9} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(app (\ X#8.S#11) T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]);E#9} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#7=(letrec {X#8=T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#11);E#9} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#9
       ;EE#19[X#18,(app (\ X#8.S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#9
       ;EE#19[X#18,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {}
   Delta3 = {(S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22)];E#9;EE#19[X#18,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];EE#19[X#18,[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#9;EE#19[X#18,(app (\ X#8.S#11) S#10)]},
           T#14         |->  A#20[(app A#21[(var X#18)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9;EE#19[X#18,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#9;EE#19[X#18,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9;EE#19[X#18,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9;EE#19[X#18,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#9
       ;EE#20[X#7,(var X#18)]
       ;EE#21[X#19,(app (\ X#8.S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#9
       ;EE#20[X#7,(var X#18)]
       ;EE#21[X#19,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {}
   Delta3 = {(S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24)];E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#15         |->  X#18,
           E#16         |->  {E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(app (\ X#8.S#11) S#10)]},
           T#14         |->  A#22[(app A#23[(var X#19)] T#24)],
           A#17         |->  A#22[(app A#23 T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9;EE#20[X#7,(var X#18)];EE#21[X#19,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (\ X#8.S#11) T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {X#8=T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#11)]
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#21,A#17,T#14,T#6,A#20}
   Delta2 = {}
   Delta3 = {(T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(\ X#8.[.])),
             (T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {X#8=[.]} in S#11)),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app (\ X#8.S#11) T#22)];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#9;EE#19[X#7,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[(app (\ X#8.S#11) T#22)],
           T#21         |->  (app (\ X#8.S#11) T#22),
           S#10         |->  T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (\ X#8.S#11) T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#18=A#20[(app (\ X#8.S#11) T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (\ X#8.S#11) T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#18=A#20[(letrec {X#8=T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#11)];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(letrec {X#8=S#10} in S#11)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {}
   Delta3 = {(S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22)];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#9;EE#19[X#7,(var X#18)]},
           T#14         |->  A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#18=A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(app (\ X#8.S#11) S#10)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#18=A#20[(app A#21[(letrec {X#8=S#10} in S#11)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (\ X#8.S#11) T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= (letrec {X#8=T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#11)
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {}
   Delta3 = {(T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(\ X#8.[.])),
             (T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {X#8=[.]} in S#11)),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=(app (\ X#8.S#11) T#20);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#9;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  (app (\ X#8.S#11) T#20),
           S#10         |->  T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#18=(app (\ X#8.S#11) T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#18=(app (\ X#8.S#11) T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=(app (\ X#8.S#11) T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#18=(letrec {X#8=T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]} in S#11);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#4
       ;X#2= (var X#1)
       ;E#15
       ;EE#13[X#7,(app (\ X#8.S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#2= S#4
       ;E#15
       ;EE#13[X#7,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {(S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#7)],
           E#9   |->  {X#1=(var X#2);X#2=S#4;E#15},
           E#14  |->  {X#1=(var X#2);E#15},
           E#3   |->  {E#15;EE#13[X#7,(app (\ X#8.S#11) S#10)]}}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#2=S#4;E#15;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#1=S#4;X#2=(var X#1);E#15;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#2=S#4;E#15;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#1=(var X#2);X#2=S#4;E#15;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(app (\ X#8.S#11) S#10)]
       ;X#7= (var X#1)
       ;E#15
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#1= (var X#7)
       ;X#7= A#14[(letrec {X#8=S#10} in S#11)]
       ;E#15
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {(S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),[.]),
             ((var X#7),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {[.1]=A#14[[.2]]},
           X#2          |->  X#7,
           S#4          |->  A#14[(app (\ X#8.S#11) S#10)],
           E#9          |->  {X#1=(var X#7);E#15},
           E#3          |->  {E#15}}

and instantiated rules:

                                  (letrec {X#1=(var X#7);X#7=A#14[(app (\ X#8.S#11) S#10)];E#15} in A#12[(var X#7)])
    -xch1->                       (letrec {X#1=A#14[(app (\ X#8.S#11) S#10)];X#7=(var X#1);E#15} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#1=(var X#7);X#7=A#14[(app (\ X#8.S#11) S#10)];E#15} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#1=(var X#7);X#7=A#14[(letrec {X#8=S#10} in S#11)];E#15} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(var X#15)]
       ;X#7= (var X#1)
       ;E#17
       ;EE#16[X#15,(app (\ X#8.S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#1= (var X#7)
       ;X#7= A#14[(var X#15)]
       ;E#17
       ;EE#16[X#15,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {(S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),[.]),
             ((var X#7),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {[.1]=A#14[(var X#15)];EE#16[X#15,[.2]]},
           X#2          |->  X#7,
           S#4          |->  A#14[(var X#15)],
           E#9          |->  {X#1=(var X#7);E#17},
           E#3          |->  {E#17;EE#16[X#15,(app (\ X#8.S#11) S#10)]}}

and instantiated rules:

                                  (letrec {X#1=(var X#7);X#7=A#14[(var X#15)];E#17;EE#16[X#15,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#1=A#14[(var X#15)];X#7=(var X#1);E#17;EE#16[X#15,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#1=(var X#7);X#7=A#14[(var X#15)];E#17;EE#16[X#15,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#1=(var X#7);X#7=A#14[(var X#15)];E#17;EE#16[X#15,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(var X#16)]
       ;X#15= (var X#1)
       ;E#19
       ;EE#17[X#7,(var X#15)]
       ;EE#18[X#16,(app (\ X#8.S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#1= (var X#15)
       ;X#15= A#14[(var X#16)]
       ;E#19
       ;EE#17[X#7,(var X#15)]
       ;EE#18[X#16,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {(S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),[.]),
             ((var X#15),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#2          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           E#9          |->  {X#1=(var X#15);E#19},
           E#3          |->  {E#19;EE#17[X#7,(var X#15)];EE#18[X#16,(app (\ X#8.S#11) S#10)]}}

and instantiated rules:

                                  (letrec {X#1=(var X#15);X#15=A#14[(var X#16)];E#19;EE#17[X#7,(var X#15)];EE#18[X#16,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#1=A#14[(var X#16)];X#15=(var X#1);E#19;EE#17[X#7,(var X#15)];EE#18[X#16,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#1=(var X#15);X#15=A#14[(var X#16)];E#19;EE#17[X#7,(var X#15)];EE#18[X#16,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#1=(var X#15);X#15=A#14[(var X#16)];E#19;EE#17[X#7,(var X#15)];EE#18[X#16,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#7)
       ;X#7= A#14[(var X#16)]
       ;E#9
       ;EE#18[X#16,(app (\ X#8.S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;X#7= (var X#15)
       ;E#9
       ;EE#18[X#16,(letrec {X#8=S#10} in S#11)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {(S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#7),[.]),
             ((var X#15),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];[.1]=(var X#15);EE#18[X#16,[.2]]},
           X#2          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           EE#17[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#7,
           E#3          |->  {E#9;EE#18[X#16,(app (\ X#8.S#11) S#10)]},
           A#19         |->  [.],
           X#15         |->  X#15}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];X#7=(var X#15);E#9;EE#18[X#16,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#15=(var X#7);X#7=A#14[(var X#16)];E#9;EE#18[X#16,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];X#7=(var X#15);E#9;EE#18[X#16,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#15=A#14[(var X#16)];X#7=(var X#15);E#9;EE#18[X#16,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#20)
       ;X#20= A#14[(var X#16)]
       ;E#9
       ;EE#18[X#16,(app (\ X#8.S#11) S#10)]
       ;EE#21[X#7,(var X#20)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;X#20= (var X#15)
       ;E#9
       ;EE#18[X#16,(letrec {X#8=S#10} in S#11)]
       ;EE#21[X#7,(var X#20)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {(S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#20),[.]),
             ((var X#15),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];X#20=(var X#15);EE#18[X#16,[.2]];EE#21[[.1],(var X#20)]},
           X#2          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           EE#17[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#3          |->  {E#9;EE#18[X#16,(app (\ X#8.S#11) S#10)];EE#21[X#7,(var X#20)]},
           A#19         |->  [.],
           X#15         |->  X#15}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];X#20=(var X#15);E#9;EE#18[X#16,(app (\ X#8.S#11) S#10)];EE#21[X#7,(var X#20)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#15=(var X#20);X#20=A#14[(var X#16)];E#9;EE#18[X#16,(app (\ X#8.S#11) S#10)];EE#21[X#7,(var X#20)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];X#20=(var X#15);E#9;EE#18[X#16,(app (\ X#8.S#11) S#10)];EE#21[X#7,(var X#20)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#15=A#14[(var X#16)];X#20=(var X#15);E#9;EE#18[X#16,(letrec {X#8=S#10} in S#11)];EE#21[X#7,(var X#20)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(app (\ X#8.S#11) S#10)]
       ;X#15= (var X#1)
       ;E#17
       ;EE#16[X#7,(var X#15)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#1= (var X#15)
       ;X#15= A#14[(letrec {X#8=S#10} in S#11)]
       ;E#17
       ;EE#16[X#7,(var X#15)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {(S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#1),[.]),
             ((var X#15),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[[.2]];EE#16[[.1],(var X#15)]},
           X#2          |->  X#15,
           S#4          |->  A#14[(app (\ X#8.S#11) S#10)],
           E#9          |->  {X#1=(var X#15);E#17},
           E#3          |->  {E#17;EE#16[X#7,(var X#15)]}}

and instantiated rules:

                                  (letrec {X#1=(var X#15);X#15=A#14[(app (\ X#8.S#11) S#10)];E#17;EE#16[X#7,(var X#15)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#1=A#14[(app (\ X#8.S#11) S#10)];X#15=(var X#1);E#17;EE#16[X#7,(var X#15)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#1=(var X#15);X#15=A#14[(app (\ X#8.S#11) S#10)];E#17;EE#16[X#7,(var X#15)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#1=(var X#15);X#15=A#14[(letrec {X#8=S#10} in S#11)];E#17;EE#16[X#7,(var X#15)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#7)
       ;X#7= A#14[(app (\ X#8.S#11) S#10)]
       ;E#9
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= A#14[(letrec {X#8=S#10} in S#11)]
       ;X#7= (var X#15)
       ;E#9
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {(S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#7),[.]),
             ((var X#15),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[[.2]];[.1]=(var X#15)},
           X#2          |->  X#15,
           S#4          |->  A#14[(app (\ X#8.S#11) S#10)],
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#7,
           E#3          |->  {E#9},
           A#17         |->  [.],
           X#15         |->  X#15}

and instantiated rules:

                                  (letrec {X#15=A#14[(app (\ X#8.S#11) S#10)];X#7=(var X#15);E#9} in A#12[(var X#7)])
    -xch1->                       (letrec {X#15=(var X#7);X#7=A#14[(app (\ X#8.S#11) S#10)];E#9} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=A#14[(app (\ X#8.S#11) S#10)];X#7=(var X#15);E#9} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#15=A#14[(letrec {X#8=S#10} in S#11)];X#7=(var X#15);E#9} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#18)
       ;X#18= A#14[(app (\ X#8.S#11) S#10)]
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= A#14[(letrec {X#8=S#10} in S#11)]
       ;X#18= (var X#15)
       ;E#9
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {(S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#18),[.]),
             ((var X#15),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {E#9;EE#13[X#7,(letrec {X#8=S#10} in S#11)]} in A#12[(var X#7)])
    and constraints: (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#9;EE#13[X#7,(app (\ X#8.S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[[.2]];X#18=(var X#15);EE#19[[.1],(var X#18)]},
           X#2          |->  X#15,
           S#4          |->  A#14[(app (\ X#8.S#11) S#10)],
           EE#16[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#3          |->  {E#9;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           X#15         |->  X#15}

and instantiated rules:

                                  (letrec {X#15=A#14[(app (\ X#8.S#11) S#10)];X#18=(var X#15);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#15=(var X#18);X#18=A#14[(app (\ X#8.S#11) S#10)];E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=A#14[(app (\ X#8.S#11) S#10)];X#18=(var X#15);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lbeta3->                  (letrec {X#15=A#14[(letrec {X#8=S#10} in S#11)];X#18=(var X#15);E#9;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#10)
       ;E#9
     in
        A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
     )
    ,
     (letrec
        X#7= (\ X#8.S#10)
       ;E#9
     in
        A#13[(app A#14[(\ X#8.S#10)] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#11,T#12,T#6}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#13[(app A#14[[.]] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(\ X#8.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(\ X#8.S#10);E#9} in A#13[(app A#14[(var X#7)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#7)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -xch1->                       (letrec {X#7=(\ X#8.S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#13[(app A#14[(\ X#8.S#10)] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
       ;X#7= (\ X#8.S#10)
       ;E#15
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;X#7= (\ X#8.S#10)
       ;E#15
     in
        A#11[(\ X#8.S#10)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(\ X#8.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#13=T#12;X#7=(\ X#8.S#10);E#15} in A#11[(var X#7)]),
           E#9   |->  {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15},
           E#14  |->  {X#7=(\ X#8.S#10);E#15}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(\ X#8.S#10);E#15} in A#11[(var X#7)])
    -xch1->                       (letrec {X#13=T#12[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];X#7=(\ X#8.S#10);E#15} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(\ X#8.S#10);E#15} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(\ X#8.S#10);E#15} in A#11[(\ X#8.S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#8.S#10);X#7=(var X#1);E#12} in A#11[(var X#7)])
    ,
     (letrec {X#1=(var X#7);X#7=(\ X#8.S#10);E#12} in A#11[(\ X#8.S#10)])
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#7),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(\ X#8.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6  |->  [.],
           S#5  |->  A#11[(var X#7)],
           X#2  |->  X#7,
           S#4  |->  (\ X#8.S#10),
           E#9  |->  {X#1=(var X#7);E#12},
           E#3  |->  {E#12}}

and instantiated rules:

                                  (letrec {X#1=(var X#7);X#7=(\ X#8.S#10);E#12} in A#11[(var X#7)])
    -xch1->                       (letrec {X#1=(\ X#8.S#10);X#7=(var X#1);E#12} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#1=(var X#7);X#7=(\ X#8.S#10);E#12} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#1=(var X#7);X#7=(\ X#8.S#10);E#12} in A#11[(\ X#8.S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#4;X#2=(var X#1);X#7=(\ X#8.S#10);E#13} in A#11[(var X#7)])
    ,
     (letrec {X#1=(var X#2);X#2=S#4;X#7=(\ X#8.S#10);E#13} in A#11[(\ X#8.S#10)])
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(\ X#8.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#11[(var X#7)],
           E#9   |->  {X#1=(var X#2);X#2=S#4;E#13},
           E#12  |->  {X#1=(var X#2);E#13},
           E#3   |->  {X#7=(\ X#8.S#10);E#13}}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#2=S#4;X#7=(\ X#8.S#10);E#13} in A#11[(var X#7)])
    -xch1->                       (letrec {X#1=S#4;X#2=(var X#1);X#7=(\ X#8.S#10);E#13} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#2=S#4;X#7=(\ X#8.S#10);E#13} in A#11[(var X#7)])
    -SR,cp-in1->                  (letrec {X#1=(var X#2);X#2=S#4;X#7=(\ X#8.S#10);E#13} in A#11[(\ X#8.S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;VV#13|X#9,(var X#7)|
     in
        A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;VV#13|X#9,(var X#7)|
     in
        A#15[(app A#16[(\ X#8.S#11)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#14,T#6}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#9),A#15[(app A#16[[.]] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(var X#9)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#9)] T#17)],
           A#12  |->  A#15[(app A#16 T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -xch1->                       (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(var X#9)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#15[(app A#16[(\ X#8.S#11)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
       ;X#7= (\ X#8.S#11)
       ;E#17
       ;VV#13|X#9,(var X#7)|
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;X#7= (\ X#8.S#11)
       ;E#17
       ;VV#13|X#9,(var X#7)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {X#15=T#14;X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|} in A#12[(var X#9)]),
           E#10  |->  {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17},
           E#16  |->  {X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -xch1->                       (letrec {X#15=T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(\ X#8.S#11);E#17;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#8.S#11)
       ;X#7= (var X#1)
       ;E#14
       ;VV#13|X#9,(var X#7)|
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#7)
       ;X#7= (\ X#8.S#11)
       ;E#14
       ;VV#13|X#9,(var X#7)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#7),[.]),
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#9)],
           X#2   |->  X#7,
           S#4   |->  (\ X#8.S#11),
           E#10  |->  {X#1=(var X#7);E#14},
           E#3   |->  {E#14;VV#13|X#9,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#1=(var X#7);X#7=(\ X#8.S#11);E#14;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -xch1->                       (letrec {X#1=(\ X#8.S#11);X#7=(var X#1);E#14;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#7);X#7=(\ X#8.S#11);E#14;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#1=(var X#7);X#7=(\ X#8.S#11);E#14;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#7=(var X#9);X#9=(\ X#8.S#11);E#10} in A#12[(var X#9)])
    ,
     (letrec {X#7=(\ X#8.S#11);X#9=(var X#7);E#10} in A#12[(\ X#8.S#11)])
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#9),[.]),
             ((var X#7),[.]),
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           X#2          |->  X#7,
           S#4          |->  (\ X#8.S#11),
           VV#13|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#9,
           X#7          |->  X#7,
           E#3          |->  {E#10}}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#7);E#10} in A#12[(var X#9)])
    -xch1->                       (letrec {X#7=(var X#9);X#9=(\ X#8.S#11);E#10} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#7);E#10} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);X#9=(var X#7);E#10} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (\ X#8.S#11)
       ;X#7= (var X#15)
       ;E#10
       ;VV#16|X#9,(var X#15)|
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#15= (var X#7)
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;VV#16|X#9,(var X#15)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#15),[.]),
             ((var X#7),[.]),
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           X#2          |->  X#7,
           S#4          |->  (\ X#8.S#11),
           VV#13|.1,.2| |-> {X#15=[.2];VV#16|[.1],(var X#15)|},
           X#1          |->  X#15,
           X#7          |->  X#7,
           E#3          |->  {E#10;VV#16|X#9,(var X#15)|}}

and instantiated rules:

                                  (letrec {X#15=(var X#7);X#7=(\ X#8.S#11);E#10;VV#16|X#9,(var X#15)|} in A#12[(var X#9)])
    -xch1->                       (letrec {X#15=(\ X#8.S#11);X#7=(var X#15);E#10;VV#16|X#9,(var X#15)|} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#15=(var X#7);X#7=(\ X#8.S#11);E#10;VV#16|X#9,(var X#15)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#15=(var X#7);X#7=(\ X#8.S#11);E#10;VV#16|X#9,(var X#15)|} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#4
       ;X#2= (var X#1)
       ;X#7= (\ X#8.S#11)
       ;E#15
       ;VV#13|X#9,(var X#7)|
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#2= S#4
       ;X#7= (\ X#8.S#11)
       ;E#15
       ;VV#13|X#9,(var X#7)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#9)],
           E#10  |->  {X#1=(var X#2);X#2=S#4;E#15},
           E#14  |->  {X#1=(var X#2);E#15},
           E#3   |->  {X#7=(\ X#8.S#11);E#15;VV#13|X#9,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#2=S#4;X#7=(\ X#8.S#11);E#15;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -xch1->                       (letrec {X#1=S#4;X#2=(var X#1);X#7=(\ X#8.S#11);E#15;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#2=S#4;X#7=(\ X#8.S#11);E#15;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#1=(var X#2);X#2=S#4;X#7=(\ X#8.S#11);E#15;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#7);X#7=(\ X#8.S#11);X#9=(var X#1);E#15} in A#12[(var X#9)])
    ,
     (letrec
        X#1= (var X#9)
       ;X#7= (\ X#8.S#11)
       ;X#9= (var X#7)
       ;E#15
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#9),[.]),
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {[.1]=[.2]},
           X#2          |->  X#9,
           S#4          |->  (var X#7),
           E#10         |->  {X#1=(var X#9);E#15},
           E#3          |->  {X#7=(\ X#8.S#11);E#15}}

and instantiated rules:

                                  (letrec {X#1=(var X#9);X#7=(\ X#8.S#11);X#9=(var X#7);E#15} in A#12[(var X#9)])
    -xch1->                       (letrec {X#1=(var X#7);X#7=(\ X#8.S#11);X#9=(var X#1);E#15} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#9);X#7=(\ X#8.S#11);X#9=(var X#7);E#15} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#1=(var X#9);X#7=(\ X#8.S#11);X#9=(var X#7);E#15} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#15)
       ;X#7= (\ X#8.S#11)
       ;X#9= (var X#1)
       ;E#17
       ;VV#16|X#15,(var X#7)|
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#9)
       ;X#7= (\ X#8.S#11)
       ;X#9= (var X#15)
       ;E#17
       ;VV#16|X#15,(var X#7)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#9),[.]),
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {[.1]=(var X#15);VV#16|X#15,[.2]|},
           X#2          |->  X#9,
           S#4          |->  (var X#15),
           E#10         |->  {X#1=(var X#9);E#17},
           E#3          |->  {X#7=(\ X#8.S#11);E#17;VV#16|X#15,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#1=(var X#9);X#7=(\ X#8.S#11);X#9=(var X#15);E#17;VV#16|X#15,(var X#7)|} in A#12[(var X#9)])
    -xch1->                       (letrec {X#1=(var X#15);X#7=(\ X#8.S#11);X#9=(var X#1);E#17;VV#16|X#15,(var X#7)|} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#9);X#7=(\ X#8.S#11);X#9=(var X#15);E#17;VV#16|X#15,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#1=(var X#9);X#7=(\ X#8.S#11);X#9=(var X#15);E#17;VV#16|X#15,(var X#7)|} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#16)
       ;X#15= (var X#1)
       ;X#7= (\ X#8.S#11)
       ;E#19
       ;VV#17|X#9,(var X#15)|
       ;VV#18|X#16,(var X#7)|
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#15)
       ;X#15= (var X#16)
       ;X#7= (\ X#8.S#11)
       ;E#19
       ;VV#17|X#9,(var X#15)|
       ;VV#18|X#16,(var X#7)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#15),[.]),
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {X#15=(var X#16);VV#17|[.1],(var X#15)|;VV#18|X#16,[.2]|},
           X#2          |->  X#15,
           S#4          |->  (var X#16),
           E#10         |->  {X#1=(var X#15);E#19},
           E#3          |->  {X#7=(\ X#8.S#11);E#19;VV#17|X#9,(var X#15)|;VV#18|X#16,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#1=(var X#15);X#15=(var X#16);X#7=(\ X#8.S#11);E#19;VV#17|X#9,(var X#15)|;VV#18|X#16,(var X#7)|} in A#12[(var X#9)])
    -xch1->                       (letrec {X#1=(var X#16);X#15=(var X#1);X#7=(\ X#8.S#11);E#19;VV#17|X#9,(var X#15)|;VV#18|X#16,(var X#7)|} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#15);X#15=(var X#16);X#7=(\ X#8.S#11);E#19;VV#17|X#9,(var X#15)|;VV#18|X#16,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#1=(var X#15);X#15=(var X#16);X#7=(\ X#8.S#11);E#19;VV#17|X#9,(var X#15)|;VV#18|X#16,(var X#7)|} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#9)
       ;X#7= (\ X#8.S#11)
       ;X#9= (var X#16)
       ;E#10
       ;VV#18|X#16,(var X#7)|
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#15= (var X#16)
       ;X#7= (\ X#8.S#11)
       ;X#9= (var X#15)
       ;E#10
       ;VV#18|X#16,(var X#7)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#9),[.]),
             ((var X#15),[.]),
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {X#15=(var X#16);[.1]=(var X#15);VV#18|X#16,[.2]|},
           X#2          |->  X#15,
           S#4          |->  (var X#16),
           VV#17|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#9,
           X#15         |->  X#15,
           E#3          |->  {X#7=(\ X#8.S#11);E#10;VV#18|X#16,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#15=(var X#16);X#7=(\ X#8.S#11);X#9=(var X#15);E#10;VV#18|X#16,(var X#7)|} in A#12[(var X#9)])
    -xch1->                       (letrec {X#15=(var X#9);X#7=(\ X#8.S#11);X#9=(var X#16);E#10;VV#18|X#16,(var X#7)|} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#15=(var X#16);X#7=(\ X#8.S#11);X#9=(var X#15);E#10;VV#18|X#16,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#15=(var X#16);X#7=(\ X#8.S#11);X#9=(var X#15);E#10;VV#18|X#16,(var X#7)|} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#20)
       ;X#20= (var X#16)
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;VV#18|X#16,(var X#7)|
       ;VV#21|X#9,(var X#20)|
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#15= (var X#16)
       ;X#20= (var X#15)
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;VV#18|X#16,(var X#7)|
       ;VV#21|X#9,(var X#20)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#20),[.]),
             ((var X#15),[.]),
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {X#15=(var X#16);X#20=(var X#15);VV#18|X#16,[.2]|;VV#21|[.1],(var X#20)|},
           X#2          |->  X#15,
           S#4          |->  (var X#16),
           VV#17|.1,.2| |-> {X#20=[.2];VV#21|[.1],(var X#20)|},
           X#1          |->  X#20,
           X#15         |->  X#15,
           E#3          |->  {X#7=(\ X#8.S#11);E#10;VV#18|X#16,(var X#7)|;VV#21|X#9,(var X#20)|}}

and instantiated rules:

                                  (letrec {X#15=(var X#16);X#20=(var X#15);X#7=(\ X#8.S#11);E#10;VV#18|X#16,(var X#7)|;VV#21|X#9,(var X#20)|} in A#12[(var X#9)])
    -xch1->                       (letrec {X#15=(var X#20);X#20=(var X#16);X#7=(\ X#8.S#11);E#10;VV#18|X#16,(var X#7)|;VV#21|X#9,(var X#20)|} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#15=(var X#16);X#20=(var X#15);X#7=(\ X#8.S#11);E#10;VV#18|X#16,(var X#7)|;VV#21|X#9,(var X#20)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#15=(var X#16);X#20=(var X#15);X#7=(\ X#8.S#11);E#10;VV#18|X#16,(var X#7)|;VV#21|X#9,(var X#20)|} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#7)
       ;X#15= (var X#1)
       ;X#7= (\ X#8.S#11)
       ;E#17
       ;VV#16|X#9,(var X#15)|
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#15)
       ;X#15= (var X#7)
       ;X#7= (\ X#8.S#11)
       ;E#17
       ;VV#16|X#9,(var X#15)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#15),[.]),
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {X#15=[.2];VV#16|[.1],(var X#15)|},
           X#2          |->  X#15,
           S#4          |->  (var X#7),
           E#10         |->  {X#1=(var X#15);E#17},
           E#3          |->  {X#7=(\ X#8.S#11);E#17;VV#16|X#9,(var X#15)|}}

and instantiated rules:

                                  (letrec {X#1=(var X#15);X#15=(var X#7);X#7=(\ X#8.S#11);E#17;VV#16|X#9,(var X#15)|} in A#12[(var X#9)])
    -xch1->                       (letrec {X#1=(var X#7);X#15=(var X#1);X#7=(\ X#8.S#11);E#17;VV#16|X#9,(var X#15)|} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#15);X#15=(var X#7);X#7=(\ X#8.S#11);E#17;VV#16|X#9,(var X#15)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#1=(var X#15);X#15=(var X#7);X#7=(\ X#8.S#11);E#17;VV#16|X#9,(var X#15)|} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#15=(var X#9);X#7=(\ X#8.S#11);X#9=(var X#7);E#10} in A#12[(var X#9)])
    ,
     (letrec
        X#15= (var X#7)
       ;X#7= (\ X#8.S#11)
       ;X#9= (var X#15)
       ;E#10
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#9),[.]),
             ((var X#15),[.]),
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {X#15=[.2];[.1]=(var X#15)},
           X#2          |->  X#15,
           S#4          |->  (var X#7),
           VV#16|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#9,
           X#15         |->  X#15,
           E#3          |->  {X#7=(\ X#8.S#11);E#10}}

and instantiated rules:

                                  (letrec {X#15=(var X#7);X#7=(\ X#8.S#11);X#9=(var X#15);E#10} in A#12[(var X#9)])
    -xch1->                       (letrec {X#15=(var X#9);X#7=(\ X#8.S#11);X#9=(var X#7);E#10} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#15=(var X#7);X#7=(\ X#8.S#11);X#9=(var X#15);E#10} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#15=(var X#7);X#7=(\ X#8.S#11);X#9=(var X#15);E#10} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#18)
       ;X#18= (var X#7)
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;VV#19|X#9,(var X#18)|
     in
        A#12[(var X#9)]
     )
    ,
     (letrec
        X#15= (var X#7)
       ;X#18= (var X#15)
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;VV#19|X#9,(var X#18)|
     in
        A#12[(\ X#8.S#11)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#18),[.]),
             ((var X#15),[.]),
             ((var X#7),[.]),
             ((var X#9),A#12[[.]]),
             ((var X#7),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(\ X#8.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;VV#13|X#9,(var X#7)|} in A#12[(var X#9)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#12[[.]]),((var X#7),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#9)],
           VV#13|.1,.2| |-> {X#15=[.2];X#18=(var X#15);VV#19|[.1],(var X#18)|},
           X#2          |->  X#15,
           S#4          |->  (var X#7),
           VV#16|.1,.2| |-> {X#18=[.2];VV#19|[.1],(var X#18)|},
           X#1          |->  X#18,
           X#15         |->  X#15,
           E#3          |->  {X#7=(\ X#8.S#11);E#10;VV#19|X#9,(var X#18)|}}

and instantiated rules:

                                  (letrec {X#15=(var X#7);X#18=(var X#15);X#7=(\ X#8.S#11);E#10;VV#19|X#9,(var X#18)|} in A#12[(var X#9)])
    -xch1->                       (letrec {X#15=(var X#18);X#18=(var X#7);X#7=(\ X#8.S#11);E#10;VV#19|X#9,(var X#18)|} in A#12[(var X#9)])
    ................................................................................
                                  (letrec {X#15=(var X#7);X#18=(var X#15);X#7=(\ X#8.S#11);E#10;VV#19|X#9,(var X#18)|} in A#12[(var X#9)])
    -SR,cp-in2->                  (letrec {X#15=(var X#7);X#18=(var X#15);X#7=(\ X#8.S#11);E#10;VV#19|X#9,(var X#18)|} in A#12[(\ X#8.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;EE#14[X#9,A#12[(var X#7)]]
     in
        A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;E#10
       ;EE#14[X#9,A#12[(\ X#8.S#11)]]
     in
        A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#13,T#15,T#6,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#16[(app A#17[[.]] T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]),
             ((var X#9),A#16[(app A#17[[.]] T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#16[(app A#17[(var X#9)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#9)] T#18)],
           A#13  |->  A#16[(app A#17 T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -xch1->                       (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
       ;X#7= (\ X#8.S#11)
       ;E#18
       ;EE#14[X#9,A#12[(var X#7)]]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;X#7= (\ X#8.S#11)
       ;E#18
       ;EE#14[X#9,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#6,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#16=T#15;X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)]),
           E#10  |->  {X#16=T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#18},
           E#17  |->  {X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(var X#7)]]}}

and instantiated rules:

                                  (letrec {X#16=T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -xch1->                       (letrec {X#16=T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#16=T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(\ X#8.S#11);E#18;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]]
       ;E#10
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[A#21[(app A#22[(\ X#8.S#11)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]]
       ;E#10
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#6,A#12,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#21[(app A#22[[.]] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#11);X#9=A#19[A#21[(app A#22[(var X#7)] T#23)]];E#10} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#9,
           E#17         |->  {X#7=(\ X#8.S#11);E#10},
           A#18         |->  A#19,
           T#15         |->  A#19[A#21[(app A#22[(var X#7)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#7)] T#23)],
           A#12         |->  A#21[(app A#22 T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]];E#10} in A#13[(var X#9)])
    -xch1->                       (letrec {X#7=(\ X#8.S#11);X#9=A#19[A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]];E#10} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]];E#10} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#19[A#21[(app A#22[(\ X#8.S#11)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]];E#10} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[(app A#20[A#12[(var X#7)]] T#21[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#10
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[(app A#20[A#12[(\ X#8.S#11)]] T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#10
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[A#12[(var X#7)]] T#21)];E#10} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]},
           X#16         |->  X#9,
           E#17         |->  {X#7=(\ X#8.S#11);E#10},
           T#15         |->  A#19[(app A#20[A#12[(var X#7)]] T#21)],
           A#18         |->  A#19[(app A#20 T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[A#12[(var X#7)]] T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10} in A#13[(var X#9)])
    -xch1->                       (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[A#12[(var X#7)]] T#21[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#10} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[A#12[(var X#7)]] T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[A#12[(\ X#8.S#11)]] T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[(app A#20[(var X#7)] T#21[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#10
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#19[(app A#20[(\ X#8.S#11)] T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#10
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#15,T#6,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#19[(app A#20[[.]] T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[(var X#7)] T#21)];E#10} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#9,
           E#17         |->  {X#7=(\ X#8.S#11);E#10},
           A#18         |->  [.],
           T#15         |->  A#19[(app A#20[(var X#7)] T#21)],
           A#12         |->  A#19[(app A#20 T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[(var X#7)] T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10} in A#13[(var X#9)])
    -xch1->                       (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[(var X#7)] T#21[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#10} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[(var X#7)] T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#19[(app A#20[(\ X#8.S#11)] T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#10
       ;EE#20[X#19,A#12[(var X#7)]]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#11)
       ;X#9= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#10
       ;EE#20[X#19,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#11);X#9=A#21[(app A#22[(var X#19)] T#23)];E#10;EE#20[X#19,A#12[(var X#7)]]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];EE#20[X#19,[.2]]},
           X#16         |->  X#9,
           E#17         |->  {X#7=(\ X#8.S#11);E#10;EE#20[X#19,A#12[(var X#7)]]},
           T#15         |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#11);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10;EE#20[X#19,A#12[(var X#7)]]} in A#13[(var X#9)])
    -xch1->                       (letrec {X#7=(\ X#8.S#11);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#10;EE#20[X#19,A#12[(var X#7)]]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10;EE#20[X#19,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10;EE#20[X#19,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#21[X#9,(var X#19)]
       ;EE#22[X#20,A#12[(var X#7)]]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#21[X#9,(var X#19)]
       ;EE#22[X#20,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(var X#7)]]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(var X#7)]]},
           T#15         |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(var X#7)]]} in A#13[(var X#9)])
    -xch1->                       (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(var X#7)]]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#21[X#9,(var X#19)];EE#22[X#20,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(app A#24[(var X#7)] T#25[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[(\ X#8.S#11)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#6,A#12,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#23[(app A#24[[.]] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[A#23[(app A#24[(var X#7)] T#25)]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]},
           A#18         |->  A#21,
           T#15         |->  A#21[A#23[(app A#24[(var X#7)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#7)] T#25)],
           A#12         |->  A#23[(app A#24 T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#7)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -xch1->                       (letrec {X#19=A#21[A#23[(app A#24[(var X#7)] T#25[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#7)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#19=A#21[A#23[(app A#24[(\ X#8.S#11)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[A#12[(var X#7)]] T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[A#12[(\ X#8.S#11)]] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app A#22[A#12[(var X#7)]] T#23)];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]},
           T#15         |->  A#21[(app A#22[A#12[(var X#7)]] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[A#12[(var X#7)]] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -xch1->                       (letrec {X#19=A#21[(app A#22[A#12[(var X#7)]] T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[A#12[(var X#7)]] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#19=A#21[(app A#22[A#12[(\ X#8.S#11)]] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(\ X#8.S#11)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#15,T#6,A#12}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#21[(app A#22[[.]] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app A#22[(var X#7)] T#23)];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]},
           A#18         |->  [.],
           T#15         |->  A#21[(app A#22[(var X#7)] T#23)],
           A#12         |->  A#21[(app A#22 T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -xch1->                       (letrec {X#19=A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(var X#7)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#19=A#21[(app A#22[(\ X#8.S#11)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#8.S#11)
       ;X#7= (var X#1)
       ;E#15
       ;EE#14[X#9,A#12[(var X#7)]]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#7)
       ;X#7= (\ X#8.S#11)
       ;E#15
       ;EE#14[X#9,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#7),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#9)],
           X#2   |->  X#7,
           S#4   |->  (\ X#8.S#11),
           E#10  |->  {X#1=(var X#7);E#15},
           E#3   |->  {E#15;EE#14[X#9,A#12[(var X#7)]]}}

and instantiated rules:

                                  (letrec {X#1=(var X#7);X#7=(\ X#8.S#11);E#15;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -xch1->                       (letrec {X#1=(\ X#8.S#11);X#7=(var X#1);E#15;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#7);X#7=(\ X#8.S#11);E#15;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#1=(var X#7);X#7=(\ X#8.S#11);E#15;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#4
       ;X#2= (var X#1)
       ;X#7= (\ X#8.S#11)
       ;E#16
       ;EE#14[X#9,A#12[(var X#7)]]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#2= S#4
       ;X#7= (\ X#8.S#11)
       ;E#16
       ;EE#14[X#9,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#9)],
           E#10  |->  {X#1=(var X#2);X#2=S#4;E#16},
           E#15  |->  {X#1=(var X#2);E#16},
           E#3   |->  {X#7=(\ X#8.S#11);E#16;EE#14[X#9,A#12[(var X#7)]]}}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#2=S#4;X#7=(\ X#8.S#11);E#16;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -xch1->                       (letrec {X#1=S#4;X#2=(var X#1);X#7=(\ X#8.S#11);E#16;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#2=S#4;X#7=(\ X#8.S#11);E#16;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#1=(var X#2);X#2=S#4;X#7=(\ X#8.S#11);E#16;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#15[A#12[(var X#7)]]
       ;X#7= (\ X#8.S#11)
       ;X#9= (var X#1)
       ;E#16
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#9)
       ;X#7= (\ X#8.S#11)
       ;X#9= A#15[A#12[(\ X#8.S#11)]]
       ;E#16
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#9),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#2          |->  X#9,
           S#4          |->  A#15[A#12[(var X#7)]],
           E#10         |->  {X#1=(var X#9);E#16},
           E#3          |->  {X#7=(\ X#8.S#11);E#16}}

and instantiated rules:

                                  (letrec {X#1=(var X#9);X#7=(\ X#8.S#11);X#9=A#15[A#12[(var X#7)]];E#16} in A#13[(var X#9)])
    -xch1->                       (letrec {X#1=A#15[A#12[(var X#7)]];X#7=(\ X#8.S#11);X#9=(var X#1);E#16} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#9);X#7=(\ X#8.S#11);X#9=A#15[A#12[(var X#7)]];E#16} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#1=(var X#9);X#7=(\ X#8.S#11);X#9=A#15[A#12[(\ X#8.S#11)]];E#16} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#15[(var X#16)]
       ;X#7= (\ X#8.S#11)
       ;X#9= (var X#1)
       ;E#18
       ;EE#17[X#16,A#12[(var X#7)]]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#9)
       ;X#7= (\ X#8.S#11)
       ;X#9= A#15[(var X#16)]
       ;E#18
       ;EE#17[X#16,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#9),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=A#15[(var X#16)];EE#17[X#16,[.2]]},
           X#2          |->  X#9,
           S#4          |->  A#15[(var X#16)],
           E#10         |->  {X#1=(var X#9);E#18},
           E#3          |->  {X#7=(\ X#8.S#11);E#18;EE#17[X#16,A#12[(var X#7)]]}}

and instantiated rules:

                                  (letrec {X#1=(var X#9);X#7=(\ X#8.S#11);X#9=A#15[(var X#16)];E#18;EE#17[X#16,A#12[(var X#7)]]} in A#13[(var X#9)])
    -xch1->                       (letrec {X#1=A#15[(var X#16)];X#7=(\ X#8.S#11);X#9=(var X#1);E#18;EE#17[X#16,A#12[(var X#7)]]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#9);X#7=(\ X#8.S#11);X#9=A#15[(var X#16)];E#18;EE#17[X#16,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#1=(var X#9);X#7=(\ X#8.S#11);X#9=A#15[(var X#16)];E#18;EE#17[X#16,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#15[(var X#17)]
       ;X#16= (var X#1)
       ;X#7= (\ X#8.S#11)
       ;E#20
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#17,A#12[(var X#7)]]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#16)
       ;X#16= A#15[(var X#17)]
       ;X#7= (\ X#8.S#11)
       ;E#20
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#17,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#16),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#15[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#2          |->  X#16,
           S#4          |->  A#15[(var X#17)],
           E#10         |->  {X#1=(var X#16);E#20},
           E#3          |->  {X#7=(\ X#8.S#11);E#20;EE#18[X#9,(var X#16)];EE#19[X#17,A#12[(var X#7)]]}}

and instantiated rules:

                                  (letrec {X#1=(var X#16);X#16=A#15[(var X#17)];X#7=(\ X#8.S#11);E#20;EE#18[X#9,(var X#16)];EE#19[X#17,A#12[(var X#7)]]} in A#13[(var X#9)])
    -xch1->                       (letrec {X#1=A#15[(var X#17)];X#16=(var X#1);X#7=(\ X#8.S#11);E#20;EE#18[X#9,(var X#16)];EE#19[X#17,A#12[(var X#7)]]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#16);X#16=A#15[(var X#17)];X#7=(\ X#8.S#11);E#20;EE#18[X#9,(var X#16)];EE#19[X#17,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#1=(var X#16);X#16=A#15[(var X#17)];X#7=(\ X#8.S#11);E#20;EE#18[X#9,(var X#16)];EE#19[X#17,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#9)
       ;X#7= (\ X#8.S#11)
       ;X#9= A#15[(var X#17)]
       ;E#10
       ;EE#19[X#17,A#12[(var X#7)]]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#15[(var X#17)]
       ;X#7= (\ X#8.S#11)
       ;X#9= (var X#16)
       ;E#10
       ;EE#19[X#17,A#12[(\ X#8.S#11)]]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {}
   Delta3 = {((var X#9),[.]),
             ((var X#16),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#15[(var X#17)];[.1]=(var X#16);EE#19[X#17,[.2]]},
           X#2          |->  X#16,
           S#4          |->  A#15[(var X#17)],
           EE#18[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#9,
           E#3          |->  {X#7=(\ X#8.S#11);E#10;EE#19[X#17,A#12[(var X#7)]]},
           A#20         |->  [.],
           X#16         |->  X#16}

and instantiated rules:

                                  (letrec {X#16=A#15[(var X#17)];X#7=(\ X#8.S#11);X#9=(var X#16);E#10;EE#19[X#17,A#12[(var X#7)]]} in A#13[(var X#9)])
    -xch1->                       (letrec {X#16=(var X#9);X#7=(\ X#8.S#11);X#9=A#15[(var X#17)];E#10;EE#19[X#17,A#12[(var X#7)]]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#15[(var X#17)];X#7=(\ X#8.S#11);X#9=(var X#16);E#10;EE#19[X#17,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#16=A#15[(var X#17)];X#7=(\ X#8.S#11);X#9=(var X#16);E#10;EE#19[X#17,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#21)
       ;X#21= A#15[(var X#17)]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#19[X#17,A#12[(var X#7)]]
       ;EE#22[X#9,(var X#21)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#15[(var X#17)]
       ;X#21= (var X#16)
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#19[X#17,A#12[(\ X#8.S#11)]]
       ;EE#22[X#9,(var X#21)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {}
   Delta3 = {((var X#21),[.]),
             ((var X#16),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#15[(var X#17)];X#21=(var X#16);EE#19[X#17,[.2]];EE#22[[.1],(var X#21)]},
           X#2          |->  X#16,
           S#4          |->  A#15[(var X#17)],
           EE#18[.1,.2] |-> {X#21=[.2];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#3          |->  {X#7=(\ X#8.S#11);E#10;EE#19[X#17,A#12[(var X#7)]];EE#22[X#9,(var X#21)]},
           A#20         |->  [.],
           X#16         |->  X#16}

and instantiated rules:

                                  (letrec {X#16=A#15[(var X#17)];X#21=(var X#16);X#7=(\ X#8.S#11);E#10;EE#19[X#17,A#12[(var X#7)]];EE#22[X#9,(var X#21)]} in A#13[(var X#9)])
    -xch1->                       (letrec {X#16=(var X#21);X#21=A#15[(var X#17)];X#7=(\ X#8.S#11);E#10;EE#19[X#17,A#12[(var X#7)]];EE#22[X#9,(var X#21)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#15[(var X#17)];X#21=(var X#16);X#7=(\ X#8.S#11);E#10;EE#19[X#17,A#12[(var X#7)]];EE#22[X#9,(var X#21)]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#16=A#15[(var X#17)];X#21=(var X#16);X#7=(\ X#8.S#11);E#10;EE#19[X#17,A#12[(\ X#8.S#11)]];EE#22[X#9,(var X#21)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#15[A#12[(var X#7)]]
       ;X#16= (var X#1)
       ;X#7= (\ X#8.S#11)
       ;E#18
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#16)
       ;X#16= A#15[A#12[(\ X#8.S#11)]]
       ;X#7= (\ X#8.S#11)
       ;E#18
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#16),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#15[[.2]];EE#17[[.1],(var X#16)]},
           X#2          |->  X#16,
           S#4          |->  A#15[A#12[(var X#7)]],
           E#10         |->  {X#1=(var X#16);E#18},
           E#3          |->  {X#7=(\ X#8.S#11);E#18;EE#17[X#9,(var X#16)]}}

and instantiated rules:

                                  (letrec {X#1=(var X#16);X#16=A#15[A#12[(var X#7)]];X#7=(\ X#8.S#11);E#18;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -xch1->                       (letrec {X#1=A#15[A#12[(var X#7)]];X#16=(var X#1);X#7=(\ X#8.S#11);E#18;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#16);X#16=A#15[A#12[(var X#7)]];X#7=(\ X#8.S#11);E#18;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#1=(var X#16);X#16=A#15[A#12[(\ X#8.S#11)]];X#7=(\ X#8.S#11);E#18;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#9)
       ;X#7= (\ X#8.S#11)
       ;X#9= A#15[A#12[(var X#7)]]
       ;E#10
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#15[A#12[(\ X#8.S#11)]]
       ;X#7= (\ X#8.S#11)
       ;X#9= (var X#16)
       ;E#10
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {}
   Delta3 = {((var X#9),[.]),
             ((var X#16),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#15[[.2]];[.1]=(var X#16)},
           X#2          |->  X#16,
           S#4          |->  A#15[A#12[(var X#7)]],
           EE#17[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#9,
           E#3          |->  {X#7=(\ X#8.S#11);E#10},
           A#18         |->  [.],
           X#16         |->  X#16}

and instantiated rules:

                                  (letrec {X#16=A#15[A#12[(var X#7)]];X#7=(\ X#8.S#11);X#9=(var X#16);E#10} in A#13[(var X#9)])
    -xch1->                       (letrec {X#16=(var X#9);X#7=(\ X#8.S#11);X#9=A#15[A#12[(var X#7)]];E#10} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#15[A#12[(var X#7)]];X#7=(\ X#8.S#11);X#9=(var X#16);E#10} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#16=A#15[A#12[(\ X#8.S#11)]];X#7=(\ X#8.S#11);X#9=(var X#16);E#10} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#19)
       ;X#19= A#15[A#12[(var X#7)]]
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#15[A#12[(\ X#8.S#11)]]
       ;X#19= (var X#16)
       ;X#7= (\ X#8.S#11)
       ;E#10
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {}
   Delta3 = {((var X#19),[.]),
             ((var X#16),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#9),A#13[[.]]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(\ X#8.S#11)]]} in A#13[(var X#9)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#11);E#10;EE#14[X#9,A#12[(var X#7)]]} in A#13[(var X#9)])}
      Delta1=  {A#12}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#9),A#13[[.]]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#15[[.2]];X#19=(var X#16);EE#20[[.1],(var X#19)]},
           X#2          |->  X#16,
           S#4          |->  A#15[A#12[(var X#7)]],
           EE#17[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#3          |->  {X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]},
           A#18         |->  [.],
           X#16         |->  X#16}

and instantiated rules:

                                  (letrec {X#16=A#15[A#12[(var X#7)]];X#19=(var X#16);X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -xch1->                       (letrec {X#16=(var X#19);X#19=A#15[A#12[(var X#7)]];X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#15[A#12[(var X#7)]];X#19=(var X#16);X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -SR,cp-e1->                   (letrec {X#16=A#15[A#12[(\ X#8.S#11)]];X#19=(var X#16);X#7=(\ X#8.S#11);E#10;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#14,T#17,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#9),A#18[(app A#19[[.]] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#18[(app A#19[[.]] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] T#20)]),
           T#17  |->  A#18[(app A#19[(var X#9)] T#20)],
           A#14  |->  A#18[(app A#19 T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -xch1->                       (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#18[(app A#19[(var X#9)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= T#17[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
       ;X#7= (\ X#8.S#12)
       ;E#20
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;X#7= (\ X#8.S#12)
       ;E#20
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#18=T#17;X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           E#11  |->  {X#18=T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#20},
           E#19  |->  {X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#18=T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#18=T#17[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[A#23[(app A#24[(\ X#8.S#12)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#22,A#20,T#17,T#6,A#13,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#23[(app A#24[[.]] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#12);X#9=A#21[A#23[(app A#24[(var X#10)] T#25)]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#21[[.2]]},
           X#18         |->  X#9,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;VV#16|X#10,(var X#7)|},
           A#20         |->  A#21,
           T#17         |->  A#21[A#23[(app A#24[(var X#10)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#10)] T#25)],
           A#13         |->  A#23[(app A#24 T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#7=(\ X#8.S#12);X#9=A#21[A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#21[A#23[(app A#24[(\ X#8.S#12)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[(app A#22[A#13[(var X#10)]] T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[(app A#22[A#13[(\ X#8.S#12)]] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#20,T#17,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[A#13[(var X#10)]] T#23)];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#21[(app A#22[[.2]] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]},
           X#18         |->  X#9,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;VV#16|X#10,(var X#7)|},
           T#17         |->  A#21[(app A#22[A#13[(var X#10)]] T#23)],
           A#20         |->  A#21[(app A#22 T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[A#13[(var X#10)]] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[A#13[(var X#10)]] T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[A#13[(var X#10)]] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[A#13[(\ X#8.S#12)]] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[(app A#22[(var X#10)] T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#21[(app A#22[(\ X#8.S#12)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#17,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#21[(app A#22[[.]] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[(var X#10)] T#23)];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#18         |->  X#9,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;VV#16|X#10,(var X#7)|},
           A#20         |->  [.],
           T#17         |->  A#21[(app A#22[(var X#10)] T#23)],
           A#13         |->  A#21[(app A#22 T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[(var X#10)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[(var X#10)] T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[(var X#10)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#21[(app A#22[(\ X#8.S#12)] T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#11
       ;EE#22[X#21,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#7= (\ X#8.S#12)
       ;X#9= A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#11
       ;EE#22[X#21,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#20,T#17,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(\ X#8.S#12);X#9=A#23[(app A#24[(var X#21)] T#25)];E#11;EE#22[X#21,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {[.1]=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];EE#22[X#21,[.2]]},
           X#18         |->  X#9,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;EE#22[X#21,A#13[(var X#10)]];VV#16|X#10,(var X#7)|},
           T#17         |->  A#23[(app A#24[(var X#21)] T#25)],
           A#20         |->  A#23[(app A#24 T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(\ X#8.S#12);X#9=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#11;EE#22[X#21,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#7=(\ X#8.S#12);X#9=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#11;EE#22[X#21,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);X#9=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#11;EE#22[X#21,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);X#9=A#23[(app A#24[(var X#21)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#11;EE#22[X#21,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#23[X#9,(var X#21)]
       ;EE#24[X#22,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#21= A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#23[X#9,(var X#21)]
       ;EE#24[X#22,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#20,T#17,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#21=A#25[(app A#26[(var X#22)] T#27)];X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];EE#23[[.1],(var X#21)];EE#24[X#22,[.2]]},
           X#18         |->  X#21,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(var X#10)]];VV#16|X#10,(var X#7)|},
           T#17         |->  A#25[(app A#26[(var X#22)] T#27)],
           A#20         |->  A#25[(app A#26 T#27[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#21=A#25[(app A#26[(var X#22)] T#27[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#23[X#9,(var X#21)];EE#24[X#22,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#23[A#25[(app A#26[(var X#10)] T#27[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#21= A#23[A#25[(app A#26[(\ X#8.S#12)] T#27[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#24,A#20,T#17,T#6,A#13,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#25[(app A#26[[.]] T#27[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#21=A#23[A#25[(app A#26[(var X#10)] T#27)]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#21=A#23[[.2]];EE#22[[.1],(var X#21)]},
           X#18         |->  X#21,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|},
           A#20         |->  A#23,
           T#17         |->  A#23[A#25[(app A#26[(var X#10)] T#27)]],
           T#24         |->  A#25[(app A#26[(var X#10)] T#27)],
           A#13         |->  A#25[(app A#26 T#27[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#21=A#23[A#25[(app A#26[(var X#10)] T#27[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#21=A#23[A#25[(app A#26[(var X#10)] T#27[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#21=A#23[A#25[(app A#26[(var X#10)] T#27[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#21=A#23[A#25[(app A#26[(\ X#8.S#12)] T#27[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#23[(app A#24[A#13[(var X#10)]] T#25[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#21= A#23[(app A#24[A#13[(\ X#8.S#12)]] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#20,T#17,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#21=A#23[(app A#24[A#13[(var X#10)]] T#25)];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#21=A#23[(app A#24[[.2]] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];EE#22[[.1],(var X#21)]},
           X#18         |->  X#21,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|},
           T#17         |->  A#23[(app A#24[A#13[(var X#10)]] T#25)],
           A#20         |->  A#23[(app A#24 T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#21=A#23[(app A#24[A#13[(var X#10)]] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#21=A#23[(app A#24[A#13[(var X#10)]] T#25[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#21=A#23[(app A#24[A#13[(var X#10)]] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#21=A#23[(app A#24[A#13[(\ X#8.S#12)]] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#21= A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#21= A#23[(app A#24[(\ X#8.S#12)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {T#17,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#23[(app A#24[[.]] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#21=A#23[(app A#24[(var X#10)] T#25)];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)]),
           EE#15[.1,.2] |-> {X#21=[.2];EE#22[[.1],(var X#21)]},
           X#18         |->  X#21,
           E#19         |->  {X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|},
           A#20         |->  [.],
           T#17         |->  A#23[(app A#24[(var X#10)] T#25)],
           A#13         |->  A#23[(app A#24 T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#21=A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#21=A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#21=A#23[(app A#24[(var X#10)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#21=A#23[(app A#24[(\ X#8.S#12)] T#25[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#8.S#12)
       ;X#7= (var X#1)
       ;E#17
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#7)
       ;X#7= (\ X#8.S#12)
       ;E#17
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#7),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#14[(var X#9)],
           X#2   |->  X#7,
           S#4   |->  (\ X#8.S#12),
           E#11  |->  {X#1=(var X#7);E#17},
           E#3   |->  {E#17;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#1=(var X#7);X#7=(\ X#8.S#12);E#17;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#1=(\ X#8.S#12);X#7=(var X#1);E#17;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#7);X#7=(\ X#8.S#12);E#17;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#1=(var X#7);X#7=(\ X#8.S#12);E#17;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (\ X#8.S#12)
       ;X#7= (var X#10)
       ;E#11
       ;EE#15[X#9,A#13[(var X#10)]]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#10= (var X#7)
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#10),[.]),
             ((var X#7),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           X#2          |->  X#7,
           S#4          |->  (\ X#8.S#12),
           VV#16|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#10,
           X#7          |->  X#7,
           E#3          |->  {E#11;EE#15[X#9,A#13[(var X#10)]]}}

and instantiated rules:

                                  (letrec {X#10=(var X#7);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]]} in A#14[(var X#9)])
    -xch1->                       (letrec {X#10=(\ X#8.S#12);X#7=(var X#10);E#11;EE#15[X#9,A#13[(var X#10)]]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#10=(var X#7);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]]} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#10=(var X#7);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (\ X#8.S#12)
       ;X#7= (var X#18)
       ;E#11
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#19|X#10,(var X#18)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= (var X#7)
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#19|X#10,(var X#18)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#18),[.]),
             ((var X#7),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           X#2          |->  X#7,
           S#4          |->  (\ X#8.S#12),
           VV#16|.1,.2| |-> {X#18=[.2];VV#19|[.1],(var X#18)|},
           X#1          |->  X#18,
           X#7          |->  X#7,
           E#3          |->  {E#11;EE#15[X#9,A#13[(var X#10)]];VV#19|X#10,(var X#18)|}}

and instantiated rules:

                                  (letrec {X#18=(var X#7);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#19|X#10,(var X#18)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#18=(\ X#8.S#12);X#7=(var X#18);E#11;EE#15[X#9,A#13[(var X#10)]];VV#19|X#10,(var X#18)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=(var X#7);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#19|X#10,(var X#18)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=(var X#7);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#19|X#10,(var X#18)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#4
       ;X#2= (var X#1)
       ;X#7= (\ X#8.S#12)
       ;E#18
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#2= S#4
       ;X#7= (\ X#8.S#12)
       ;E#18
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#14[(var X#9)],
           E#11  |->  {X#1=(var X#2);X#2=S#4;E#18},
           E#17  |->  {X#1=(var X#2);E#18},
           E#3   |->  {X#7=(\ X#8.S#12);E#18;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#2=S#4;X#7=(\ X#8.S#12);E#18;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#1=S#4;X#2=(var X#1);X#7=(\ X#8.S#12);E#18;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#2=S#4;X#7=(\ X#8.S#12);E#18;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#1=(var X#2);X#2=S#4;X#7=(\ X#8.S#12);E#18;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#7)
       ;X#10= (var X#1)
       ;X#7= (\ X#8.S#12)
       ;E#18
       ;EE#15[X#9,A#13[(var X#10)]]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#10)
       ;X#10= (var X#7)
       ;X#7= (\ X#8.S#12)
       ;E#18
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#10),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {[.1]=[.2]},
           X#2          |->  X#10,
           S#4          |->  (var X#7),
           E#11         |->  {X#1=(var X#10);E#18},
           E#3          |->  {X#7=(\ X#8.S#12);E#18;EE#15[X#9,A#13[(var X#10)]]}}

and instantiated rules:

                                  (letrec {X#1=(var X#10);X#10=(var X#7);X#7=(\ X#8.S#12);E#18;EE#15[X#9,A#13[(var X#10)]]} in A#14[(var X#9)])
    -xch1->                       (letrec {X#1=(var X#7);X#10=(var X#1);X#7=(\ X#8.S#12);E#18;EE#15[X#9,A#13[(var X#10)]]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#10);X#10=(var X#7);X#7=(\ X#8.S#12);E#18;EE#15[X#9,A#13[(var X#10)]]} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#1=(var X#10);X#10=(var X#7);X#7=(\ X#8.S#12);E#18;EE#15[X#9,A#13[(\ X#8.S#12)]]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#18)
       ;X#10= (var X#1)
       ;X#7= (\ X#8.S#12)
       ;E#20
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#19|X#18,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#10)
       ;X#10= (var X#18)
       ;X#7= (\ X#8.S#12)
       ;E#20
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#19|X#18,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#10),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {[.1]=(var X#18);VV#19|X#18,[.2]|},
           X#2          |->  X#10,
           S#4          |->  (var X#18),
           E#11         |->  {X#1=(var X#10);E#20},
           E#3          |->  {X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#19|X#18,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#1=(var X#10);X#10=(var X#18);X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#19|X#18,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#1=(var X#18);X#10=(var X#1);X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#19|X#18,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#10);X#10=(var X#18);X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#19|X#18,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#1=(var X#10);X#10=(var X#18);X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#19|X#18,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#19)
       ;X#18= (var X#1)
       ;X#7= (\ X#8.S#12)
       ;E#22
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#20|X#10,(var X#18)|
       ;VV#21|X#19,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#18)
       ;X#18= (var X#19)
       ;X#7= (\ X#8.S#12)
       ;E#22
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#20|X#10,(var X#18)|
       ;VV#21|X#19,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#18),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {X#18=(var X#19);VV#20|[.1],(var X#18)|;VV#21|X#19,[.2]|},
           X#2          |->  X#18,
           S#4          |->  (var X#19),
           E#11         |->  {X#1=(var X#18);E#22},
           E#3          |->  {X#7=(\ X#8.S#12);E#22;EE#15[X#9,A#13[(var X#10)]];VV#20|X#10,(var X#18)|;VV#21|X#19,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#1=(var X#18);X#18=(var X#19);X#7=(\ X#8.S#12);E#22;EE#15[X#9,A#13[(var X#10)]];VV#20|X#10,(var X#18)|;VV#21|X#19,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#1=(var X#19);X#18=(var X#1);X#7=(\ X#8.S#12);E#22;EE#15[X#9,A#13[(var X#10)]];VV#20|X#10,(var X#18)|;VV#21|X#19,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#18);X#18=(var X#19);X#7=(\ X#8.S#12);E#22;EE#15[X#9,A#13[(var X#10)]];VV#20|X#10,(var X#18)|;VV#21|X#19,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#1=(var X#18);X#18=(var X#19);X#7=(\ X#8.S#12);E#22;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#20|X#10,(var X#18)|;VV#21|X#19,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#19)
       ;X#18= (var X#10)
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#21|X#19,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#10= (var X#18)
       ;X#18= (var X#19)
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#21|X#19,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#10),[.]),
             ((var X#18),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {X#18=(var X#19);[.1]=(var X#18);VV#21|X#19,[.2]|},
           X#2          |->  X#18,
           S#4          |->  (var X#19),
           VV#20|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#10,
           X#18         |->  X#18,
           E#3          |->  {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#21|X#19,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#10=(var X#18);X#18=(var X#19);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#21|X#19,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#10=(var X#19);X#18=(var X#10);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#21|X#19,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#10=(var X#18);X#18=(var X#19);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#21|X#19,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#10=(var X#18);X#18=(var X#19);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#21|X#19,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (var X#23)
       ;X#23= (var X#19)
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#21|X#19,(var X#7)|
       ;VV#24|X#10,(var X#23)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= (var X#19)
       ;X#23= (var X#18)
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#21|X#19,(var X#7)|
       ;VV#24|X#10,(var X#23)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#23),[.]),
             ((var X#18),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {X#18=(var X#19);X#23=(var X#18);VV#21|X#19,[.2]|;VV#24|[.1],(var X#23)|},
           X#2          |->  X#18,
           S#4          |->  (var X#19),
           VV#20|.1,.2| |-> {X#23=[.2];VV#24|[.1],(var X#23)|},
           X#1          |->  X#23,
           X#18         |->  X#18,
           E#3          |->  {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#21|X#19,(var X#7)|;VV#24|X#10,(var X#23)|}}

and instantiated rules:

                                  (letrec {X#18=(var X#19);X#23=(var X#18);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#21|X#19,(var X#7)|;VV#24|X#10,(var X#23)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#18=(var X#23);X#23=(var X#19);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#21|X#19,(var X#7)|;VV#24|X#10,(var X#23)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=(var X#19);X#23=(var X#18);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#21|X#19,(var X#7)|;VV#24|X#10,(var X#23)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=(var X#19);X#23=(var X#18);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#21|X#19,(var X#7)|;VV#24|X#10,(var X#23)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#7)
       ;X#18= (var X#1)
       ;X#7= (\ X#8.S#12)
       ;E#20
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#19|X#10,(var X#18)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#18)
       ;X#18= (var X#7)
       ;X#7= (\ X#8.S#12)
       ;E#20
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#19|X#10,(var X#18)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#18),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {X#18=[.2];VV#19|[.1],(var X#18)|},
           X#2          |->  X#18,
           S#4          |->  (var X#7),
           E#11         |->  {X#1=(var X#18);E#20},
           E#3          |->  {X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#19|X#10,(var X#18)|}}

and instantiated rules:

                                  (letrec {X#1=(var X#18);X#18=(var X#7);X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#19|X#10,(var X#18)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#1=(var X#7);X#18=(var X#1);X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#19|X#10,(var X#18)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#18);X#18=(var X#7);X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(var X#10)]];VV#19|X#10,(var X#18)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#1=(var X#18);X#18=(var X#7);X#7=(\ X#8.S#12);E#20;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#19|X#10,(var X#18)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#7)
       ;X#18= (var X#10)
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(var X#10)]]
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#10= (var X#18)
       ;X#18= (var X#7)
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#10),[.]),
             ((var X#18),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {X#18=[.2];[.1]=(var X#18)},
           X#2          |->  X#18,
           S#4          |->  (var X#7),
           VV#19|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#10,
           X#18         |->  X#18,
           E#3          |->  {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]]}}

and instantiated rules:

                                  (letrec {X#10=(var X#18);X#18=(var X#7);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]]} in A#14[(var X#9)])
    -xch1->                       (letrec {X#10=(var X#7);X#18=(var X#10);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]]} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#10=(var X#18);X#18=(var X#7);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]]} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#10=(var X#18);X#18=(var X#7);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]]} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (var X#21)
       ;X#21= (var X#7)
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(var X#10)]]
       ;VV#22|X#10,(var X#21)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= (var X#7)
       ;X#21= (var X#18)
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#15[X#9,A#13[(\ X#8.S#12)]]
       ;VV#22|X#10,(var X#21)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#21),[.]),
             ((var X#18),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           VV#16|.1,.2| |-> {X#18=[.2];X#21=(var X#18);VV#22|[.1],(var X#21)|},
           X#2          |->  X#18,
           S#4          |->  (var X#7),
           VV#19|.1,.2| |-> {X#21=[.2];VV#22|[.1],(var X#21)|},
           X#1          |->  X#21,
           X#18         |->  X#18,
           E#3          |->  {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#22|X#10,(var X#21)|}}

and instantiated rules:

                                  (letrec {X#18=(var X#7);X#21=(var X#18);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#22|X#10,(var X#21)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#18=(var X#21);X#21=(var X#7);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#22|X#10,(var X#21)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=(var X#7);X#21=(var X#18);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#22|X#10,(var X#21)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=(var X#7);X#21=(var X#18);X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#22|X#10,(var X#21)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#17[A#13[(var X#10)]]
       ;X#7= (\ X#8.S#12)
       ;X#9= (var X#1)
       ;E#18
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#9)
       ;X#7= (\ X#8.S#12)
       ;X#9= A#17[A#13[(\ X#8.S#12)]]
       ;E#18
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#9),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#2          |->  X#9,
           S#4          |->  A#17[A#13[(var X#10)]],
           E#11         |->  {X#1=(var X#9);E#18},
           E#3          |->  {X#7=(\ X#8.S#12);E#18;VV#16|X#10,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#1=(var X#9);X#7=(\ X#8.S#12);X#9=A#17[A#13[(var X#10)]];E#18;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#1=A#17[A#13[(var X#10)]];X#7=(\ X#8.S#12);X#9=(var X#1);E#18;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#9);X#7=(\ X#8.S#12);X#9=A#17[A#13[(var X#10)]];E#18;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#1=(var X#9);X#7=(\ X#8.S#12);X#9=A#17[A#13[(\ X#8.S#12)]];E#18;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#17[(var X#18)]
       ;X#7= (\ X#8.S#12)
       ;X#9= (var X#1)
       ;E#20
       ;EE#19[X#18,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#9)
       ;X#7= (\ X#8.S#12)
       ;X#9= A#17[(var X#18)]
       ;E#20
       ;EE#19[X#18,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#9),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {[.1]=A#17[(var X#18)];EE#19[X#18,[.2]]},
           X#2          |->  X#9,
           S#4          |->  A#17[(var X#18)],
           E#11         |->  {X#1=(var X#9);E#20},
           E#3          |->  {X#7=(\ X#8.S#12);E#20;EE#19[X#18,A#13[(var X#10)]];VV#16|X#10,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#1=(var X#9);X#7=(\ X#8.S#12);X#9=A#17[(var X#18)];E#20;EE#19[X#18,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#1=A#17[(var X#18)];X#7=(\ X#8.S#12);X#9=(var X#1);E#20;EE#19[X#18,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#9);X#7=(\ X#8.S#12);X#9=A#17[(var X#18)];E#20;EE#19[X#18,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#1=(var X#9);X#7=(\ X#8.S#12);X#9=A#17[(var X#18)];E#20;EE#19[X#18,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#17[(var X#19)]
       ;X#18= (var X#1)
       ;X#7= (\ X#8.S#12)
       ;E#22
       ;EE#20[X#9,(var X#18)]
       ;EE#21[X#19,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#18)
       ;X#18= A#17[(var X#19)]
       ;X#7= (\ X#8.S#12)
       ;E#22
       ;EE#20[X#9,(var X#18)]
       ;EE#21[X#19,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#18),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {X#18=A#17[(var X#19)];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#2          |->  X#18,
           S#4          |->  A#17[(var X#19)],
           E#11         |->  {X#1=(var X#18);E#22},
           E#3          |->  {X#7=(\ X#8.S#12);E#22;EE#20[X#9,(var X#18)];EE#21[X#19,A#13[(var X#10)]];VV#16|X#10,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#1=(var X#18);X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);E#22;EE#20[X#9,(var X#18)];EE#21[X#19,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#1=A#17[(var X#19)];X#18=(var X#1);X#7=(\ X#8.S#12);E#22;EE#20[X#9,(var X#18)];EE#21[X#19,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#18);X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);E#22;EE#20[X#9,(var X#18)];EE#21[X#19,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#1=(var X#18);X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);E#22;EE#20[X#9,(var X#18)];EE#21[X#19,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (var X#9)
       ;X#7= (\ X#8.S#12)
       ;X#9= A#17[(var X#19)]
       ;E#11
       ;EE#21[X#19,A#13[(var X#10)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#17[(var X#19)]
       ;X#7= (\ X#8.S#12)
       ;X#9= (var X#18)
       ;E#11
       ;EE#21[X#19,A#13[(\ X#8.S#12)]]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#9),[.]),
             ((var X#18),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {X#18=A#17[(var X#19)];[.1]=(var X#18);EE#21[X#19,[.2]]},
           X#2          |->  X#18,
           S#4          |->  A#17[(var X#19)],
           EE#20[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#9,
           E#3          |->  {X#7=(\ X#8.S#12);E#11;EE#21[X#19,A#13[(var X#10)]];VV#16|X#10,(var X#7)|},
           A#22         |->  [.],
           X#18         |->  X#18}

and instantiated rules:

                                  (letrec {X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);X#9=(var X#18);E#11;EE#21[X#19,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#18=(var X#9);X#7=(\ X#8.S#12);X#9=A#17[(var X#19)];E#11;EE#21[X#19,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);X#9=(var X#18);E#11;EE#21[X#19,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=A#17[(var X#19)];X#7=(\ X#8.S#12);X#9=(var X#18);E#11;EE#21[X#19,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (var X#23)
       ;X#23= A#17[(var X#19)]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#21[X#19,A#13[(var X#10)]]
       ;EE#24[X#9,(var X#23)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#17[(var X#19)]
       ;X#23= (var X#18)
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#21[X#19,A#13[(\ X#8.S#12)]]
       ;EE#24[X#9,(var X#23)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#23),[.]),
             ((var X#18),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {X#18=A#17[(var X#19)];X#23=(var X#18);EE#21[X#19,[.2]];EE#24[[.1],(var X#23)]},
           X#2          |->  X#18,
           S#4          |->  A#17[(var X#19)],
           EE#20[.1,.2] |-> {X#23=[.2];EE#24[[.1],(var X#23)]},
           X#1          |->  X#23,
           E#3          |->  {X#7=(\ X#8.S#12);E#11;EE#21[X#19,A#13[(var X#10)]];EE#24[X#9,(var X#23)];VV#16|X#10,(var X#7)|},
           A#22         |->  [.],
           X#18         |->  X#18}

and instantiated rules:

                                  (letrec {X#18=A#17[(var X#19)];X#23=(var X#18);X#7=(\ X#8.S#12);E#11;EE#21[X#19,A#13[(var X#10)]];EE#24[X#9,(var X#23)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#18=(var X#23);X#23=A#17[(var X#19)];X#7=(\ X#8.S#12);E#11;EE#21[X#19,A#13[(var X#10)]];EE#24[X#9,(var X#23)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#17[(var X#19)];X#23=(var X#18);X#7=(\ X#8.S#12);E#11;EE#21[X#19,A#13[(var X#10)]];EE#24[X#9,(var X#23)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=A#17[(var X#19)];X#23=(var X#18);X#7=(\ X#8.S#12);E#11;EE#21[X#19,A#13[(\ X#8.S#12)]];EE#24[X#9,(var X#23)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#17[A#13[(var X#10)]]
       ;X#18= (var X#1)
       ;X#7= (\ X#8.S#12)
       ;E#20
       ;EE#19[X#9,(var X#18)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#1= (var X#18)
       ;X#18= A#17[A#13[(\ X#8.S#12)]]
       ;X#7= (\ X#8.S#12)
       ;E#20
       ;EE#19[X#9,(var X#18)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#18),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {X#18=A#17[[.2]];EE#19[[.1],(var X#18)]},
           X#2          |->  X#18,
           S#4          |->  A#17[A#13[(var X#10)]],
           E#11         |->  {X#1=(var X#18);E#20},
           E#3          |->  {X#7=(\ X#8.S#12);E#20;EE#19[X#9,(var X#18)];VV#16|X#10,(var X#7)|}}

and instantiated rules:

                                  (letrec {X#1=(var X#18);X#18=A#17[A#13[(var X#10)]];X#7=(\ X#8.S#12);E#20;EE#19[X#9,(var X#18)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#1=A#17[A#13[(var X#10)]];X#18=(var X#1);X#7=(\ X#8.S#12);E#20;EE#19[X#9,(var X#18)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#1=(var X#18);X#18=A#17[A#13[(var X#10)]];X#7=(\ X#8.S#12);E#20;EE#19[X#9,(var X#18)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#1=(var X#18);X#18=A#17[A#13[(\ X#8.S#12)]];X#7=(\ X#8.S#12);E#20;EE#19[X#9,(var X#18)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (var X#9)
       ;X#7= (\ X#8.S#12)
       ;X#9= A#17[A#13[(var X#10)]]
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#17[A#13[(\ X#8.S#12)]]
       ;X#7= (\ X#8.S#12)
       ;X#9= (var X#18)
       ;E#11
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#9),[.]),
             ((var X#18),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {X#18=A#17[[.2]];[.1]=(var X#18)},
           X#2          |->  X#18,
           S#4          |->  A#17[A#13[(var X#10)]],
           EE#19[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#9,
           E#3          |->  {X#7=(\ X#8.S#12);E#11;VV#16|X#10,(var X#7)|},
           A#20         |->  [.],
           X#18         |->  X#18}

and instantiated rules:

                                  (letrec {X#18=A#17[A#13[(var X#10)]];X#7=(\ X#8.S#12);X#9=(var X#18);E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#18=(var X#9);X#7=(\ X#8.S#12);X#9=A#17[A#13[(var X#10)]];E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#17[A#13[(var X#10)]];X#7=(\ X#8.S#12);X#9=(var X#18);E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=A#17[A#13[(\ X#8.S#12)]];X#7=(\ X#8.S#12);X#9=(var X#18);E#11;VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (var X#21)
       ;X#21= A#17[A#13[(var X#10)]]
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
    ,
     (letrec
        X#18= A#17[A#13[(\ X#8.S#12)]]
       ;X#21= (var X#18)
       ;X#7= (\ X#8.S#12)
       ;E#11
       ;EE#22[X#9,(var X#21)]
       ;VV#16|X#10,(var X#7)|
     in
        A#14[(var X#9)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#21),[.]),
             ((var X#18),[.]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]]),
             ((var X#10),A#13[[.]]),
             ((var X#7),[.]),
             ((var X#9),A#14[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(\ X#8.S#12)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(\ X#8.S#12);E#11;EE#15[X#9,A#13[(var X#10)]];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#9),A#14[[.]]),((var X#10),A#13[[.]]),((var X#7),[.]),((var X#9),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#9)],
           EE#15[.1,.2] |-> {X#18=A#17[[.2]];X#21=(var X#18);EE#22[[.1],(var X#21)]},
           X#2          |->  X#18,
           S#4          |->  A#17[A#13[(var X#10)]],
           EE#19[.1,.2] |-> {X#21=[.2];EE#22[[.1],(var X#21)]},
           X#1          |->  X#21,
           E#3          |->  {X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|},
           A#20         |->  [.],
           X#18         |->  X#18}

and instantiated rules:

                                  (letrec {X#18=A#17[A#13[(var X#10)]];X#21=(var X#18);X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -xch1->                       (letrec {X#18=(var X#21);X#21=A#17[A#13[(var X#10)]];X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    ................................................................................
                                  (letrec {X#18=A#17[A#13[(var X#10)]];X#21=(var X#18);X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    -SR,cp-e2->                   (letrec {X#18=A#17[A#13[(\ X#8.S#12)]];X#21=(var X#18);X#7=(\ X#8.S#12);E#11;EE#22[X#9,(var X#21)];VV#16|X#10,(var X#7)|} in A#14[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (letrec {E#8} in T#11[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])
     )
    ,
     (letrec {E#7;E#8} in T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])
  )

where

   Delta1 = {T#10,T#6}
   Delta2 = {E#7,E#8}
   Delta3 = {[{E#7},(letrec {E#8} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {[{E#7},(letrec {E#8} in [.])],((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in (letrec {E#8} in T#11)),
           T#10  |->  (letrec {E#8} in T#11),
           S#9   |->  T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#7} in (letrec {E#8} in T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))
    -xch1->                       (letrec {E#7} in (letrec {E#8} in T#11[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]))
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))
    -SR,llet-in1->                (letrec {E#7;E#8} in T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (letrec {X#12=T#11[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#14} in S#9)
     )
    ,
     (letrec
        X#12= T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;E#14
       ;E#7
     in
        S#9
     )
  )

where

   Delta1 = {T#10,T#6}
   Delta2 = {E#7,E#8}
   Delta3 = {[{E#7},(letrec {X#12=T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#14} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {[{E#7},(letrec {E#8} in [.])],((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in (letrec {X#12=T#11;E#14} in S#9)),
           T#10  |->  (letrec {X#12=T#11;E#14} in S#9),
           E#8   |->  {X#12=T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#14},
           E#13  |->  {E#14}}

and instantiated rules:

                                  (letrec {E#7} in (letrec {X#12=T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#14} in S#9))
    -xch1->                       (letrec {E#7} in (letrec {X#12=T#11[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#14} in S#9))
    ................................................................................
                                  (letrec {E#7} in (letrec {X#12=T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#14} in S#9))
    -SR,llet-in1->                (letrec {X#12=T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#14;E#7} in S#9)
    

================================================================================
Critical Pair:

  (
     (letrec {E#7} in (letrec {X#1=S#4;X#2=(var X#1);E#12} in S#9))
    ,
     (letrec {X#1=(var X#2);X#2=S#4;E#12;E#7} in S#9)
  )

where

   Delta1 = {T#6}
   Delta2 = {E#7,E#8}
   Delta3 = {[{E#7},(letrec {X#1=(var X#2);X#2=S#4;E#12} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {[{E#7},(letrec {E#8} in [.])],((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in [.]),
           T#10  |->  [.],
           S#5   |->  S#9,
           E#8   |->  {X#1=(var X#2);X#2=S#4;E#12},
           E#11  |->  {X#1=(var X#2);E#12},
           E#3   |->  {E#12}}

and instantiated rules:

                                  (letrec {E#7} in (letrec {X#1=(var X#2);X#2=S#4;E#12} in S#9))
    -xch1->                       (letrec {E#7} in (letrec {X#1=S#4;X#2=(var X#1);E#12} in S#9))
    ................................................................................
                                  (letrec {E#7} in (letrec {X#1=(var X#2);X#2=S#4;E#12} in S#9))
    -SR,llet-in1->                (letrec {X#1=(var X#2);X#2=S#4;E#12;E#7} in S#9)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
       ;E#13
     in
        (letrec {E#8} in S#9)
     )
    ,
     (letrec
        X#11= T#10[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;E#13
       ;E#8
     in
        S#9
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#7,E#8}
   Delta3 = {[{X#11=T#10[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#13},(letrec {E#8} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {[{E#7},(letrec {E#8} in [.])],((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {X#11=T#10;E#13} in (letrec {E#8} in S#9)),
           E#7   |->  {X#11=T#10[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#13} in (letrec {E#8} in S#9))
    -xch1->                       (letrec {X#11=T#10[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#13} in (letrec {E#8} in S#9))
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#13} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {X#11=T#10[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#13;E#8} in S#9)
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#4;X#2=(var X#1);E#11} in (letrec {E#8} in S#9))
    ,
     (letrec {X#1=(var X#2);X#2=S#4;E#11;E#8} in S#9)
  )

where

   Delta1 = {}
   Delta2 = {E#7,E#8}
   Delta3 = {[{X#1=(var X#2);X#2=S#4;E#11},(letrec {E#8} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {E#7;E#8} in S#9)
    and constraints: E#7/= {}, E#8/= {}, ({E#7},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in (letrec {E#8} in S#9))}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {[{E#7},(letrec {E#8} in [.])],((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  (letrec {E#8} in S#9),
           E#7   |->  {X#1=(var X#2);X#2=S#4;E#11},
           E#10  |->  {X#1=(var X#2);E#11},
           E#3   |->  {E#11}}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#2=S#4;E#11} in (letrec {E#8} in S#9))
    -xch1->                       (letrec {X#1=S#4;X#2=(var X#1);E#11} in (letrec {E#8} in S#9))
    ................................................................................
                                  (letrec {X#1=(var X#2);X#2=S#4;E#11} in (letrec {E#8} in S#9))
    -SR,llet-in1->                (letrec {X#1=(var X#2);X#2=S#4;E#11;E#8} in S#9)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#8} in S#10)
       ;E#9
     in
        A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
     )
    ,
     (letrec
        X#7= S#10
       ;E#8
       ;E#9
     in
        A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#11,T#12,T#6}
   Delta2 = {E#8}
   Delta3 = {(A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])],(letrec {E#8} in [.])),
             [{E#9},(letrec {E#8} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#13[(app A#14[[.]] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]),
             ((var X#7),A#13[(app A#14[[.]] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#13[(app A#14[(var X#7)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#7)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -xch1->                       (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#8} in T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])
       ;E#9
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#7= T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;E#8
       ;E#9
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#12,T#6}
   Delta2 = {E#8}
   Delta3 = {(A#11[(var X#7)],(letrec {E#8} in [.])),
             [{E#9},(letrec {E#8} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(letrec {E#8} in T#15);E#9} in A#11[(var X#7)]),
           X#13  |->  X#7,
           E#14  |->  {E#9},
           T#12  |->  (letrec {E#8} in T#15),
           S#10  |->  T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#8} in T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]);E#9} in A#11[(var X#7)])
    -xch1->                       (letrec {X#7=(letrec {E#8} in T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]);E#9} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#8;E#9} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {X#16=T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#18} in S#10)
       ;E#9
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;X#7= S#10
       ;E#18
       ;E#9
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#12,T#6}
   Delta2 = {E#8}
   Delta3 = {(A#11[(var X#7)],(letrec {X#16=T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#18} in [.])),
             [{E#9},(letrec {X#16=T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#18} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(letrec {X#16=T#15;E#18} in S#10);E#9} in A#11[(var X#7)]),
           X#13  |->  X#7,
           E#14  |->  {E#9},
           T#12  |->  (letrec {X#16=T#15;E#18} in S#10),
           E#8   |->  {X#16=T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {X#7=(letrec {X#16=T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#18} in S#10);E#9} in A#11[(var X#7)])
    -xch1->                       (letrec {X#7=(letrec {X#16=T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#18} in S#10);E#9} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(letrec {X#16=T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#18} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#16=T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=S#10;E#18;E#9} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {X#1=S#4;X#2=(var X#1);E#16} in S#10)
       ;E#9
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#1=(var X#2);X#2=S#4;X#7=S#10;E#16;E#9} in A#11[(var X#7)])
  )

where

   Delta1 = {T#6}
   Delta2 = {E#8}
   Delta3 = {(A#11[(var X#7)],(letrec {X#1=(var X#2);X#2=S#4;E#16} in [.])),
             [{E#9},(letrec {X#1=(var X#2);X#2=S#4;E#16} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=[.];E#9} in A#11[(var X#7)]),
           X#13  |->  X#7,
           E#14  |->  {E#9},
           T#12  |->  [.],
           S#5   |->  S#10,
           E#8   |->  {X#1=(var X#2);X#2=S#4;E#16},
           E#15  |->  {X#1=(var X#2);E#16},
           E#3   |->  {E#16}}

and instantiated rules:

                                  (letrec {X#7=(letrec {X#1=(var X#2);X#2=S#4;E#16} in S#10);E#9} in A#11[(var X#7)])
    -xch1->                       (letrec {X#7=(letrec {X#1=S#4;X#2=(var X#1);E#16} in S#10);E#9} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(letrec {X#1=(var X#2);X#2=S#4;E#16} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#1=(var X#2);X#2=S#4;X#7=S#10;E#16;E#9} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
       ;X#7= (letrec {E#8} in S#10)
       ;E#15
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;X#7= S#10
       ;E#15
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#8}
   Delta3 = {(A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15},(letrec {E#8} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#13=T#12;X#7=(letrec {E#8} in S#10);E#15} in A#11[(var X#7)]),
           E#9   |->  {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15},
           E#14  |->  {X#7=(letrec {E#8} in S#10);E#15}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(letrec {E#8} in S#10);E#15} in A#11[(var X#7)])
    -xch1->                       (letrec {X#13=T#12[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];X#7=(letrec {E#8} in S#10);E#15} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(letrec {E#8} in S#10);E#15} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=S#10;E#15;E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {E#8} in S#10);X#7=(var X#1);E#12} in A#11[(var X#7)])
    ,
     (letrec {X#1=(var X#7);X#7=S#10;E#12;E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {}
   Delta2 = {E#8}
   Delta3 = {(A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#1=(var X#7);E#12},(letrec {E#8} in [.])],
             ((var X#1),[.]),
             ((var X#7),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6  |->  [.],
           S#5  |->  A#11[(var X#7)],
           X#2  |->  X#7,
           S#4  |->  (letrec {E#8} in S#10),
           E#9  |->  {X#1=(var X#7);E#12},
           E#3  |->  {E#12}}

and instantiated rules:

                                  (letrec {X#1=(var X#7);X#7=(letrec {E#8} in S#10);E#12} in A#11[(var X#7)])
    -xch1->                       (letrec {X#1=(letrec {E#8} in S#10);X#7=(var X#1);E#12} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#1=(var X#7);X#7=(letrec {E#8} in S#10);E#12} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#1=(var X#7);X#7=S#10;E#12;E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#4
       ;X#2= (var X#1)
       ;X#7= (letrec {E#8} in S#10)
       ;E#13
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#1=(var X#2);X#2=S#4;X#7=S#10;E#13;E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {}
   Delta2 = {E#8}
   Delta3 = {(A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#1=(var X#2);X#2=S#4;E#13},(letrec {E#8} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#7=S#10;E#8;E#9} in A#11[(var X#7)])
    and constraints: E#8/= {}, (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#8} in S#10);E#9} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9},(letrec {E#8} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#11[(var X#7)],
           E#9   |->  {X#1=(var X#2);X#2=S#4;E#13},
           E#12  |->  {X#1=(var X#2);E#13},
           E#3   |->  {X#7=(letrec {E#8} in S#10);E#13}}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#2=S#4;X#7=(letrec {E#8} in S#10);E#13} in A#11[(var X#7)])
    -xch1->                       (letrec {X#1=S#4;X#2=(var X#1);X#7=(letrec {E#8} in S#10);E#13} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#2=S#4;X#7=(letrec {E#8} in S#10);E#13} in A#11[(var X#7)])
    -SR,llet-e1->                 (letrec {X#1=(var X#2);X#2=S#4;X#7=S#10;E#13;E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#9} in S#11)
       ;E#10
       ;EE#13[X#8,(var X#7)]
     in
        A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
     )
    ,
     (letrec
        X#7= S#11
       ;E#10
       ;E#9
       ;EE#13[X#8,(var X#7)]
     in
        A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),
             (A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])],(letrec {E#9} in [.])),
             [{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#8),A#15[(app A#16[[.]] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]),
             ((var X#7),[.]),
             ((var X#8),A#15[(app A#16[[.]] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#8)] T#17)],
           A#12  |->  A#15[(app A#16 T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -xch1->                       (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#9} in T#17[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])
       ;E#10
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#7= T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;E#10
       ;E#9
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(letrec {E#9} in T#17);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)]),
           X#15  |->  X#7,
           E#16  |->  {E#10;EE#13[X#8,(var X#7)]},
           T#14  |->  (letrec {E#9} in T#17),
           S#11  |->  T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#7=(letrec {E#9} in T#17[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {X#18=T#17[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#20} in S#11)
       ;E#10
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;X#7= S#11
       ;E#10
       ;E#20
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#18=T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#10;E#20;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {X#18=T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#20} in [.])),
             [{E#10;EE#13[X#8,(var X#7)]},(letrec {X#18=T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#20} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=(letrec {X#18=T#17;E#20} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)]),
           X#15  |->  X#7,
           E#16  |->  {E#10;EE#13[X#8,(var X#7)]},
           T#14  |->  (letrec {X#18=T#17;E#20} in S#11),
           E#9   |->  {X#18=T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#20},
           E#19  |->  {E#20}}

and instantiated rules:

                                  (letrec {X#7=(letrec {X#18=T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#20} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#7=(letrec {X#18=T#17[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#20} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {X#18=T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#20} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#18=T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=S#11;E#10;E#20;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {X#1=S#4;X#2=(var X#1);E#18} in S#11)
       ;E#10
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#2= S#4
       ;X#7= S#11
       ;E#10
       ;E#18
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#1=(var X#2);X#2=S#4;E#10;E#18;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {X#1=(var X#2);X#2=S#4;E#18} in [.])),
             [{E#10;EE#13[X#8,(var X#7)]},(letrec {X#1=(var X#2);X#2=S#4;E#18} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#7=[.];E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)]),
           X#15  |->  X#7,
           E#16  |->  {E#10;EE#13[X#8,(var X#7)]},
           T#14  |->  [.],
           S#5   |->  S#11,
           E#9   |->  {X#1=(var X#2);X#2=S#4;E#18},
           E#17  |->  {X#1=(var X#2);E#18},
           E#3   |->  {E#18}}

and instantiated rules:

                                  (letrec {X#7=(letrec {X#1=(var X#2);X#2=S#4;E#18} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#7=(letrec {X#1=S#4;X#2=(var X#1);E#18} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {X#1=(var X#2);X#2=S#4;E#18} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#1=(var X#2);X#2=S#4;X#7=S#11;E#10;E#18;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
       ;X#7= (letrec {E#9} in S#11)
       ;E#17
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;X#7= S#11
       ;E#17
       ;E#9
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17;E#9;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#15=T#14;X#7=(letrec {E#9} in S#11);E#17;EE#13[X#8,(var X#7)]} in A#12[(var X#8)]),
           E#10  |->  {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17},
           E#16  |->  {X#7=(letrec {E#9} in S#11);E#17;EE#13[X#8,(var X#7)]}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(letrec {E#9} in S#11);E#17;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#15=T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];X#7=(letrec {E#9} in S#11);E#17;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=(letrec {E#9} in S#11);E#17;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];X#7=S#11;E#17;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#9} in S#11)
       ;X#8= A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#10
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#7= S#11
       ;X#8= A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#10
       ;E#9
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10;E#9} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10},(letrec {E#9} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#18[(app A#19[(var X#7)] T#20)];E#10} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]},
           X#15         |->  X#8,
           E#16         |->  {X#7=(letrec {E#9} in S#11);E#10},
           T#14         |->  A#18[(app A#19[(var X#7)] T#20)],
           A#17         |->  A#18[(app A#19 T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10} in A#12[(var X#8)])
    -xch1->                       (letrec {X#7=(letrec {E#9} in S#11);X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#10} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;X#8=A#18[(app A#19[(var X#7)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (letrec {E#9} in S#11)
       ;X#8= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#10
       ;EE#19[X#18,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#7= S#11
       ;X#8= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#10
       ;E#9
       ;EE#19[X#18,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10;E#9;EE#19[X#18,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10;EE#19[X#18,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#20[(app A#21[(var X#18)] T#22)];E#10;EE#19[X#18,(var X#7)]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];EE#19[X#18,[.2]]},
           X#15         |->  X#8,
           E#16         |->  {X#7=(letrec {E#9} in S#11);E#10;EE#19[X#18,(var X#7)]},
           T#14         |->  A#20[(app A#21[(var X#18)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10;EE#19[X#18,(var X#7)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#7=(letrec {E#9} in S#11);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#10;EE#19[X#18,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10;EE#19[X#18,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10;E#9;EE#19[X#18,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;X#7= (letrec {E#9} in S#11)
       ;E#10
       ;EE#20[X#8,(var X#18)]
       ;EE#21[X#19,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;X#7= S#11
       ;E#10
       ;E#9
       ;EE#20[X#8,(var X#18)]
       ;EE#21[X#19,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10;E#9;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24)];X#7=(letrec {E#9} in S#11);E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#15         |->  X#18,
           E#16         |->  {X#7=(letrec {E#9} in S#11);E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]},
           T#14         |->  A#22[(app A#23[(var X#19)] T#24)],
           A#17         |->  A#22[(app A#23 T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(letrec {E#9} in S#11);E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];X#7=(letrec {E#9} in S#11);E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(letrec {E#9} in S#11);E#10;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=S#11;E#10;E#9;EE#20[X#8,(var X#18)];EE#21[X#19,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;X#7= (letrec {E#9} in S#11)
       ;E#10
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;X#7= S#11
       ;E#10
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10;E#9;EE#19[X#8,(var X#18)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#10;EE#19[X#8,(var X#18)]},(letrec {E#9} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app A#21[(var X#7)] T#22)];X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]},
           T#14         |->  A#20[(app A#21[(var X#7)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];X#7=S#11;E#10;E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#9} in S#11)
       ;X#7= (var X#1)
       ;E#14
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#1= (var X#7)
       ;X#7= S#11
       ;E#14
       ;E#9
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#1=(var X#7);E#14;E#9;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#1=(var X#7);E#14;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#1),[.]),
             ((var X#7),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#8)],
           X#2   |->  X#7,
           S#4   |->  (letrec {E#9} in S#11),
           E#10  |->  {X#1=(var X#7);E#14},
           E#3   |->  {E#14;EE#13[X#8,(var X#7)]}}

and instantiated rules:

                                  (letrec {X#1=(var X#7);X#7=(letrec {E#9} in S#11);E#14;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#1=(letrec {E#9} in S#11);X#7=(var X#1);E#14;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#1=(var X#7);X#7=(letrec {E#9} in S#11);E#14;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#1=(var X#7);X#7=S#11;E#14;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#7=(var X#8);X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    ,
     (letrec {X#7=S#11;X#8=(var X#7);E#10;E#9} in A#12[(var X#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#8=(var X#7);E#10;E#9} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#8=(var X#7);E#10},(letrec {E#9} in [.])],
             ((var X#8),[.]),
             ((var X#7),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           X#2          |->  X#7,
           S#4          |->  (letrec {E#9} in S#11),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#8,
           E#3          |->  {E#10},
           A#14         |->  [.],
           X#7          |->  X#7}

and instantiated rules:

                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=(var X#7);E#10} in A#12[(var X#8)])
    -xch1->                       (letrec {X#7=(var X#8);X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);X#8=(var X#7);E#10} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;X#8=(var X#7);E#10;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#9} in S#11)
       ;X#7= (var X#15)
       ;E#10
       ;EE#16[X#8,(var X#15)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= (var X#7)
       ;X#7= S#11
       ;E#10
       ;E#9
       ;EE#16[X#8,(var X#15)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#15=(var X#7);E#10;E#9;EE#16[X#8,(var X#15)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#15=(var X#7);E#10;EE#16[X#8,(var X#15)]},(letrec {E#9} in [.])],
             ((var X#15),[.]),
             ((var X#7),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           X#2          |->  X#7,
           S#4          |->  (letrec {E#9} in S#11),
           EE#13[.1,.2] |-> {X#15=[.2];EE#16[[.1],(var X#15)]},
           X#1          |->  X#15,
           E#3          |->  {E#10;EE#16[X#8,(var X#15)]},
           A#14         |->  [.],
           X#7          |->  X#7}

and instantiated rules:

                                  (letrec {X#15=(var X#7);X#7=(letrec {E#9} in S#11);E#10;EE#16[X#8,(var X#15)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#15=(letrec {E#9} in S#11);X#7=(var X#15);E#10;EE#16[X#8,(var X#15)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#15=(var X#7);X#7=(letrec {E#9} in S#11);E#10;EE#16[X#8,(var X#15)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#15=(var X#7);X#7=S#11;E#10;E#9;EE#16[X#8,(var X#15)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#4
       ;X#2= (var X#1)
       ;X#7= (letrec {E#9} in S#11)
       ;E#15
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#2= S#4
       ;X#7= S#11
       ;E#15
       ;E#9
       ;EE#13[X#8,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#1=(var X#2);X#2=S#4;E#15;E#9;EE#13[X#8,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#1=(var X#2);X#2=S#4;E#15;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#8)],
           E#10  |->  {X#1=(var X#2);X#2=S#4;E#15},
           E#14  |->  {X#1=(var X#2);E#15},
           E#3   |->  {X#7=(letrec {E#9} in S#11);E#15;EE#13[X#8,(var X#7)]}}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#2=S#4;X#7=(letrec {E#9} in S#11);E#15;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#1=S#4;X#2=(var X#1);X#7=(letrec {E#9} in S#11);E#15;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#2=S#4;X#7=(letrec {E#9} in S#11);E#15;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#1=(var X#2);X#2=S#4;X#7=S#11;E#15;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(var X#7)]
       ;X#7= (letrec {E#9} in S#11)
       ;X#8= (var X#1)
       ;E#15
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#1= (var X#8)
       ;X#7= S#11
       ;X#8= A#14[(var X#7)]
       ;E#15
       ;E#9
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#1=(var X#8);X#8=A#14[(var X#7)];E#15;E#9} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#1=(var X#8);X#8=A#14[(var X#7)];E#15},(letrec {E#9} in [.])],
             ((var X#1),[.]),
             ((var X#8),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {[.1]=A#14[[.2]]},
           X#2          |->  X#8,
           S#4          |->  A#14[(var X#7)],
           E#10         |->  {X#1=(var X#8);E#15},
           E#3          |->  {X#7=(letrec {E#9} in S#11);E#15}}

and instantiated rules:

                                  (letrec {X#1=(var X#8);X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#7)];E#15} in A#12[(var X#8)])
    -xch1->                       (letrec {X#1=A#14[(var X#7)];X#7=(letrec {E#9} in S#11);X#8=(var X#1);E#15} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#1=(var X#8);X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#7)];E#15} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#1=(var X#8);X#7=S#11;X#8=A#14[(var X#7)];E#15;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(var X#15)]
       ;X#7= (letrec {E#9} in S#11)
       ;X#8= (var X#1)
       ;E#17
       ;EE#16[X#15,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#1= (var X#8)
       ;X#7= S#11
       ;X#8= A#14[(var X#15)]
       ;E#17
       ;E#9
       ;EE#16[X#15,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#1=(var X#8);X#8=A#14[(var X#15)];E#17;E#9;EE#16[X#15,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#1=(var X#8);X#8=A#14[(var X#15)];E#17;EE#16[X#15,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#1),[.]),
             ((var X#8),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {[.1]=A#14[(var X#15)];EE#16[X#15,[.2]]},
           X#2          |->  X#8,
           S#4          |->  A#14[(var X#15)],
           E#10         |->  {X#1=(var X#8);E#17},
           E#3          |->  {X#7=(letrec {E#9} in S#11);E#17;EE#16[X#15,(var X#7)]}}

and instantiated rules:

                                  (letrec {X#1=(var X#8);X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#15)];E#17;EE#16[X#15,(var X#7)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#1=A#14[(var X#15)];X#7=(letrec {E#9} in S#11);X#8=(var X#1);E#17;EE#16[X#15,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#1=(var X#8);X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#15)];E#17;EE#16[X#15,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#1=(var X#8);X#7=S#11;X#8=A#14[(var X#15)];E#17;E#9;EE#16[X#15,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(var X#16)]
       ;X#15= (var X#1)
       ;X#7= (letrec {E#9} in S#11)
       ;E#19
       ;EE#17[X#8,(var X#15)]
       ;EE#18[X#16,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#1= (var X#15)
       ;X#15= A#14[(var X#16)]
       ;X#7= S#11
       ;E#19
       ;E#9
       ;EE#17[X#8,(var X#15)]
       ;EE#18[X#16,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#1=(var X#15);X#15=A#14[(var X#16)];E#19;E#9;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#1=(var X#15);X#15=A#14[(var X#16)];E#19;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#1),[.]),
             ((var X#15),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#2          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           E#10         |->  {X#1=(var X#15);E#19},
           E#3          |->  {X#7=(letrec {E#9} in S#11);E#19;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]}}

and instantiated rules:

                                  (letrec {X#1=(var X#15);X#15=A#14[(var X#16)];X#7=(letrec {E#9} in S#11);E#19;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#1=A#14[(var X#16)];X#15=(var X#1);X#7=(letrec {E#9} in S#11);E#19;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#1=(var X#15);X#15=A#14[(var X#16)];X#7=(letrec {E#9} in S#11);E#19;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#1=(var X#15);X#15=A#14[(var X#16)];X#7=S#11;E#19;E#9;EE#17[X#8,(var X#15)];EE#18[X#16,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#8)
       ;X#7= (letrec {E#9} in S#11)
       ;X#8= A#14[(var X#16)]
       ;E#10
       ;EE#18[X#16,(var X#7)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;X#7= S#11
       ;X#8= (var X#15)
       ;E#10
       ;E#9
       ;EE#18[X#16,(var X#7)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#15=A#14[(var X#16)];X#8=(var X#15);E#10;E#9;EE#18[X#16,(var X#7)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#15=A#14[(var X#16)];X#8=(var X#15);E#10;EE#18[X#16,(var X#7)]},(letrec {E#9} in [.])],
             ((var X#8),[.]),
             ((var X#15),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];[.1]=(var X#15);EE#18[X#16,[.2]]},
           X#2          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           EE#17[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#8,
           E#3          |->  {X#7=(letrec {E#9} in S#11);E#10;EE#18[X#16,(var X#7)]},
           A#19         |->  [.],
           X#15         |->  X#15}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];X#7=(letrec {E#9} in S#11);X#8=(var X#15);E#10;EE#18[X#16,(var X#7)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#15=(var X#8);X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#16)];E#10;EE#18[X#16,(var X#7)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];X#7=(letrec {E#9} in S#11);X#8=(var X#15);E#10;EE#18[X#16,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#15=A#14[(var X#16)];X#7=S#11;X#8=(var X#15);E#10;E#9;EE#18[X#16,(var X#7)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#20)
       ;X#20= A#14[(var X#16)]
       ;X#7= (letrec {E#9} in S#11)
       ;E#10
       ;EE#18[X#16,(var X#7)]
       ;EE#21[X#8,(var X#20)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;X#20= (var X#15)
       ;X#7= S#11
       ;E#10
       ;E#9
       ;EE#18[X#16,(var X#7)]
       ;EE#21[X#8,(var X#20)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#15=A#14[(var X#16)];X#20=(var X#15);E#10;E#9;EE#18[X#16,(var X#7)];EE#21[X#8,(var X#20)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#15=A#14[(var X#16)];X#20=(var X#15);E#10;EE#18[X#16,(var X#7)];EE#21[X#8,(var X#20)]},(letrec {E#9} in [.])],
             ((var X#20),[.]),
             ((var X#15),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];X#20=(var X#15);EE#18[X#16,[.2]];EE#21[[.1],(var X#20)]},
           X#2          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           EE#17[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#3          |->  {X#7=(letrec {E#9} in S#11);E#10;EE#18[X#16,(var X#7)];EE#21[X#8,(var X#20)]},
           A#19         |->  [.],
           X#15         |->  X#15}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];X#20=(var X#15);X#7=(letrec {E#9} in S#11);E#10;EE#18[X#16,(var X#7)];EE#21[X#8,(var X#20)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#15=(var X#20);X#20=A#14[(var X#16)];X#7=(letrec {E#9} in S#11);E#10;EE#18[X#16,(var X#7)];EE#21[X#8,(var X#20)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];X#20=(var X#15);X#7=(letrec {E#9} in S#11);E#10;EE#18[X#16,(var X#7)];EE#21[X#8,(var X#20)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#15=A#14[(var X#16)];X#20=(var X#15);X#7=S#11;E#10;E#9;EE#18[X#16,(var X#7)];EE#21[X#8,(var X#20)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(var X#7)]
       ;X#15= (var X#1)
       ;X#7= (letrec {E#9} in S#11)
       ;E#17
       ;EE#16[X#8,(var X#15)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#1= (var X#15)
       ;X#15= A#14[(var X#7)]
       ;X#7= S#11
       ;E#17
       ;E#9
       ;EE#16[X#8,(var X#15)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#1=(var X#15);X#15=A#14[(var X#7)];E#17;E#9;EE#16[X#8,(var X#15)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#1=(var X#15);X#15=A#14[(var X#7)];E#17;EE#16[X#8,(var X#15)]},(letrec {E#9} in [.])],
             ((var X#1),[.]),
             ((var X#15),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {X#15=A#14[[.2]];EE#16[[.1],(var X#15)]},
           X#2          |->  X#15,
           S#4          |->  A#14[(var X#7)],
           E#10         |->  {X#1=(var X#15);E#17},
           E#3          |->  {X#7=(letrec {E#9} in S#11);E#17;EE#16[X#8,(var X#15)]}}

and instantiated rules:

                                  (letrec {X#1=(var X#15);X#15=A#14[(var X#7)];X#7=(letrec {E#9} in S#11);E#17;EE#16[X#8,(var X#15)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#1=A#14[(var X#7)];X#15=(var X#1);X#7=(letrec {E#9} in S#11);E#17;EE#16[X#8,(var X#15)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#1=(var X#15);X#15=A#14[(var X#7)];X#7=(letrec {E#9} in S#11);E#17;EE#16[X#8,(var X#15)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#1=(var X#15);X#15=A#14[(var X#7)];X#7=S#11;E#17;E#9;EE#16[X#8,(var X#15)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#8)
       ;X#7= (letrec {E#9} in S#11)
       ;X#8= A#14[(var X#7)]
       ;E#10
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= A#14[(var X#7)]
       ;X#7= S#11
       ;X#8= (var X#15)
       ;E#10
       ;E#9
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#15=A#14[(var X#7)];X#8=(var X#15);E#10;E#9} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#15=A#14[(var X#7)];X#8=(var X#15);E#10},(letrec {E#9} in [.])],
             ((var X#8),[.]),
             ((var X#15),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {X#15=A#14[[.2]];[.1]=(var X#15)},
           X#2          |->  X#15,
           S#4          |->  A#14[(var X#7)],
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#8,
           E#3          |->  {X#7=(letrec {E#9} in S#11);E#10},
           A#17         |->  [.],
           X#15         |->  X#15}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#7)];X#7=(letrec {E#9} in S#11);X#8=(var X#15);E#10} in A#12[(var X#8)])
    -xch1->                       (letrec {X#15=(var X#8);X#7=(letrec {E#9} in S#11);X#8=A#14[(var X#7)];E#10} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#7)];X#7=(letrec {E#9} in S#11);X#8=(var X#15);E#10} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#15=A#14[(var X#7)];X#7=S#11;X#8=(var X#15);E#10;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#18)
       ;X#18= A#14[(var X#7)]
       ;X#7= (letrec {E#9} in S#11)
       ;E#10
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= A#14[(var X#7)]
       ;X#18= (var X#15)
       ;X#7= S#11
       ;E#10
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#7),(letrec {X#15=A#14[(var X#7)];X#18=(var X#15);E#10;E#9;EE#19[X#8,(var X#18)]} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#15=A#14[(var X#7)];X#18=(var X#15);E#10;EE#19[X#8,(var X#18)]},(letrec {E#9} in [.])],
             ((var X#18),[.]),
             ((var X#15),[.]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#7),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#7=S#11;E#10;E#9;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])
    and constraints: E#9/= {}, ((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])), (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {X#7=(letrec {E#9} in S#11);E#10;EE#13[X#8,(var X#7)]} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#7),(letrec {E#10;E#9;EE#13[X#8,(var X#7)]} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10;EE#13[X#8,(var X#7)]},(letrec {E#9} in [.])],((var X#1),[.]),((var X#2),[.]),((var X#7),[.]),((var X#8),A#12[[.]]),((var X#7),[.]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#8)],
           EE#13[.1,.2] |-> {X#15=A#14[[.2]];X#18=(var X#15);EE#19[[.1],(var X#18)]},
           X#2          |->  X#15,
           S#4          |->  A#14[(var X#7)],
           EE#16[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#3          |->  {X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]},
           A#17         |->  [.],
           X#15         |->  X#15}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#7)];X#18=(var X#15);X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -xch1->                       (letrec {X#15=(var X#18);X#18=A#14[(var X#7)];X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#7)];X#18=(var X#15);X#7=(letrec {E#9} in S#11);E#10;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -SR,llet-e2->                 (letrec {X#15=A#14[(var X#7)];X#18=(var X#15);X#7=S#11;E#10;E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     A#11[(app (letrec {E#7} in T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#8)]
    ,
     A#11[(letrec {E#7} in (app T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#8))]
  )

where

   Delta1 = {T#13,T#12,A#10,T#6,A#11}
   Delta2 = {E#7}
   Delta3 = {(S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#8,(letrec {E#7} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {A#10  |->  A#11,
           T#6   |->  A#11[(app (letrec {E#7} in T#14) S#8)],
           T#12  |->  (app (letrec {E#7} in T#14) S#8),
           T#13  |->  (letrec {E#7} in T#14),
           S#9   |->  T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  A#11[(app (letrec {E#7} in T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#8)]
    -xch1->                       A#11[(app (letrec {E#7} in T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#8)]
    ................................................................................
                                  A#11[(app (letrec {E#7} in T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#8)]
    -SR,lapp1->                   A#11[(letrec {E#7} in (app T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#8))]
    

================================================================================
Critical Pair:

  (
     A#11[(app (letrec {X#15=T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#17} in S#9) S#8)]
    ,
     A#11[(letrec
              X#15= T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
             ;E#17
           in
              (app S#9 S#8)
           )]
  )

where

   Delta1 = {T#13,T#12,A#10,T#6,A#11}
   Delta2 = {E#7}
   Delta3 = {(S#8,(letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#8,(letrec {E#7} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {A#10  |->  A#11,
           T#6   |->  A#11[(app (letrec {X#15=T#14;E#17} in S#9) S#8)],
           T#12  |->  (app (letrec {X#15=T#14;E#17} in S#9) S#8),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#9),
           E#7   |->  {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  A#11[(app (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17} in S#9) S#8)]
    -xch1->                       A#11[(app (letrec {X#15=T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#17} in S#9) S#8)]
    ................................................................................
                                  A#11[(app (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17} in S#9) S#8)]
    -SR,lapp1->                   A#11[(letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17} in (app S#9 S#8))]
    

================================================================================
Critical Pair:

  (
     A#11[(app (letrec {X#1=S#4;X#2=(var X#1);E#15} in S#9) S#8)]
    ,
     A#11[(letrec {X#1=(var X#2);X#2=S#4;E#15} in (app S#9 S#8))]
  )

where

   Delta1 = {T#12,A#10,T#6,A#11}
   Delta2 = {E#7}
   Delta3 = {(S#8,(letrec {X#1=(var X#2);X#2=S#4;E#15} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#8,(letrec {E#7} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {A#10  |->  A#11,
           T#6   |->  A#11[(app [.] S#8)],
           T#12  |->  (app [.] S#8),
           T#13  |->  [.],
           S#5   |->  S#9,
           E#7   |->  {X#1=(var X#2);X#2=S#4;E#15},
           E#14  |->  {X#1=(var X#2);E#15},
           E#3   |->  {E#15}}

and instantiated rules:

                                  A#11[(app (letrec {X#1=(var X#2);X#2=S#4;E#15} in S#9) S#8)]
    -xch1->                       A#11[(app (letrec {X#1=S#4;X#2=(var X#1);E#15} in S#9) S#8)]
    ................................................................................
                                  A#11[(app (letrec {X#1=(var X#2);X#2=S#4;E#15} in S#9) S#8)]
    -SR,lapp1->                   A#11[(letrec {X#1=(var X#2);X#2=S#4;E#15} in (app S#9 S#8))]
    

================================================================================
Critical Pair:

  (
     A#11[(app (letrec {E#7} in S#9) T#13[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
    ,
     A#11[(letrec {E#7} in (app S#9 T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))]
  )

where

   Delta1 = {T#12,A#10,T#6,A#11}
   Delta2 = {E#7}
   Delta3 = {(T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#8,(letrec {E#7} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {A#10  |->  A#11,
           T#6   |->  A#11[(app (letrec {E#7} in S#9) T#13)],
           T#12  |->  (app (letrec {E#7} in S#9) T#13),
           S#8   |->  T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  A#11[(app (letrec {E#7} in S#9) T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
    -xch1->                       A#11[(app (letrec {E#7} in S#9) T#13[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
    ................................................................................
                                  A#11[(app (letrec {E#7} in S#9) T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
    -SR,lapp1->                   A#11[(letrec {E#7} in (app S#9 T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))]
    

================================================================================
Critical Pair:

  (
     A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
    ,
     A#11[(app A#12[(letrec {E#7} in (app S#9 S#8))] T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
  )

where

   Delta1 = {A#10,T#6}
   Delta2 = {E#7}
   Delta3 = {(S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#8,(letrec {E#7} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13)],
           A#10  |->  A#11[(app A#12 T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
    -xch1->                       A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
    ................................................................................
                                  A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
    -SR,lapp1->                   A#11[(app A#12[(letrec {E#7} in (app S#9 S#8))] T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#7} in T#12[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#8)
    ,
     (letrec {E#7} in (app T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#8))
  )

where

   Delta1 = {T#11,T#6}
   Delta2 = {E#7}
   Delta3 = {(S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#8,(letrec {E#7} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {A#10  |->  [.],
           T#6   |->  (app (letrec {E#7} in T#12) S#8),
           T#11  |->  (letrec {E#7} in T#12),
           S#9   |->  T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (app (letrec {E#7} in T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#8)
    -xch1->                       (app (letrec {E#7} in T#12[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#8)
    ................................................................................
                                  (app (letrec {E#7} in T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#8)
    -SR,lapp1->                   (letrec {E#7} in (app T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#8))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#13=T#12[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#15} in S#9) S#8)
    ,
     (letrec
        X#13= T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;E#15
     in
        (app S#9 S#8)
     )
  )

where

   Delta1 = {T#11,T#6}
   Delta2 = {E#7}
   Delta3 = {(S#8,(letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#8,(letrec {E#7} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {A#10  |->  [.],
           T#6   |->  (app (letrec {X#13=T#12;E#15} in S#9) S#8),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#9),
           E#7   |->  {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (app (letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15} in S#9) S#8)
    -xch1->                       (app (letrec {X#13=T#12[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#15} in S#9) S#8)
    ................................................................................
                                  (app (letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15} in S#9) S#8)
    -SR,lapp1->                   (letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15} in (app S#9 S#8))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#1=S#4;X#2=(var X#1);E#13} in S#9) S#8)
    ,
     (letrec {X#1=(var X#2);X#2=S#4;E#13} in (app S#9 S#8))
  )

where

   Delta1 = {T#6}
   Delta2 = {E#7}
   Delta3 = {(S#8,(letrec {X#1=(var X#2);X#2=S#4;E#13} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#8,(letrec {E#7} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {A#10  |->  [.],
           T#6   |->  (app [.] S#8),
           T#11  |->  [.],
           S#5   |->  S#9,
           E#7   |->  {X#1=(var X#2);X#2=S#4;E#13},
           E#12  |->  {X#1=(var X#2);E#13},
           E#3   |->  {E#13}}

and instantiated rules:

                                  (app (letrec {X#1=(var X#2);X#2=S#4;E#13} in S#9) S#8)
    -xch1->                       (app (letrec {X#1=S#4;X#2=(var X#1);E#13} in S#9) S#8)
    ................................................................................
                                  (app (letrec {X#1=(var X#2);X#2=S#4;E#13} in S#9) S#8)
    -SR,lapp1->                   (letrec {X#1=(var X#2);X#2=S#4;E#13} in (app S#9 S#8))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#7} in S#9) T#11[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])
    ,
     (letrec {E#7} in (app S#9 T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))
  )

where

   Delta1 = {T#6}
   Delta2 = {E#7}
   Delta3 = {(T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  A#10[(app (letrec {E#7} in S#9) S#8)]
    -SR,lapp1->                   A#10[(letrec {E#7} in (app S#9 S#8))]
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        A#10[(app (letrec {E#7} in S#9) S#8)]}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {(S#8,(letrec {E#7} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {A#10  |->  [.],
           T#6   |->  (app (letrec {E#7} in S#9) T#11),
           S#8   |->  T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (app (letrec {E#7} in S#9) T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])
    -xch1->                       (app (letrec {E#7} in S#9) T#11[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])
    ................................................................................
                                  (app (letrec {E#7} in S#9) T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])
    -SR,lapp1->                   (letrec {E#7} in (app S#9 T#11[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#13[(app (letrec {E#8} in T#16[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#9)]
     )
    ,
     (letrec
        E#7
     in
        A#13[(letrec {E#8} in (app T#16[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#9))]
     )
  )

where

   Delta1 = {T#15,T#14,A#11,T#12,T#6,A#13}
   Delta2 = {E#7,E#8}
   Delta3 = {(S#9,(letrec {E#8} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {(S#9,(letrec {E#8} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in A#13[(app (letrec {E#8} in T#16) S#9)]),
           A#11  |->  A#13,
           T#12  |->  A#13[(app (letrec {E#8} in T#16) S#9)],
           T#14  |->  (app (letrec {E#8} in T#16) S#9),
           T#15  |->  (letrec {E#8} in T#16),
           S#10  |->  T#16[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#7} in A#13[(app (letrec {E#8} in T#16[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#9)])
    -xch1->                       (letrec {E#7} in A#13[(app (letrec {E#8} in T#16[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#9)])
    ................................................................................
                                  (letrec {E#7} in A#13[(app (letrec {E#8} in T#16[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#13[(letrec {E#8} in (app T#16[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#13[(app (letrec {X#17=T#16[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#19} in S#10) S#9)]
     )
    ,
     (letrec
        E#7
     in
        A#13[(letrec
                 X#17= T#16[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
                ;E#19
              in
                 (app S#10 S#9)
              )]
     )
  )

where

   Delta1 = {T#15,T#14,A#11,T#12,T#6,A#13}
   Delta2 = {E#7,E#8}
   Delta3 = {(S#9,(letrec {X#17=T#16[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#19} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {(S#9,(letrec {E#8} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in A#13[(app (letrec {X#17=T#16;E#19} in S#10) S#9)]),
           A#11  |->  A#13,
           T#12  |->  A#13[(app (letrec {X#17=T#16;E#19} in S#10) S#9)],
           T#14  |->  (app (letrec {X#17=T#16;E#19} in S#10) S#9),
           T#15  |->  (letrec {X#17=T#16;E#19} in S#10),
           E#8   |->  {X#17=T#16[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#19},
           E#18  |->  {E#19}}

and instantiated rules:

                                  (letrec {E#7} in A#13[(app (letrec {X#17=T#16[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#19} in S#10) S#9)])
    -xch1->                       (letrec {E#7} in A#13[(app (letrec {X#17=T#16[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#19} in S#10) S#9)])
    ................................................................................
                                  (letrec {E#7} in A#13[(app (letrec {X#17=T#16[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#19} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#13[(letrec {X#17=T#16[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#19} in (app S#10 S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec {E#7} in A#13[(app (letrec {X#1=S#4;X#2=(var X#1);E#17} in S#10) S#9)])
    ,
     (letrec {E#7} in A#13[(letrec {X#1=(var X#2);X#2=S#4;E#17} in (app S#10 S#9))])
  )

where

   Delta1 = {T#14,A#11,T#12,T#6,A#13}
   Delta2 = {E#7,E#8}
   Delta3 = {(S#9,(letrec {X#1=(var X#2);X#2=S#4;E#17} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {(S#9,(letrec {E#8} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in A#13[(app [.] S#9)]),
           A#11  |->  A#13,
           T#12  |->  A#13[(app [.] S#9)],
           T#14  |->  (app [.] S#9),
           T#15  |->  [.],
           S#5   |->  S#10,
           E#8   |->  {X#1=(var X#2);X#2=S#4;E#17},
           E#16  |->  {X#1=(var X#2);E#17},
           E#3   |->  {E#17}}

and instantiated rules:

                                  (letrec {E#7} in A#13[(app (letrec {X#1=(var X#2);X#2=S#4;E#17} in S#10) S#9)])
    -xch1->                       (letrec {E#7} in A#13[(app (letrec {X#1=S#4;X#2=(var X#1);E#17} in S#10) S#9)])
    ................................................................................
                                  (letrec {E#7} in A#13[(app (letrec {X#1=(var X#2);X#2=S#4;E#17} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#13[(letrec {X#1=(var X#2);X#2=S#4;E#17} in (app S#10 S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#13[(app (letrec {E#8} in S#10) T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
     )
    ,
     (letrec
        E#7
     in
        A#13[(letrec {E#8} in (app S#10 T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))]
     )
  )

where

   Delta1 = {T#14,A#11,T#12,T#6,A#13}
   Delta2 = {E#7,E#8}
   Delta3 = {(T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {E#8} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {(S#9,(letrec {E#8} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in A#13[(app (letrec {E#8} in S#10) T#15)]),
           A#11  |->  A#13,
           T#12  |->  A#13[(app (letrec {E#8} in S#10) T#15)],
           T#14  |->  (app (letrec {E#8} in S#10) T#15),
           S#9   |->  T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#7} in A#13[(app (letrec {E#8} in S#10) T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -xch1->                       (letrec {E#7} in A#13[(app (letrec {E#8} in S#10) T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#7} in A#13[(app (letrec {E#8} in S#10) T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -SR,lapp2->                   (letrec {E#7} in A#13[(letrec {E#8} in (app S#10 T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
     )
    ,
     (letrec
        E#7
     in
        A#13[(app A#14[(letrec {E#8} in (app S#10 S#9))] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#11,T#12,T#6}
   Delta2 = {E#7,E#8}
   Delta3 = {(S#9,(letrec {E#8} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {(S#9,(letrec {E#8} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15)]),
           T#12  |->  A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {E#7} in A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -xch1->                       (letrec {E#7} in A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#7} in A#13[(app A#14[(app (letrec {E#8} in S#10) S#9)] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -SR,lapp2->                   (letrec {E#7} in A#13[(app A#14[(letrec {E#8} in (app S#10 S#9))] T#15[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (app (letrec {E#8} in T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#9)
     )
    ,
     (letrec
        E#7
     in
        (letrec {E#8} in (app T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#9))
     )
  )

where

   Delta1 = {T#13,T#12,T#6}
   Delta2 = {E#7,E#8}
   Delta3 = {(S#9,(letrec {E#8} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {(S#9,(letrec {E#8} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in (app (letrec {E#8} in T#14) S#9)),
           A#11  |->  [.],
           T#12  |->  (app (letrec {E#8} in T#14) S#9),
           T#13  |->  (letrec {E#8} in T#14),
           S#10  |->  T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#7} in (app (letrec {E#8} in T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#9))
    -xch1->                       (letrec {E#7} in (app (letrec {E#8} in T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#9))
    ................................................................................
                                  (letrec {E#7} in (app (letrec {E#8} in T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#9))
    -SR,lapp2->                   (letrec {E#7} in (letrec {E#8} in (app T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#9)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (app (letrec {X#15=T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#17} in S#10) S#9)
     )
    ,
     (letrec
        E#7
     in
        (letrec
           X#15= T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
          ;E#17
        in
           (app S#10 S#9)
        )
     )
  )

where

   Delta1 = {T#13,T#12,T#6}
   Delta2 = {E#7,E#8}
   Delta3 = {(S#9,(letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {(S#9,(letrec {E#8} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in (app (letrec {X#15=T#14;E#17} in S#10) S#9)),
           A#11  |->  [.],
           T#12  |->  (app (letrec {X#15=T#14;E#17} in S#10) S#9),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#10),
           E#8   |->  {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {E#7} in (app (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17} in S#10) S#9))
    -xch1->                       (letrec {E#7} in (app (letrec {X#15=T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#17} in S#10) S#9))
    ................................................................................
                                  (letrec {E#7} in (app (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17} in S#10) S#9))
    -SR,lapp2->                   (letrec {E#7} in (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17} in (app S#10 S#9)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#7} in (app (letrec {X#1=S#4;X#2=(var X#1);E#15} in S#10) S#9))
    ,
     (letrec {E#7} in (letrec {X#1=(var X#2);X#2=S#4;E#15} in (app S#10 S#9)))
  )

where

   Delta1 = {T#12,T#6}
   Delta2 = {E#7,E#8}
   Delta3 = {(S#9,(letrec {X#1=(var X#2);X#2=S#4;E#15} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {(S#9,(letrec {E#8} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in (app [.] S#9)),
           A#11  |->  [.],
           T#12  |->  (app [.] S#9),
           T#13  |->  [.],
           S#5   |->  S#10,
           E#8   |->  {X#1=(var X#2);X#2=S#4;E#15},
           E#14  |->  {X#1=(var X#2);E#15},
           E#3   |->  {E#15}}

and instantiated rules:

                                  (letrec {E#7} in (app (letrec {X#1=(var X#2);X#2=S#4;E#15} in S#10) S#9))
    -xch1->                       (letrec {E#7} in (app (letrec {X#1=S#4;X#2=(var X#1);E#15} in S#10) S#9))
    ................................................................................
                                  (letrec {E#7} in (app (letrec {X#1=(var X#2);X#2=S#4;E#15} in S#10) S#9))
    -SR,lapp2->                   (letrec {E#7} in (letrec {X#1=(var X#2);X#2=S#4;E#15} in (app S#10 S#9)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (app (letrec {E#8} in S#10) T#13[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])
     )
    ,
     (letrec
        E#7
     in
        (letrec {E#8} in (app S#10 T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))
     )
  )

where

   Delta1 = {T#12,T#6}
   Delta2 = {E#7,E#8}
   Delta3 = {(T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {E#8} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {(S#9,(letrec {E#8} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {E#7} in (app (letrec {E#8} in S#10) T#13)),
           A#11  |->  [.],
           T#12  |->  (app (letrec {E#8} in S#10) T#13),
           S#9   |->  T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#7} in (app (letrec {E#8} in S#10) T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))
    -xch1->                       (letrec {E#7} in (app (letrec {E#8} in S#10) T#13[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]))
    ................................................................................
                                  (letrec {E#7} in (app (letrec {E#8} in S#10) T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))
    -SR,lapp2->                   (letrec {E#7} in (letrec {E#8} in (app S#10 T#13[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
       ;E#15
     in
        A#11[(app (letrec {E#8} in S#10) S#9)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;E#15
     in
        A#11[(letrec {E#8} in (app S#10 S#9))]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#7,E#8}
   Delta3 = {(S#9,(letrec {E#8} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {(S#9,(letrec {E#8} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {X#13=T#12;E#15} in A#11[(app (letrec {E#8} in S#10) S#9)]),
           E#7   |->  {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -xch1->                       (letrec {X#13=T#12[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#15} in A#11[(app (letrec {E#8} in S#10) S#9)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {X#13=T#12[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#15} in A#11[(letrec {E#8} in (app S#10 S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#4;X#2=(var X#1);E#13} in A#11[(app (letrec {E#8} in S#10) S#9)])
    ,
     (letrec {X#1=(var X#2);X#2=S#4;E#13} in A#11[(letrec {E#8} in (app S#10 S#9))])
  )

where

   Delta1 = {}
   Delta2 = {E#7,E#8}
   Delta3 = {(S#9,(letrec {E#8} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {E#7} in A#11[(letrec {E#8} in (app S#10 S#9))])
    and constraints: E#7/= {}, E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#7} in A#11[(app (letrec {E#8} in S#10) S#9)])}
      Delta1=  {}
      Delta2=  {E#7,E#8}
      Delta3=  {(S#9,(letrec {E#8} in [.])),((var X#1),[.]),((var X#2),[.])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#11[(app (letrec {E#8} in S#10) S#9)],
           E#7   |->  {X#1=(var X#2);X#2=S#4;E#13},
           E#12  |->  {X#1=(var X#2);E#13},
           E#3   |->  {E#13}}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#2=S#4;E#13} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -xch1->                       (letrec {X#1=S#4;X#2=(var X#1);E#13} in A#11[(app (letrec {E#8} in S#10) S#9)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#2=S#4;E#13} in A#11[(app (letrec {E#8} in S#10) S#9)])
    -SR,lapp2->                   (letrec {X#1=(var X#2);X#2=S#4;E#13} in A#11[(letrec {E#8} in (app S#10 S#9))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
       ;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]
     in
        A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
     )
    ,
     (letrec
        E#8
       ;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]
     in
        A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#15[(app A#16[[.]] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]),
             ((var X#7),A#15[(app A#16[[.]] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#7)] T#17)],
           A#12  |->  A#15[(app A#16 T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -xch1->                       (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#15[(app A#16[(var X#7)] T#17[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
       ;E#17
       ;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
       ;E#17
       ;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#15=T#14;E#17;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)]),
           E#8   |->  {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17},
           E#16  |->  {E#17;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#15=T#14[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#17;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#15=T#14[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#17;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app (letrec {E#9} in T#21[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#10)]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(letrec {E#9} in (app T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#10))]
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,T#19,A#17,T#14,T#6,A#18}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#18[(app (letrec {E#9} in T#21) S#10)];E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  A#18,
           T#14         |->  A#18[(app (letrec {E#9} in T#21) S#10)],
           T#19         |->  (app (letrec {E#9} in T#21) S#10),
           T#20         |->  (letrec {E#9} in T#21),
           S#11         |->  T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=A#18[(app (letrec {E#9} in T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#10)];E#8} in A#12[(var X#7)])
    -xch1->                       (letrec {X#7=A#18[(app (letrec {E#9} in T#21[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#10)];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app (letrec {E#9} in T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#10)];E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#18[(letrec {E#9} in (app T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#10))];E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app (letrec {X#22=T#21[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#24} in S#11) S#10)]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(letrec
                      X#22= T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
                     ;E#24
                   in
                      (app S#11 S#10)
                   )]
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,T#19,A#17,T#14,T#6,A#18}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {X#22=T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#24} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#18[(app (letrec {X#22=T#21;E#24} in S#11) S#10)];E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  A#18,
           T#14         |->  A#18[(app (letrec {X#22=T#21;E#24} in S#11) S#10)],
           T#19         |->  (app (letrec {X#22=T#21;E#24} in S#11) S#10),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#11),
           E#9          |->  {X#22=T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#7=A#18[(app (letrec {X#22=T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#24} in S#11) S#10)];E#8} in A#12[(var X#7)])
    -xch1->                       (letrec {X#7=A#18[(app (letrec {X#22=T#21[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#24} in S#11) S#10)];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app (letrec {X#22=T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#24} in S#11) S#10)];E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#18[(letrec {X#22=T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#24} in (app S#11 S#10))];E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app (letrec {X#1=S#4;X#2=(var X#1);E#22} in S#11) S#10)]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(letrec {X#1=(var X#2);X#2=S#4;E#22} in (app S#11 S#10))]
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#19,A#17,T#14,T#6,A#18}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {X#1=(var X#2);X#2=S#4;E#22} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#18[(app [.] S#10)];E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  A#18,
           T#14         |->  A#18[(app [.] S#10)],
           T#19         |->  (app [.] S#10),
           T#20         |->  [.],
           S#5          |->  S#11,
           E#9          |->  {X#1=(var X#2);X#2=S#4;E#22},
           E#21         |->  {X#1=(var X#2);E#22},
           E#3          |->  {E#22}}

and instantiated rules:

                                  (letrec {X#7=A#18[(app (letrec {X#1=(var X#2);X#2=S#4;E#22} in S#11) S#10)];E#8} in A#12[(var X#7)])
    -xch1->                       (letrec {X#7=A#18[(app (letrec {X#1=S#4;X#2=(var X#1);E#22} in S#11) S#10)];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app (letrec {X#1=(var X#2);X#2=S#4;E#22} in S#11) S#10)];E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#18[(letrec {X#1=(var X#2);X#2=S#4;E#22} in (app S#11 S#10))];E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app (letrec {E#9} in S#11) T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(letrec {E#9} in (app S#11 T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))]
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#19,A#17,T#14,T#6,A#18}
   Delta2 = {E#9}
   Delta3 = {(T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#18[(app (letrec {E#9} in S#11) T#20)];E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  A#18,
           T#14         |->  A#18[(app (letrec {E#9} in S#11) T#20)],
           T#19         |->  (app (letrec {E#9} in S#11) T#20),
           S#10         |->  T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=A#18[(app (letrec {E#9} in S#11) T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8} in A#12[(var X#7)])
    -xch1->                       (letrec {X#7=A#18[(app (letrec {E#9} in S#11) T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app (letrec {E#9} in S#11) T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#18[(letrec {E#9} in (app S#11 T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))];E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#18[(app A#19[(letrec {E#9} in (app S#11 S#10))] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20)];E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           T#14         |->  A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20)],
           A#17         |->  A#18[(app A#19 T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8} in A#12[(var X#7)])
    -xch1->                       (letrec {X#7=A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#18[(app A#19[(app (letrec {E#9} in S#11) S#10)] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#18[(app A#19[(letrec {E#9} in (app S#11 S#10))] T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (app (letrec {E#9} in T#19[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#10)
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= (letrec {E#9} in (app T#19[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#10))
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#18,T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(app (letrec {E#9} in T#19) S#10);E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  [.],
           T#14         |->  (app (letrec {E#9} in T#19) S#10),
           T#18         |->  (letrec {E#9} in T#19),
           S#11         |->  T#19[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=(app (letrec {E#9} in T#19[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#10);E#8} in A#12[(var X#7)])
    -xch1->                       (letrec {X#7=(app (letrec {E#9} in T#19[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#10);E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(app (letrec {E#9} in T#19[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#10);E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=(letrec {E#9} in (app T#19[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#10));E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (app (letrec {X#20=T#19[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#22} in S#11) S#10)
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= (letrec
                X#20= T#19[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
               ;E#22
             in
                (app S#11 S#10)
             )
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#18,T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {X#20=T#19[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#22} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(app (letrec {X#20=T#19;E#22} in S#11) S#10);E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  [.],
           T#14         |->  (app (letrec {X#20=T#19;E#22} in S#11) S#10),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#11),
           E#9          |->  {X#20=T#19[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#7=(app (letrec {X#20=T#19[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#22} in S#11) S#10);E#8} in A#12[(var X#7)])
    -xch1->                       (letrec {X#7=(app (letrec {X#20=T#19[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#22} in S#11) S#10);E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(app (letrec {X#20=T#19[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#22} in S#11) S#10);E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=(letrec {X#20=T#19[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#22} in (app S#11 S#10));E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (app (letrec {X#1=S#4;X#2=(var X#1);E#20} in S#11) S#10)
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= (letrec {X#1=(var X#2);X#2=S#4;E#20} in (app S#11 S#10))
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {X#1=(var X#2);X#2=S#4;E#20} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(app [.] S#10);E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  [.],
           T#14         |->  (app [.] S#10),
           T#18         |->  [.],
           S#5          |->  S#11,
           E#9          |->  {X#1=(var X#2);X#2=S#4;E#20},
           E#19         |->  {X#1=(var X#2);E#20},
           E#3          |->  {E#20}}

and instantiated rules:

                                  (letrec {X#7=(app (letrec {X#1=(var X#2);X#2=S#4;E#20} in S#11) S#10);E#8} in A#12[(var X#7)])
    -xch1->                       (letrec {X#7=(app (letrec {X#1=S#4;X#2=(var X#1);E#20} in S#11) S#10);E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(app (letrec {X#1=(var X#2);X#2=S#4;E#20} in S#11) S#10);E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=(letrec {X#1=(var X#2);X#2=S#4;E#20} in (app S#11 S#10));E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= (app (letrec {E#9} in S#11) T#18[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= (letrec {E#9} in (app S#11 T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {(T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=(app (letrec {E#9} in S#11) T#18);E#8} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {E#8},
           A#17         |->  [.],
           T#14         |->  (app (letrec {E#9} in S#11) T#18),
           S#10         |->  T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#7=(app (letrec {E#9} in S#11) T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]);E#8} in A#12[(var X#7)])
    -xch1->                       (letrec {X#7=(app (letrec {E#9} in S#11) T#18[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]);E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=(app (letrec {E#9} in S#11) T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]);E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=(letrec {E#9} in (app S#11 T#18[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]));E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#7= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#8
       ;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#7= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#8
       ;EE#19[X#18,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22)];E#8;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];EE#19[X#18,[.2]]},
           X#15         |->  X#7,
           E#16         |->  {E#8;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]},
           T#14         |->  A#20[(app A#21[(var X#18)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#8;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8;EE#19[X#18,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#7=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8;EE#19[X#18,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#8
       ;EE#20[X#7,(var X#18)]
       ;EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#8
       ;EE#20[X#7,(var X#18)]
       ;EE#21[X#19,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24)];E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]},
           T#14         |->  A#22[(app A#23[(var X#19)] T#24)],
           A#17         |->  A#22[(app A#23 T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8;EE#20[X#7,(var X#18)];EE#21[X#19,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (letrec {E#9} in T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#10)]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {E#9} in (app T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#10))]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,T#21,A#17,T#14,T#6,A#20}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app (letrec {E#9} in T#23) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[(app (letrec {E#9} in T#23) S#10)],
           T#21         |->  (app (letrec {E#9} in T#23) S#10),
           T#22         |->  (letrec {E#9} in T#23),
           S#11         |->  T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (letrec {E#9} in T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#18=A#20[(app (letrec {E#9} in T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (letrec {E#9} in T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#20[(letrec {E#9} in (app T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#10))];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (letrec {X#24=T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#26} in S#11) S#10)]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(letrec
                       X#24= T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
                      ;E#26
                    in
                       (app S#11 S#10)
                    )]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,T#21,A#17,T#14,T#6,A#20}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {X#24=T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#26} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app (letrec {X#24=T#23;E#26} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[(app (letrec {X#24=T#23;E#26} in S#11) S#10)],
           T#21         |->  (app (letrec {X#24=T#23;E#26} in S#11) S#10),
           T#22         |->  (letrec {X#24=T#23;E#26} in S#11),
           E#9          |->  {X#24=T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#26},
           E#25         |->  {E#26}}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (letrec {X#24=T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#26} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#18=A#20[(app (letrec {X#24=T#23[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#26} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (letrec {X#24=T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#26} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#20[(letrec {X#24=T#23[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#26} in (app S#11 S#10))];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (letrec {X#1=S#4;X#2=(var X#1);E#24} in S#11) S#10)]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {X#1=(var X#2);X#2=S#4;E#24} in (app S#11 S#10))]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#21,A#17,T#14,T#6,A#20}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {X#1=(var X#2);X#2=S#4;E#24} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app [.] S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[(app [.] S#10)],
           T#21         |->  (app [.] S#10),
           T#22         |->  [.],
           S#5          |->  S#11,
           E#9          |->  {X#1=(var X#2);X#2=S#4;E#24},
           E#23         |->  {X#1=(var X#2);E#24},
           E#3          |->  {E#24}}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (letrec {X#1=(var X#2);X#2=S#4;E#24} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#18=A#20[(app (letrec {X#1=S#4;X#2=(var X#1);E#24} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (letrec {X#1=(var X#2);X#2=S#4;E#24} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#20[(letrec {X#1=(var X#2);X#2=S#4;E#24} in (app S#11 S#10))];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app (letrec {E#9} in S#11) T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(letrec {E#9} in (app S#11 T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#21,A#17,T#14,T#6,A#20}
   Delta2 = {E#9}
   Delta3 = {(T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app (letrec {E#9} in S#11) T#22)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[(app (letrec {E#9} in S#11) T#22)],
           T#21         |->  (app (letrec {E#9} in S#11) T#22),
           S#10         |->  T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app (letrec {E#9} in S#11) T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#18=A#20[(app (letrec {E#9} in S#11) T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app (letrec {E#9} in S#11) T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#20[(letrec {E#9} in (app S#11 T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(letrec {E#9} in (app S#11 S#10))] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#17,T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           T#14         |->  A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#18=A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(app (letrec {E#9} in S#11) S#10)] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=A#20[(app A#21[(letrec {E#9} in (app S#11 S#10))] T#22[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)])];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (letrec {E#9} in T#21[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#10)
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= (letrec {E#9} in (app T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#10))
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=(app (letrec {E#9} in T#21) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  (app (letrec {E#9} in T#21) S#10),
           T#20         |->  (letrec {E#9} in T#21),
           S#11         |->  T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#18=(app (letrec {E#9} in T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#18=(app (letrec {E#9} in T#21[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=(app (letrec {E#9} in T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=(letrec {E#9} in (app T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)] S#10));E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (letrec {X#22=T#21[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#24} in S#11) S#10)
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= (letrec
                 X#22= T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
                ;E#24
              in
                 (app S#11 S#10)
              )
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {X#22=T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#24} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=(app (letrec {X#22=T#21;E#24} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  (app (letrec {X#22=T#21;E#24} in S#11) S#10),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#11),
           E#9          |->  {X#22=T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#18=(app (letrec {X#22=T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#24} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#18=(app (letrec {X#22=T#21[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)];E#24} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=(app (letrec {X#22=T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#24} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=(letrec {X#22=T#21[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)];E#24} in (app S#11 S#10));E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (letrec {X#1=S#4;X#2=(var X#1);E#22} in S#11) S#10)
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= (letrec {X#1=(var X#2);X#2=S#4;E#22} in (app S#11 S#10))
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {X#1=(var X#2);X#2=S#4;E#22} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=(app [.] S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  (app [.] S#10),
           T#20         |->  [.],
           S#5          |->  S#11,
           E#9          |->  {X#1=(var X#2);X#2=S#4;E#22},
           E#21         |->  {X#1=(var X#2);E#22},
           E#3          |->  {E#22}}

and instantiated rules:

                                  (letrec {X#18=(app (letrec {X#1=(var X#2);X#2=S#4;E#22} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#18=(app (letrec {X#1=S#4;X#2=(var X#1);E#22} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=(app (letrec {X#1=(var X#2);X#2=S#4;E#22} in S#11) S#10);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=(letrec {X#1=(var X#2);X#2=S#4;E#22} in (app S#11 S#10));E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (app (letrec {E#9} in S#11) T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)])
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#18= (letrec {E#9} in (app S#11 T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]))
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#14,T#6}
   Delta2 = {E#9}
   Delta3 = {(T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)],(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#18=(app (letrec {E#9} in S#11) T#20);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  (app (letrec {E#9} in S#11) T#20),
           S#10         |->  T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#18=(app (letrec {E#9} in S#11) T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#18=(app (letrec {E#9} in S#11) T#20[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#18=(app (letrec {E#9} in S#11) T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#18=(letrec {E#9} in (app S#11 T#20[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]));E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#4
       ;X#2= (var X#1)
       ;E#15
       ;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#1= (var X#2)
       ;X#2= S#4
       ;E#15
       ;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#2),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#7)],
           E#8   |->  {X#1=(var X#2);X#2=S#4;E#15},
           E#14  |->  {X#1=(var X#2);E#15},
           E#3   |->  {E#15;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]}}

and instantiated rules:

                                  (letrec {X#1=(var X#2);X#2=S#4;E#15;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#1=S#4;X#2=(var X#1);E#15;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#1=(var X#2);X#2=S#4;E#15;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#1=(var X#2);X#2=S#4;E#15;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(app (letrec {E#9} in S#11) S#10)]
       ;X#7= (var X#1)
       ;E#15
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#1= (var X#7)
       ;X#7= A#14[(letrec {E#9} in (app S#11 S#10))]
       ;E#15
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#7),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {[.1]=A#14[[.2]]},
           X#2          |->  X#7,
           S#4          |->  A#14[(app (letrec {E#9} in S#11) S#10)],
           E#8          |->  {X#1=(var X#7);E#15},
           E#3          |->  {E#15}}

and instantiated rules:

                                  (letrec {X#1=(var X#7);X#7=A#14[(app (letrec {E#9} in S#11) S#10)];E#15} in A#12[(var X#7)])
    -xch1->                       (letrec {X#1=A#14[(app (letrec {E#9} in S#11) S#10)];X#7=(var X#1);E#15} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#1=(var X#7);X#7=A#14[(app (letrec {E#9} in S#11) S#10)];E#15} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#1=(var X#7);X#7=A#14[(letrec {E#9} in (app S#11 S#10))];E#15} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(var X#15)]
       ;X#7= (var X#1)
       ;E#17
       ;EE#16[X#15,(app (letrec {E#9} in S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#1= (var X#7)
       ;X#7= A#14[(var X#15)]
       ;E#17
       ;EE#16[X#15,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#7),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {[.1]=A#14[(var X#15)];EE#16[X#15,[.2]]},
           X#2          |->  X#7,
           S#4          |->  A#14[(var X#15)],
           E#8          |->  {X#1=(var X#7);E#17},
           E#3          |->  {E#17;EE#16[X#15,(app (letrec {E#9} in S#11) S#10)]}}

and instantiated rules:

                                  (letrec {X#1=(var X#7);X#7=A#14[(var X#15)];E#17;EE#16[X#15,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#1=A#14[(var X#15)];X#7=(var X#1);E#17;EE#16[X#15,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#1=(var X#7);X#7=A#14[(var X#15)];E#17;EE#16[X#15,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#1=(var X#7);X#7=A#14[(var X#15)];E#17;EE#16[X#15,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(var X#16)]
       ;X#15= (var X#1)
       ;E#19
       ;EE#17[X#7,(var X#15)]
       ;EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#1= (var X#15)
       ;X#15= A#14[(var X#16)]
       ;E#19
       ;EE#17[X#7,(var X#15)]
       ;EE#18[X#16,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#15),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#2          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           E#8          |->  {X#1=(var X#15);E#19},
           E#3          |->  {E#19;EE#17[X#7,(var X#15)];EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]}}

and instantiated rules:

                                  (letrec {X#1=(var X#15);X#15=A#14[(var X#16)];E#19;EE#17[X#7,(var X#15)];EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#1=A#14[(var X#16)];X#15=(var X#1);E#19;EE#17[X#7,(var X#15)];EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#1=(var X#15);X#15=A#14[(var X#16)];E#19;EE#17[X#7,(var X#15)];EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#1=(var X#15);X#15=A#14[(var X#16)];E#19;EE#17[X#7,(var X#15)];EE#18[X#16,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#7)
       ;X#7= A#14[(var X#16)]
       ;E#8
       ;EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;X#7= (var X#15)
       ;E#8
       ;EE#18[X#16,(letrec {E#9} in (app S#11 S#10))]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#7),[.]),
             ((var X#15),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];[.1]=(var X#15);EE#18[X#16,[.2]]},
           X#2          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           EE#17[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#7,
           E#3          |->  {E#8;EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]},
           A#19         |->  [.],
           X#15         |->  X#15}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];X#7=(var X#15);E#8;EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#15=(var X#7);X#7=A#14[(var X#16)];E#8;EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];X#7=(var X#15);E#8;EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#15=A#14[(var X#16)];X#7=(var X#15);E#8;EE#18[X#16,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#20)
       ;X#20= A#14[(var X#16)]
       ;E#8
       ;EE#18[X#16,(app (letrec {E#9} in S#11) S#10)]
       ;EE#21[X#7,(var X#20)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;X#20= (var X#15)
       ;E#8
       ;EE#18[X#16,(letrec {E#9} in (app S#11 S#10))]
       ;EE#21[X#7,(var X#20)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#20),[.]),
             ((var X#15),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[(var X#16)];X#20=(var X#15);EE#18[X#16,[.2]];EE#21[[.1],(var X#20)]},
           X#2          |->  X#15,
           S#4          |->  A#14[(var X#16)],
           EE#17[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#1          |->  X#20,
           E#3          |->  {E#8;EE#18[X#16,(app (letrec {E#9} in S#11) S#10)];EE#21[X#7,(var X#20)]},
           A#19         |->  [.],
           X#15         |->  X#15}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];X#20=(var X#15);E#8;EE#18[X#16,(app (letrec {E#9} in S#11) S#10)];EE#21[X#7,(var X#20)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#15=(var X#20);X#20=A#14[(var X#16)];E#8;EE#18[X#16,(app (letrec {E#9} in S#11) S#10)];EE#21[X#7,(var X#20)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];X#20=(var X#15);E#8;EE#18[X#16,(app (letrec {E#9} in S#11) S#10)];EE#21[X#7,(var X#20)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#15=A#14[(var X#16)];X#20=(var X#15);E#8;EE#18[X#16,(letrec {E#9} in (app S#11 S#10))];EE#21[X#7,(var X#20)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(app (letrec {E#9} in S#11) S#10)]
       ;X#15= (var X#1)
       ;E#17
       ;EE#16[X#7,(var X#15)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#1= (var X#15)
       ;X#15= A#14[(letrec {E#9} in (app S#11 S#10))]
       ;E#17
       ;EE#16[X#7,(var X#15)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#1),[.]),
             ((var X#15),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[[.2]];EE#16[[.1],(var X#15)]},
           X#2          |->  X#15,
           S#4          |->  A#14[(app (letrec {E#9} in S#11) S#10)],
           E#8          |->  {X#1=(var X#15);E#17},
           E#3          |->  {E#17;EE#16[X#7,(var X#15)]}}

and instantiated rules:

                                  (letrec {X#1=(var X#15);X#15=A#14[(app (letrec {E#9} in S#11) S#10)];E#17;EE#16[X#7,(var X#15)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#1=A#14[(app (letrec {E#9} in S#11) S#10)];X#15=(var X#1);E#17;EE#16[X#7,(var X#15)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#1=(var X#15);X#15=A#14[(app (letrec {E#9} in S#11) S#10)];E#17;EE#16[X#7,(var X#15)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#1=(var X#15);X#15=A#14[(letrec {E#9} in (app S#11 S#10))];E#17;EE#16[X#7,(var X#15)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#7)
       ;X#7= A#14[(app (letrec {E#9} in S#11) S#10)]
       ;E#8
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= A#14[(letrec {E#9} in (app S#11 S#10))]
       ;X#7= (var X#15)
       ;E#8
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#7),[.]),
             ((var X#15),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[[.2]];[.1]=(var X#15)},
           X#2          |->  X#15,
           S#4          |->  A#14[(app (letrec {E#9} in S#11) S#10)],
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#7,
           E#3          |->  {E#8},
           A#17         |->  [.],
           X#15         |->  X#15}

and instantiated rules:

                                  (letrec {X#15=A#14[(app (letrec {E#9} in S#11) S#10)];X#7=(var X#15);E#8} in A#12[(var X#7)])
    -xch1->                       (letrec {X#15=(var X#7);X#7=A#14[(app (letrec {E#9} in S#11) S#10)];E#8} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=A#14[(app (letrec {E#9} in S#11) S#10)];X#7=(var X#15);E#8} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#15=A#14[(letrec {E#9} in (app S#11 S#10))];X#7=(var X#15);E#8} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (var X#18)
       ;X#18= A#14[(app (letrec {E#9} in S#11) S#10)]
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#15= A#14[(letrec {E#9} in (app S#11 S#10))]
       ;X#18= (var X#15)
       ;E#8
       ;EE#19[X#7,(var X#18)]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {(S#10,(letrec {E#9} in [.])),
             ((var X#18),[.]),
             ((var X#15),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -xch1-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
    -xch1->                       T#6[(letrec {X#1=S#4;X#2=(var X#1);E#3} in S#5)]
    and constraints: 
    ................................................................................
                                  (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {E#8;EE#13[X#7,(letrec {E#9} in (app S#11 S#10))]} in A#12[(var X#7)])
    and constraints: E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=(var X#2);X#2=S#4;E#3} in S#5)]
        =?=
        (letrec {E#8;EE#13[X#7,(app (letrec {E#9} in S#11) S#10)]} in A#12[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {(S#10,(letrec {E#9} in [.])),((var X#1),[.]),((var X#2),[.]),((var X#7),A#12[[.]]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#12[(var X#7)],
           EE#13[.1,.2] |-> {X#15=A#14[[.2]];X#18=(var X#15);EE#19[[.1],(var X#18)]},
           X#2          |->  X#15,
           S#4          |->  A#14[(app (letrec {E#9} in S#11) S#10)],
           EE#16[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#1          |->  X#18,
           E#3          |->  {E#8;EE#19[X#7,(var X#18)]},
           A#17         |->  [.],
           X#15         |->  X#15}

and instantiated rules:

                                  (letrec {X#15=A#14[(app (letrec {E#9} in S#11) S#10)];X#18=(var X#15);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -xch1->                       (letrec {X#15=(var X#18);X#18=A#14[(app (letrec {E#9} in S#11) S#10)];E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#15=A#14[(app (letrec {E#9} in S#11) S#10)];X#18=(var X#15);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    -SR,lapp3->                   (letrec {X#15=A#14[(letrec {E#9} in (app S#11 S#10))];X#18=(var X#15);E#8;EE#19[X#7,(var X#18)]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     A#8[(app (letrec {E#1} in (\ X#4.S#6)) S#5)]
    ,
     A#8[(letrec {X#4=S#5} in S#6)]
  )

where

   Delta1 = {T#9,A#7,T#3,A#8}
   Delta2 = {E#1}
   Delta3 = {((\ X#4.S#6),(letrec {E#1} in [.])),
             (S#5,(\ X#4.[.])),
             (S#5,(letrec {X#4=[.]} in S#6))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (\ X#4.S#6) S#5)]
    -SR,lbeta1->                  A#7[(letrec {X#4=S#5} in S#6)]
    and constraints: (S#5,(\ X#4.[.])), (S#5,(letrec {X#4=[.]} in S#6))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (\ X#4.S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(\ X#4.[.])),(S#5,(letrec {X#4=[.]} in S#6))}


and found solution:

    Sol = {A#7   |->  A#8,
           T#3   |->  A#8[(app [.] S#5)],
           T#9   |->  (app [.] S#5),
           T#10  |->  [.],
           S#2   |->  (\ X#4.S#6)}

and instantiated rules:

                                  A#8[(app (\ X#4.S#6) S#5)]
    -gc1->                        A#8[(app (letrec {E#1} in (\ X#4.S#6)) S#5)]
    ................................................................................
                                  A#8[(app (\ X#4.S#6) S#5)]
    -SR,lbeta1->                  A#8[(letrec {X#4=S#5} in S#6)]
    

================================================================================
Critical Pair:

  (
     A#8[(app (\ X#4.S#6) T#10[(letrec {E#1} in S#2)])]
    ,
     A#8[(letrec {X#4=T#10[S#2]} in S#6)]
  )

where

   Delta1 = {T#9,A#7,T#3,A#8}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#10[S#2],(\ X#4.[.])),
             (T#10[S#2],(letrec {X#4=[.]} in S#6))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (\ X#4.S#6) S#5)]
    -SR,lbeta1->                  A#7[(letrec {X#4=S#5} in S#6)]
    and constraints: (S#5,(\ X#4.[.])), (S#5,(letrec {X#4=[.]} in S#6))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (\ X#4.S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(\ X#4.[.])),(S#5,(letrec {X#4=[.]} in S#6))}


and found solution:

    Sol = {A#7  |->  A#8,
           T#3  |->  A#8[(app (\ X#4.S#6) T#10)],
           T#9  |->  (app (\ X#4.S#6) T#10),
           S#5  |->  T#10[S#2]}

and instantiated rules:

                                  A#8[(app (\ X#4.S#6) T#10[S#2])]
    -gc1->                        A#8[(app (\ X#4.S#6) T#10[(letrec {E#1} in S#2)])]
    ................................................................................
                                  A#8[(app (\ X#4.S#6) T#10[S#2])]
    -SR,lbeta1->                  A#8[(letrec {X#4=T#10[S#2]} in S#6)]
    

================================================================================
Critical Pair:

  (
     A#8[(letrec {E#1} in (app (\ X#4.S#6) S#5))]
    ,
     A#8[(letrec {X#4=S#5} in S#6)]
  )

where

   Delta1 = {A#7,T#3,A#8}
   Delta2 = {E#1}
   Delta3 = {((app (\ X#4.S#6) S#5),(letrec {E#1} in [.])),
             (S#5,(\ X#4.[.])),
             (S#5,(letrec {X#4=[.]} in S#6))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (\ X#4.S#6) S#5)]
    -SR,lbeta1->                  A#7[(letrec {X#4=S#5} in S#6)]
    and constraints: (S#5,(\ X#4.[.])), (S#5,(letrec {X#4=[.]} in S#6))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (\ X#4.S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(\ X#4.[.])),(S#5,(letrec {X#4=[.]} in S#6))}


and found solution:

    Sol = {A#7  |->  A#8,
           T#3  |->  A#8[[.]],
           T#9  |->  [.],
           S#2  |->  (app (\ X#4.S#6) S#5)}

and instantiated rules:

                                  A#8[(app (\ X#4.S#6) S#5)]
    -gc1->                        A#8[(letrec {E#1} in (app (\ X#4.S#6) S#5))]
    ................................................................................
                                  A#8[(app (\ X#4.S#6) S#5)]
    -SR,lbeta1->                  A#8[(letrec {X#4=S#5} in S#6)]
    

================================================================================
Critical Pair:

  (
     A#8[(letrec {E#1} in A#9[(app (\ X#4.S#6) S#5)])]
    ,
     A#8[A#9[(letrec {X#4=S#5} in S#6)]]
  )

where

   Delta1 = {A#7,T#3,A#8}
   Delta2 = {E#1}
   Delta3 = {(A#9[(app (\ X#4.S#6) S#5)],(letrec {E#1} in [.])),
             (S#5,(\ X#4.[.])),
             (S#5,(letrec {X#4=[.]} in S#6))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (\ X#4.S#6) S#5)]
    -SR,lbeta1->                  A#7[(letrec {X#4=S#5} in S#6)]
    and constraints: (S#5,(\ X#4.[.])), (S#5,(letrec {X#4=[.]} in S#6))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (\ X#4.S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(\ X#4.[.])),(S#5,(letrec {X#4=[.]} in S#6))}


and found solution:

    Sol = {A#7  |->  A#8[A#9],
           T#3  |->  A#8,
           S#2  |->  A#9[(app (\ X#4.S#6) S#5)]}

and instantiated rules:

                                  A#8[A#9[(app (\ X#4.S#6) S#5)]]
    -gc1->                        A#8[(letrec {E#1} in A#9[(app (\ X#4.S#6) S#5)])]
    ................................................................................
                                  A#8[A#9[(app (\ X#4.S#6) S#5)]]
    -SR,lbeta1->                  A#8[A#9[(letrec {X#4=S#5} in S#6)]]
    

================================================================================
Critical Pair:

  (
     A#8[(app A#9[(app (\ X#4.S#6) S#5)] T#10[(letrec {E#1} in S#2)])]
    ,
     A#8[(app A#9[(letrec {X#4=S#5} in S#6)] T#10[S#2])]
  )

where

   Delta1 = {A#7,T#3}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#5,(\ X#4.[.])),
             (S#5,(letrec {X#4=[.]} in S#6))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (\ X#4.S#6) S#5)]
    -SR,lbeta1->                  A#7[(letrec {X#4=S#5} in S#6)]
    and constraints: (S#5,(\ X#4.[.])), (S#5,(letrec {X#4=[.]} in S#6))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (\ X#4.S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(\ X#4.[.])),(S#5,(letrec {X#4=[.]} in S#6))}


and found solution:

    Sol = {T#3  |->  A#8[(app A#9[(app (\ X#4.S#6) S#5)] T#10)],
           A#7  |->  A#8[(app A#9 T#10[S#2])]}

and instantiated rules:

                                  A#8[(app A#9[(app (\ X#4.S#6) S#5)] T#10[S#2])]
    -gc1->                        A#8[(app A#9[(app (\ X#4.S#6) S#5)] T#10[(letrec {E#1} in S#2)])]
    ................................................................................
                                  A#8[(app A#9[(app (\ X#4.S#6) S#5)] T#10[S#2])]
    -SR,lbeta1->                  A#8[(app A#9[(letrec {X#4=S#5} in S#6)] T#10[S#2])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#1} in (\ X#4.S#6)) S#5)
    ,
     (letrec {X#4=S#5} in S#6)
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {((\ X#4.S#6),(letrec {E#1} in [.])),
             (S#5,(\ X#4.[.])),
             (S#5,(letrec {X#4=[.]} in S#6))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (\ X#4.S#6) S#5)]
    -SR,lbeta1->                  A#7[(letrec {X#4=S#5} in S#6)]
    and constraints: (S#5,(\ X#4.[.])), (S#5,(letrec {X#4=[.]} in S#6))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (\ X#4.S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(\ X#4.[.])),(S#5,(letrec {X#4=[.]} in S#6))}


and found solution:

    Sol = {A#7  |->  [.],
           T#3  |->  (app [.] S#5),
           T#8  |->  [.],
           S#2  |->  (\ X#4.S#6)}

and instantiated rules:

                                  (app (\ X#4.S#6) S#5)
    -gc1->                        (app (letrec {E#1} in (\ X#4.S#6)) S#5)
    ................................................................................
                                  (app (\ X#4.S#6) S#5)
    -SR,lbeta1->                  (letrec {X#4=S#5} in S#6)
    

================================================================================
Critical Pair:

  (
     (app (\ X#4.S#6) T#8[(letrec {E#1} in S#2)])
    ,
     (letrec {X#4=T#8[S#2]} in S#6)
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#8[S#2],(\ X#4.[.])),
             (T#8[S#2],(letrec {X#4=[.]} in S#6))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (\ X#4.S#6) S#5)]
    -SR,lbeta1->                  A#7[(letrec {X#4=S#5} in S#6)]
    and constraints: (S#5,(\ X#4.[.])), (S#5,(letrec {X#4=[.]} in S#6))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (\ X#4.S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(\ X#4.[.])),(S#5,(letrec {X#4=[.]} in S#6))}


and found solution:

    Sol = {A#7  |->  [.],
           T#3  |->  (app (\ X#4.S#6) T#8),
           S#5  |->  T#8[S#2]}

and instantiated rules:

                                  (app (\ X#4.S#6) T#8[S#2])
    -gc1->                        (app (\ X#4.S#6) T#8[(letrec {E#1} in S#2)])
    ................................................................................
                                  (app (\ X#4.S#6) T#8[S#2])
    -SR,lbeta1->                  (letrec {X#4=T#8[S#2]} in S#6)
    

================================================================================
Critical Pair:

  (
     (letrec {E#1} in A#7[(app (\ X#4.S#6) S#5)])
    ,
     A#7[(letrec {X#4=S#5} in S#6)]
  )

where

   Delta1 = {}
   Delta2 = {E#1}
   Delta3 = {(A#7[(app (\ X#4.S#6) S#5)],(letrec {E#1} in [.])),
             (S#5,(\ X#4.[.])),
             (S#5,(letrec {X#4=[.]} in S#6))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (\ X#4.S#6) S#5)]
    -SR,lbeta1->                  A#7[(letrec {X#4=S#5} in S#6)]
    and constraints: (S#5,(\ X#4.[.])), (S#5,(letrec {X#4=[.]} in S#6))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (\ X#4.S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(\ X#4.[.])),(S#5,(letrec {X#4=[.]} in S#6))}


and found solution:

    Sol = {T#3  |->  [.],
           S#2  |->  A#7[(app (\ X#4.S#6) S#5)]}

and instantiated rules:

                                  A#7[(app (\ X#4.S#6) S#5)]
    -gc1->                        (letrec {E#1} in A#7[(app (\ X#4.S#6) S#5)])
    ................................................................................
                                  A#7[(app (\ X#4.S#6) S#5)]
    -SR,lbeta1->                  A#7[(letrec {X#4=S#5} in S#6)]
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in A#10[(app (letrec {E#1} in (\ X#4.S#7)) S#6)])
    ,
     (letrec {E#5} in A#10[(letrec {X#4=S#6} in S#7)])
  )

where

   Delta1 = {T#11,A#8,T#9,T#3,A#10}
   Delta2 = {E#1,E#5}
   Delta3 = {((\ X#4.S#7),(letrec {E#1} in [.])),
             (S#6,(\ X#4.[.])),
             (S#6,(letrec {X#4=[.]} in S#7))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])
    -SR,lbeta2->                  (letrec {E#5} in A#8[(letrec {X#4=S#6} in S#7)])
    and constraints: E#5/= {}, (S#6,(\ X#4.[.])), (S#6,(letrec {X#4=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(\ X#4.[.])),(S#6,(letrec {X#4=[.]} in S#7))}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#10[(app [.] S#6)]),
           A#8   |->  A#10,
           T#9   |->  A#10[(app [.] S#6)],
           T#11  |->  (app [.] S#6),
           T#12  |->  [.],
           S#2   |->  (\ X#4.S#7)}

and instantiated rules:

                                  (letrec {E#5} in A#10[(app (\ X#4.S#7) S#6)])
    -gc1->                        (letrec {E#5} in A#10[(app (letrec {E#1} in (\ X#4.S#7)) S#6)])
    ................................................................................
                                  (letrec {E#5} in A#10[(app (\ X#4.S#7) S#6)])
    -SR,lbeta2->                  (letrec {E#5} in A#10[(letrec {X#4=S#6} in S#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in A#10[(app (\ X#4.S#7) T#12[(letrec {E#1} in S#2)])])
    ,
     (letrec {E#5} in A#10[(letrec {X#4=T#12[S#2]} in S#7)])
  )

where

   Delta1 = {T#11,A#8,T#9,T#3,A#10}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#12[S#2],(\ X#4.[.])),
             (T#12[S#2],(letrec {X#4=[.]} in S#7))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])
    -SR,lbeta2->                  (letrec {E#5} in A#8[(letrec {X#4=S#6} in S#7)])
    and constraints: E#5/= {}, (S#6,(\ X#4.[.])), (S#6,(letrec {X#4=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(\ X#4.[.])),(S#6,(letrec {X#4=[.]} in S#7))}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#10[(app (\ X#4.S#7) T#12)]),
           A#8   |->  A#10,
           T#9   |->  A#10[(app (\ X#4.S#7) T#12)],
           T#11  |->  (app (\ X#4.S#7) T#12),
           S#6   |->  T#12[S#2]}

and instantiated rules:

                                  (letrec {E#5} in A#10[(app (\ X#4.S#7) T#12[S#2])])
    -gc1->                        (letrec {E#5} in A#10[(app (\ X#4.S#7) T#12[(letrec {E#1} in S#2)])])
    ................................................................................
                                  (letrec {E#5} in A#10[(app (\ X#4.S#7) T#12[S#2])])
    -SR,lbeta2->                  (letrec {E#5} in A#10[(letrec {X#4=T#12[S#2]} in S#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in A#10[(letrec {E#1} in (app (\ X#4.S#7) S#6))])
    ,
     (letrec {E#5} in A#10[(letrec {X#4=S#6} in S#7)])
  )

where

   Delta1 = {A#8,T#9,T#3,A#10}
   Delta2 = {E#1,E#5}
   Delta3 = {((app (\ X#4.S#7) S#6),(letrec {E#1} in [.])),
             (S#6,(\ X#4.[.])),
             (S#6,(letrec {X#4=[.]} in S#7))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])
    -SR,lbeta2->                  (letrec {E#5} in A#8[(letrec {X#4=S#6} in S#7)])
    and constraints: E#5/= {}, (S#6,(\ X#4.[.])), (S#6,(letrec {X#4=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(\ X#4.[.])),(S#6,(letrec {X#4=[.]} in S#7))}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#10[[.]]),
           A#8   |->  A#10,
           T#9   |->  A#10[[.]],
           T#11  |->  [.],
           S#2   |->  (app (\ X#4.S#7) S#6)}

and instantiated rules:

                                  (letrec {E#5} in A#10[(app (\ X#4.S#7) S#6)])
    -gc1->                        (letrec {E#5} in A#10[(letrec {E#1} in (app (\ X#4.S#7) S#6))])
    ................................................................................
                                  (letrec {E#5} in A#10[(app (\ X#4.S#7) S#6)])
    -SR,lbeta2->                  (letrec {E#5} in A#10[(letrec {X#4=S#6} in S#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in A#10[(letrec {E#1} in A#11[(app (\ X#4.S#7) S#6)])])
    ,
     (letrec {E#5} in A#10[A#11[(letrec {X#4=S#6} in S#7)]])
  )

where

   Delta1 = {A#8,T#9,T#3,A#10}
   Delta2 = {E#1,E#5}
   Delta3 = {(A#11[(app (\ X#4.S#7) S#6)],(letrec {E#1} in [.])),
             (S#6,(\ X#4.[.])),
             (S#6,(letrec {X#4=[.]} in S#7))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])
    -SR,lbeta2->                  (letrec {E#5} in A#8[(letrec {X#4=S#6} in S#7)])
    and constraints: E#5/= {}, (S#6,(\ X#4.[.])), (S#6,(letrec {X#4=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(\ X#4.[.])),(S#6,(letrec {X#4=[.]} in S#7))}


and found solution:

    Sol = {T#3  |->  (letrec {E#5} in A#10),
           A#8  |->  A#10[A#11],
           T#9  |->  A#10,
           S#2  |->  A#11[(app (\ X#4.S#7) S#6)]}

and instantiated rules:

                                  (letrec {E#5} in A#10[A#11[(app (\ X#4.S#7) S#6)]])
    -gc1->                        (letrec {E#5} in A#10[(letrec {E#1} in A#11[(app (\ X#4.S#7) S#6)])])
    ................................................................................
                                  (letrec {E#5} in A#10[A#11[(app (\ X#4.S#7) S#6)]])
    -SR,lbeta2->                  (letrec {E#5} in A#10[A#11[(letrec {X#4=S#6} in S#7)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#10[(app A#11[(app (\ X#4.S#7) S#6)] T#12[(letrec {E#1} in S#2)])]
     )
    ,
     (letrec {E#5} in A#10[(app A#11[(letrec {X#4=S#6} in S#7)] T#12[S#2])])
  )

where

   Delta1 = {A#8,T#9,T#3}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(\ X#4.[.])),
             (S#6,(letrec {X#4=[.]} in S#7))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])
    -SR,lbeta2->                  (letrec {E#5} in A#8[(letrec {X#4=S#6} in S#7)])
    and constraints: E#5/= {}, (S#6,(\ X#4.[.])), (S#6,(letrec {X#4=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(\ X#4.[.])),(S#6,(letrec {X#4=[.]} in S#7))}


and found solution:

    Sol = {T#3  |->  (letrec {E#5} in A#10[(app A#11[(app (\ X#4.S#7) S#6)] T#12)]),
           T#9  |->  A#10[(app A#11[(app (\ X#4.S#7) S#6)] T#12)],
           A#8  |->  A#10[(app A#11 T#12[S#2])]}

and instantiated rules:

                                  (letrec {E#5} in A#10[(app A#11[(app (\ X#4.S#7) S#6)] T#12[S#2])])
    -gc1->                        (letrec {E#5} in A#10[(app A#11[(app (\ X#4.S#7) S#6)] T#12[(letrec {E#1} in S#2)])])
    ................................................................................
                                  (letrec {E#5} in A#10[(app A#11[(app (\ X#4.S#7) S#6)] T#12[S#2])])
    -SR,lbeta2->                  (letrec {E#5} in A#10[(app A#11[(letrec {X#4=S#6} in S#7)] T#12[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (app (letrec {E#1} in (\ X#4.S#7)) S#6))
    ,
     (letrec {E#5} in (letrec {X#4=S#6} in S#7))
  )

where

   Delta1 = {T#9,T#3}
   Delta2 = {E#1,E#5}
   Delta3 = {((\ X#4.S#7),(letrec {E#1} in [.])),
             (S#6,(\ X#4.[.])),
             (S#6,(letrec {X#4=[.]} in S#7))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])
    -SR,lbeta2->                  (letrec {E#5} in A#8[(letrec {X#4=S#6} in S#7)])
    and constraints: E#5/= {}, (S#6,(\ X#4.[.])), (S#6,(letrec {X#4=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(\ X#4.[.])),(S#6,(letrec {X#4=[.]} in S#7))}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in (app [.] S#6)),
           A#8   |->  [.],
           T#9   |->  (app [.] S#6),
           T#10  |->  [.],
           S#2   |->  (\ X#4.S#7)}

and instantiated rules:

                                  (letrec {E#5} in (app (\ X#4.S#7) S#6))
    -gc1->                        (letrec {E#5} in (app (letrec {E#1} in (\ X#4.S#7)) S#6))
    ................................................................................
                                  (letrec {E#5} in (app (\ X#4.S#7) S#6))
    -SR,lbeta2->                  (letrec {E#5} in (letrec {X#4=S#6} in S#7))
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (app (\ X#4.S#7) T#10[(letrec {E#1} in S#2)]))
    ,
     (letrec {E#5} in (letrec {X#4=T#10[S#2]} in S#7))
  )

where

   Delta1 = {T#9,T#3}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#10[S#2],(\ X#4.[.])),
             (T#10[S#2],(letrec {X#4=[.]} in S#7))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])
    -SR,lbeta2->                  (letrec {E#5} in A#8[(letrec {X#4=S#6} in S#7)])
    and constraints: E#5/= {}, (S#6,(\ X#4.[.])), (S#6,(letrec {X#4=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(\ X#4.[.])),(S#6,(letrec {X#4=[.]} in S#7))}


and found solution:

    Sol = {T#3  |->  (letrec {E#5} in (app (\ X#4.S#7) T#10)),
           A#8  |->  [.],
           T#9  |->  (app (\ X#4.S#7) T#10),
           S#6  |->  T#10[S#2]}

and instantiated rules:

                                  (letrec {E#5} in (app (\ X#4.S#7) T#10[S#2]))
    -gc1->                        (letrec {E#5} in (app (\ X#4.S#7) T#10[(letrec {E#1} in S#2)]))
    ................................................................................
                                  (letrec {E#5} in (app (\ X#4.S#7) T#10[S#2]))
    -SR,lbeta2->                  (letrec {E#5} in (letrec {X#4=T#10[S#2]} in S#7))
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (letrec {E#1} in A#8[(app (\ X#4.S#7) S#6)]))
    ,
     (letrec {E#5} in A#8[(letrec {X#4=S#6} in S#7)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#5}
   Delta3 = {(A#8[(app (\ X#4.S#7) S#6)],(letrec {E#1} in [.])),
             (S#6,(\ X#4.[.])),
             (S#6,(letrec {X#4=[.]} in S#7))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])
    -SR,lbeta2->                  (letrec {E#5} in A#8[(letrec {X#4=S#6} in S#7)])
    and constraints: E#5/= {}, (S#6,(\ X#4.[.])), (S#6,(letrec {X#4=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(\ X#4.[.])),(S#6,(letrec {X#4=[.]} in S#7))}


and found solution:

    Sol = {T#3  |->  (letrec {E#5} in [.]),
           T#9  |->  [.],
           S#2  |->  A#8[(app (\ X#4.S#7) S#6)]}

and instantiated rules:

                                  (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])
    -gc1->                        (letrec {E#5} in (letrec {E#1} in A#8[(app (\ X#4.S#7) S#6)]))
    ................................................................................
                                  (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])
    -SR,lbeta2->                  (letrec {E#5} in A#8[(letrec {X#4=S#6} in S#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#10=T#9[(letrec {E#1} in S#2)];E#12} in A#8[(app (\ X#4.S#7) S#6)])
    ,
     (letrec {X#10=T#9[S#2];E#12} in A#8[(letrec {X#4=S#6} in S#7)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(\ X#4.[.])),
             (S#6,(letrec {X#4=[.]} in S#7))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])
    -SR,lbeta2->                  (letrec {E#5} in A#8[(letrec {X#4=S#6} in S#7)])
    and constraints: E#5/= {}, (S#6,(\ X#4.[.])), (S#6,(letrec {X#4=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(\ X#4.[.])),(S#6,(letrec {X#4=[.]} in S#7))}


and found solution:

    Sol = {T#3   |->  (letrec {X#10=T#9;E#12} in A#8[(app (\ X#4.S#7) S#6)]),
           E#5   |->  {X#10=T#9[S#2];E#12},
           E#11  |->  {E#12}}

and instantiated rules:

                                  (letrec {X#10=T#9[S#2];E#12} in A#8[(app (\ X#4.S#7) S#6)])
    -gc1->                        (letrec {X#10=T#9[(letrec {E#1} in S#2)];E#12} in A#8[(app (\ X#4.S#7) S#6)])
    ................................................................................
                                  (letrec {X#10=T#9[S#2];E#12} in A#8[(app (\ X#4.S#7) S#6)])
    -SR,lbeta2->                  (letrec {X#10=T#9[S#2];E#12} in A#8[(letrec {X#4=S#6} in S#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#1} in (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)]))
    ,
     (letrec {E#5} in A#8[(letrec {X#4=S#6} in S#7)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#5}
   Delta3 = {((letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)]),(letrec {E#1} in [.])),
             (S#6,(\ X#4.[.])),
             (S#6,(letrec {X#4=[.]} in S#7))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])
    -SR,lbeta2->                  (letrec {E#5} in A#8[(letrec {X#4=S#6} in S#7)])
    and constraints: E#5/= {}, (S#6,(\ X#4.[.])), (S#6,(letrec {X#4=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(\ X#4.[.])),(S#6,(letrec {X#4=[.]} in S#7))}


and found solution:

    Sol = {T#3  |->  [.],
           S#2  |->  (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])}

and instantiated rules:

                                  (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])
    -gc1->                        (letrec {E#1} in (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)]))
    ................................................................................
                                  (letrec {E#5} in A#8[(app (\ X#4.S#7) S#6)])
    -SR,lbeta2->                  (letrec {E#5} in A#8[(letrec {X#4=S#6} in S#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#10[X#4,(app (\ X#5.S#8) S#7)]
     in
        A#12[(letrec {E#1} in (var X#4))]
     )
    ,
     (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#12[(var X#4)])
  )

where

   Delta1 = {A#9,T#11,T#3,A#12}
   Delta2 = {E#1}
   Delta3 = {((var X#4),(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#12[[.]]),
             ((var X#4),A#12[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#12[[.]]),
           A#9   |->  A#12,
           T#11  |->  A#12[[.]],
           T#13  |->  [.],
           S#2   |->  (var X#4)}

and instantiated rules:

                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#12[(var X#4)])
    -gc1->                        (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#12[(letrec {E#1} in (var X#4))])
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#12[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#12[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#10[X#4,(app (\ X#5.S#8) S#7)]
     in
        A#12[(letrec {E#1} in A#13[(var X#4)])]
     )
    ,
     (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#12[A#13[(var X#4)]])
  )

where

   Delta1 = {A#9,T#11,T#3,A#12}
   Delta2 = {E#1}
   Delta3 = {(A#13[(var X#4)],(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#12[A#13[[.]]]),
             ((var X#4),A#12[A#13[[.]]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#12),
           A#9   |->  A#12[A#13],
           T#11  |->  A#12,
           S#2   |->  A#13[(var X#4)]}

and instantiated rules:

                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#12[A#13[(var X#4)]])
    -gc1->                        (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#12[(letrec {E#1} in A#13[(var X#4)])])
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#12[A#13[(var X#4)]])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#12[A#13[(var X#4)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#10[X#4,(app (\ X#5.S#8) S#7)]
     in
        A#12[(app A#13[(var X#4)] T#14[(letrec {E#1} in S#2)])]
     )
    ,
     (letrec
        E#6
       ;EE#10[X#4,(letrec {X#5=S#7} in S#8)]
     in
        A#12[(app A#13[(var X#4)] T#14[S#2])]
     )
  )

where

   Delta1 = {A#9,T#11,T#3}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#12[(app A#13[[.]] T#14[S#2])]),
             ((var X#4),A#12[(app A#13[[.]] T#14[S#2])])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#12[(app A#13[(var X#4)] T#14)]),
           T#11  |->  A#12[(app A#13[(var X#4)] T#14)],
           A#9   |->  A#12[(app A#13 T#14[S#2])]}

and instantiated rules:

                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#12[(app A#13[(var X#4)] T#14[S#2])])
    -gc1->                        (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#12[(app A#13[(var X#4)] T#14[(letrec {E#1} in S#2)])])
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#12[(app A#13[(var X#4)] T#14[S#2])])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#12[(app A#13[(var X#4)] T#14[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#10[X#4,(app (\ X#5.S#8) S#7)]
     in
        (letrec {E#1} in A#9[(var X#4)])
     )
    ,
     (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {(A#9[(var X#4)],(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in [.]),
           T#11  |->  [.],
           S#2   |->  A#9[(var X#4)]}

and instantiated rules:

                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in (letrec {E#1} in A#9[(var X#4)]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#12= T#11[(letrec {E#1} in S#2)]
       ;E#14
       ;EE#10[X#4,(app (\ X#5.S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#12= T#11[S#2]
       ;E#14
       ;EE#10[X#4,(letrec {X#5=S#7} in S#8)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#12=T#11;E#14;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)]),
           E#6   |->  {X#12=T#11[S#2];E#14},
           E#13  |->  {E#14;EE#10[X#4,(app (\ X#5.S#8) S#7)]}}

and instantiated rules:

                                  (letrec {X#12=T#11[S#2];E#14;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#12=T#11[(letrec {E#1} in S#2)];E#14;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#12=T#11[S#2];E#14;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#12=T#11[S#2];E#14;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#15[(app (letrec {E#1} in (\ X#5.S#8)) S#7)]
       ;E#6
     in
        A#9[(var X#4)]
     )
    ,
     (letrec {X#4=A#15[(letrec {X#5=S#7} in S#8)];E#6} in A#9[(var X#4)])
  )

where

   Delta1 = {T#16,A#14,T#11,T#3,A#15}
   Delta2 = {E#1}
   Delta3 = {((\ X#5.S#8),(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#15[(app [.] S#7)];E#6} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#6},
           A#14         |->  A#15,
           T#11         |->  A#15[(app [.] S#7)],
           T#16         |->  (app [.] S#7),
           T#17         |->  [.],
           S#2          |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {X#4=A#15[(app (\ X#5.S#8) S#7)];E#6} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#15[(app (letrec {E#1} in (\ X#5.S#8)) S#7)];E#6} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#15[(app (\ X#5.S#8) S#7)];E#6} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#4=A#15[(letrec {X#5=S#7} in S#8)];E#6} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#15[(app (\ X#5.S#8) T#17[(letrec {E#1} in S#2)])]
       ;E#6
     in
        A#9[(var X#4)]
     )
    ,
     (letrec {X#4=A#15[(letrec {X#5=T#17[S#2]} in S#8)];E#6} in A#9[(var X#4)])
  )

where

   Delta1 = {T#16,A#14,T#11,T#3,A#15}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#17[S#2],(\ X#5.[.])),
             (T#17[S#2],(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#15[(app (\ X#5.S#8) T#17)];E#6} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#6},
           A#14         |->  A#15,
           T#11         |->  A#15[(app (\ X#5.S#8) T#17)],
           T#16         |->  (app (\ X#5.S#8) T#17),
           S#7          |->  T#17[S#2]}

and instantiated rules:

                                  (letrec {X#4=A#15[(app (\ X#5.S#8) T#17[S#2])];E#6} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#15[(app (\ X#5.S#8) T#17[(letrec {E#1} in S#2)])];E#6} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#15[(app (\ X#5.S#8) T#17[S#2])];E#6} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#4=A#15[(letrec {X#5=T#17[S#2]} in S#8)];E#6} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#15[(letrec {E#1} in (app (\ X#5.S#8) S#7))]
       ;E#6
     in
        A#9[(var X#4)]
     )
    ,
     (letrec {X#4=A#15[(letrec {X#5=S#7} in S#8)];E#6} in A#9[(var X#4)])
  )

where

   Delta1 = {A#14,T#11,T#3,A#15}
   Delta2 = {E#1}
   Delta3 = {((app (\ X#5.S#8) S#7),(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#15[[.]];E#6} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#6},
           A#14         |->  A#15,
           T#11         |->  A#15[[.]],
           T#16         |->  [.],
           S#2          |->  (app (\ X#5.S#8) S#7)}

and instantiated rules:

                                  (letrec {X#4=A#15[(app (\ X#5.S#8) S#7)];E#6} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#15[(letrec {E#1} in (app (\ X#5.S#8) S#7))];E#6} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#15[(app (\ X#5.S#8) S#7)];E#6} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#4=A#15[(letrec {X#5=S#7} in S#8)];E#6} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#15[(letrec {E#1} in A#16[(app (\ X#5.S#8) S#7)])]
       ;E#6
     in
        A#9[(var X#4)]
     )
    ,
     (letrec {X#4=A#15[A#16[(letrec {X#5=S#7} in S#8)]];E#6} in A#9[(var X#4)])
  )

where

   Delta1 = {A#14,T#11,T#3,A#15}
   Delta2 = {E#1}
   Delta3 = {(A#16[(app (\ X#5.S#8) S#7)],(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#15;E#6} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#15[A#16[[.2]]]},
           X#12         |->  X#4,
           E#13         |->  {E#6},
           A#14         |->  A#15[A#16],
           T#11         |->  A#15,
           S#2          |->  A#16[(app (\ X#5.S#8) S#7)]}

and instantiated rules:

                                  (letrec {X#4=A#15[A#16[(app (\ X#5.S#8) S#7)]];E#6} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#15[(letrec {E#1} in A#16[(app (\ X#5.S#8) S#7)])];E#6} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#15[A#16[(app (\ X#5.S#8) S#7)]];E#6} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#4=A#15[A#16[(letrec {X#5=S#7} in S#8)]];E#6} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#15[(app A#16[(app (\ X#5.S#8) S#7)] T#17[(letrec {E#1} in S#2)])]
       ;E#6
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#4= A#15[(app A#16[(letrec {X#5=S#7} in S#8)] T#17[S#2])]
       ;E#6
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#15[(app A#16[(app (\ X#5.S#8) S#7)] T#17)];E#6} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#15[(app A#16[[.2]] T#17[S#2])]},
           X#12         |->  X#4,
           E#13         |->  {E#6},
           T#11         |->  A#15[(app A#16[(app (\ X#5.S#8) S#7)] T#17)],
           A#14         |->  A#15[(app A#16 T#17[S#2])]}

and instantiated rules:

                                  (letrec {X#4=A#15[(app A#16[(app (\ X#5.S#8) S#7)] T#17[S#2])];E#6} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#15[(app A#16[(app (\ X#5.S#8) S#7)] T#17[(letrec {E#1} in S#2)])];E#6} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#15[(app A#16[(app (\ X#5.S#8) S#7)] T#17[S#2])];E#6} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#4=A#15[(app A#16[(letrec {X#5=S#7} in S#8)] T#17[S#2])];E#6} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#4=(app (letrec {E#1} in (\ X#5.S#8)) S#7);E#6} in A#9[(var X#4)])
    ,
     (letrec {X#4=(letrec {X#5=S#7} in S#8);E#6} in A#9[(var X#4)])
  )

where

   Delta1 = {T#11,T#3}
   Delta2 = {E#1}
   Delta3 = {((\ X#5.S#8),(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(app [.] S#7);E#6} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=[.2]},
           X#12         |->  X#4,
           E#13         |->  {E#6},
           A#14         |->  [.],
           T#11         |->  (app [.] S#7),
           T#15         |->  [.],
           S#2          |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {X#4=(app (\ X#5.S#8) S#7);E#6} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=(app (letrec {E#1} in (\ X#5.S#8)) S#7);E#6} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=(app (\ X#5.S#8) S#7);E#6} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#4=(letrec {X#5=S#7} in S#8);E#6} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (app (\ X#5.S#8) T#15[(letrec {E#1} in S#2)])
       ;E#6
     in
        A#9[(var X#4)]
     )
    ,
     (letrec {X#4=(letrec {X#5=T#15[S#2]} in S#8);E#6} in A#9[(var X#4)])
  )

where

   Delta1 = {T#11,T#3}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#15[S#2],(\ X#5.[.])),
             (T#15[S#2],(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(app (\ X#5.S#8) T#15);E#6} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=[.2]},
           X#12         |->  X#4,
           E#13         |->  {E#6},
           A#14         |->  [.],
           T#11         |->  (app (\ X#5.S#8) T#15),
           S#7          |->  T#15[S#2]}

and instantiated rules:

                                  (letrec {X#4=(app (\ X#5.S#8) T#15[S#2]);E#6} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=(app (\ X#5.S#8) T#15[(letrec {E#1} in S#2)]);E#6} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=(app (\ X#5.S#8) T#15[S#2]);E#6} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#4=(letrec {X#5=T#15[S#2]} in S#8);E#6} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#1} in A#14[(app (\ X#5.S#8) S#7)])
       ;E#6
     in
        A#9[(var X#4)]
     )
    ,
     (letrec {X#4=A#14[(letrec {X#5=S#7} in S#8)];E#6} in A#9[(var X#4)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {(A#14[(app (\ X#5.S#8) S#7)],(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=[.];E#6} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#14[[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#6},
           T#11         |->  [.],
           S#2          |->  A#14[(app (\ X#5.S#8) S#7)]}

and instantiated rules:

                                  (letrec {X#4=A#14[(app (\ X#5.S#8) S#7)];E#6} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=(letrec {E#1} in A#14[(app (\ X#5.S#8) S#7)]);E#6} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#14[(app (\ X#5.S#8) S#7)];E#6} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#4=A#14[(letrec {X#5=S#7} in S#8)];E#6} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#17[(letrec {E#1} in (var X#15))]
       ;E#6
       ;EE#16[X#15,(app (\ X#5.S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#4= A#17[(var X#15)]
       ;E#6
       ;EE#16[X#15,(letrec {X#5=S#7} in S#8)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#17}
   Delta2 = {E#1}
   Delta3 = {((var X#15),(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#17[[.]];E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#17[(var X#15)];EE#16[X#15,[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]},
           A#14         |->  A#17,
           T#11         |->  A#17[[.]],
           T#18         |->  [.],
           S#2          |->  (var X#15)}

and instantiated rules:

                                  (letrec {X#4=A#17[(var X#15)];E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#17[(letrec {E#1} in (var X#15))];E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#17[(var X#15)];E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#4=A#17[(var X#15)];E#6;EE#16[X#15,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#17[(letrec {E#1} in A#18[(var X#15)])]
       ;E#6
       ;EE#16[X#15,(app (\ X#5.S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#4= A#17[A#18[(var X#15)]]
       ;E#6
       ;EE#16[X#15,(letrec {X#5=S#7} in S#8)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#17}
   Delta2 = {E#1}
   Delta3 = {(A#18[(var X#15)],(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#17;E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#17[A#18[(var X#15)]];EE#16[X#15,[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]},
           A#14         |->  A#17[A#18],
           T#11         |->  A#17,
           S#2          |->  A#18[(var X#15)]}

and instantiated rules:

                                  (letrec {X#4=A#17[A#18[(var X#15)]];E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#17[(letrec {E#1} in A#18[(var X#15)])];E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#17[A#18[(var X#15)]];E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#4=A#17[A#18[(var X#15)]];E#6;EE#16[X#15,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#17[(app A#18[(var X#15)] T#19[(letrec {E#1} in S#2)])]
       ;E#6
       ;EE#16[X#15,(app (\ X#5.S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#4= A#17[(app A#18[(var X#15)] T#19[S#2])]
       ;E#6
       ;EE#16[X#15,(letrec {X#5=S#7} in S#8)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#17[(app A#18[(var X#15)] T#19)];E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#17[(app A#18[(var X#15)] T#19[S#2])];EE#16[X#15,[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]},
           T#11         |->  A#17[(app A#18[(var X#15)] T#19)],
           A#14         |->  A#17[(app A#18 T#19[S#2])]}

and instantiated rules:

                                  (letrec {X#4=A#17[(app A#18[(var X#15)] T#19[S#2])];E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#17[(app A#18[(var X#15)] T#19[(letrec {E#1} in S#2)])];E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#17[(app A#18[(var X#15)] T#19[S#2])];E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#4=A#17[(app A#18[(var X#15)] T#19[S#2])];E#6;EE#16[X#15,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#1} in A#14[(var X#15)])
       ;E#6
       ;EE#16[X#15,(app (\ X#5.S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#4= A#14[(var X#15)]
       ;E#6
       ;EE#16[X#15,(letrec {X#5=S#7} in S#8)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {(A#14[(var X#15)],(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=[.];E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#14[(var X#15)];EE#16[X#15,[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]},
           T#11         |->  [.],
           S#2          |->  A#14[(var X#15)]}

and instantiated rules:

                                  (letrec {X#4=A#14[(var X#15)];E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=(letrec {E#1} in A#14[(var X#15)]);E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#14[(var X#15)];E#6;EE#16[X#15,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#4=A#14[(var X#15)];E#6;EE#16[X#15,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#19[(letrec {E#1} in (var X#16))]
       ;E#6
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(app (\ X#5.S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#19[(var X#16)]
       ;E#6
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(letrec {X#5=S#7} in S#8)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#19}
   Delta2 = {E#1}
   Delta3 = {((var X#16),(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#19[[.]];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#19[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#12         |->  X#15,
           E#13         |->  {E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]},
           A#14         |->  A#19,
           T#11         |->  A#19[[.]],
           T#20         |->  [.],
           S#2          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#15=A#19[(var X#16)];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#19[(letrec {E#1} in (var X#16))];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#19[(var X#16)];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#15=A#19[(var X#16)];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#19[(letrec {E#1} in A#20[(var X#16)])]
       ;E#6
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(app (\ X#5.S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#19[A#20[(var X#16)]]
       ;E#6
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(letrec {X#5=S#7} in S#8)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#19}
   Delta2 = {E#1}
   Delta3 = {(A#20[(var X#16)],(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#19;E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#19[A#20[(var X#16)]];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#12         |->  X#15,
           E#13         |->  {E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]},
           A#14         |->  A#19[A#20],
           T#11         |->  A#19,
           S#2          |->  A#20[(var X#16)]}

and instantiated rules:

                                  (letrec {X#15=A#19[A#20[(var X#16)]];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#19[(letrec {E#1} in A#20[(var X#16)])];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#19[A#20[(var X#16)]];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#15=A#19[A#20[(var X#16)]];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#19[(app A#20[(var X#16)] T#21[(letrec {E#1} in S#2)])]
       ;E#6
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(app (\ X#5.S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#19[(app A#20[(var X#16)] T#21[S#2])]
       ;E#6
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(letrec {X#5=S#7} in S#8)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#19[(app A#20[(var X#16)] T#21)];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#19[(app A#20[(var X#16)] T#21[S#2])];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#12         |->  X#15,
           E#13         |->  {E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]},
           T#11         |->  A#19[(app A#20[(var X#16)] T#21)],
           A#14         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#15=A#19[(app A#20[(var X#16)] T#21[S#2])];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#19[(app A#20[(var X#16)] T#21[(letrec {E#1} in S#2)])];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#19[(app A#20[(var X#16)] T#21[S#2])];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#15=A#19[(app A#20[(var X#16)] T#21[S#2])];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#1} in A#14[(var X#16)])
       ;E#6
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(app (\ X#5.S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;E#6
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(letrec {X#5=S#7} in S#8)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {(A#14[(var X#16)],(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=[.];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#14[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#12         |->  X#15,
           E#13         |->  {E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]},
           T#11         |->  [.],
           S#2          |->  A#14[(var X#16)]}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=(letrec {E#1} in A#14[(var X#16)]);E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#15=A#14[(var X#16)];E#6;EE#17[X#4,(var X#15)];EE#18[X#16,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#17[(app (letrec {E#1} in (\ X#5.S#8)) S#7)]
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#17[(letrec {X#5=S#7} in S#8)]
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#18,A#14,T#11,T#3,A#17}
   Delta2 = {E#1}
   Delta3 = {((\ X#5.S#8),(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#17[(app [.] S#7)];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#17[[.2]];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#6;EE#16[X#4,(var X#15)]},
           A#14         |->  A#17,
           T#11         |->  A#17[(app [.] S#7)],
           T#18         |->  (app [.] S#7),
           T#19         |->  [.],
           S#2          |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {X#15=A#17[(app (\ X#5.S#8) S#7)];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#17[(app (letrec {E#1} in (\ X#5.S#8)) S#7)];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#17[(app (\ X#5.S#8) S#7)];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#15=A#17[(letrec {X#5=S#7} in S#8)];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#17[(app (\ X#5.S#8) T#19[(letrec {E#1} in S#2)])]
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#17[(letrec {X#5=T#19[S#2]} in S#8)]
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#18,A#14,T#11,T#3,A#17}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#19[S#2],(\ X#5.[.])),
             (T#19[S#2],(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#17[(app (\ X#5.S#8) T#19)];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#17[[.2]];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#6;EE#16[X#4,(var X#15)]},
           A#14         |->  A#17,
           T#11         |->  A#17[(app (\ X#5.S#8) T#19)],
           T#18         |->  (app (\ X#5.S#8) T#19),
           S#7          |->  T#19[S#2]}

and instantiated rules:

                                  (letrec {X#15=A#17[(app (\ X#5.S#8) T#19[S#2])];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#17[(app (\ X#5.S#8) T#19[(letrec {E#1} in S#2)])];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#17[(app (\ X#5.S#8) T#19[S#2])];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#15=A#17[(letrec {X#5=T#19[S#2]} in S#8)];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#17[(letrec {E#1} in (app (\ X#5.S#8) S#7))]
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#17[(letrec {X#5=S#7} in S#8)]
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#17}
   Delta2 = {E#1}
   Delta3 = {((app (\ X#5.S#8) S#7),(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#17[[.]];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#17[[.2]];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#6;EE#16[X#4,(var X#15)]},
           A#14         |->  A#17,
           T#11         |->  A#17[[.]],
           T#18         |->  [.],
           S#2          |->  (app (\ X#5.S#8) S#7)}

and instantiated rules:

                                  (letrec {X#15=A#17[(app (\ X#5.S#8) S#7)];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#17[(letrec {E#1} in (app (\ X#5.S#8) S#7))];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#17[(app (\ X#5.S#8) S#7)];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#15=A#17[(letrec {X#5=S#7} in S#8)];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#17[(letrec {E#1} in A#18[(app (\ X#5.S#8) S#7)])]
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#17[A#18[(letrec {X#5=S#7} in S#8)]]
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#17}
   Delta2 = {E#1}
   Delta3 = {(A#18[(app (\ X#5.S#8) S#7)],(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#17;E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#17[A#18[[.2]]];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#6;EE#16[X#4,(var X#15)]},
           A#14         |->  A#17[A#18],
           T#11         |->  A#17,
           S#2          |->  A#18[(app (\ X#5.S#8) S#7)]}

and instantiated rules:

                                  (letrec {X#15=A#17[A#18[(app (\ X#5.S#8) S#7)]];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#17[(letrec {E#1} in A#18[(app (\ X#5.S#8) S#7)])];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#17[A#18[(app (\ X#5.S#8) S#7)]];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#15=A#17[A#18[(letrec {X#5=S#7} in S#8)]];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#17[(app A#18[(app (\ X#5.S#8) S#7)] T#19[(letrec {E#1} in S#2)])]
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#17[(app A#18[(letrec {X#5=S#7} in S#8)] T#19[S#2])]
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#17[(app A#18[(app (\ X#5.S#8) S#7)] T#19)];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#17[(app A#18[[.2]] T#19[S#2])];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#6;EE#16[X#4,(var X#15)]},
           T#11         |->  A#17[(app A#18[(app (\ X#5.S#8) S#7)] T#19)],
           A#14         |->  A#17[(app A#18 T#19[S#2])]}

and instantiated rules:

                                  (letrec {X#15=A#17[(app A#18[(app (\ X#5.S#8) S#7)] T#19[S#2])];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#17[(app A#18[(app (\ X#5.S#8) S#7)] T#19[(letrec {E#1} in S#2)])];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#17[(app A#18[(app (\ X#5.S#8) S#7)] T#19[S#2])];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#15=A#17[(app A#18[(letrec {X#5=S#7} in S#8)] T#19[S#2])];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (app (letrec {E#1} in (\ X#5.S#8)) S#7)
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= (letrec {X#5=S#7} in S#8)
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#11,T#3}
   Delta2 = {E#1}
   Delta3 = {((\ X#5.S#8),(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=(app [.] S#7);E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=[.2];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#6;EE#16[X#4,(var X#15)]},
           A#14         |->  [.],
           T#11         |->  (app [.] S#7),
           T#17         |->  [.],
           S#2          |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {X#15=(app (\ X#5.S#8) S#7);E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=(app (letrec {E#1} in (\ X#5.S#8)) S#7);E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=(app (\ X#5.S#8) S#7);E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#15=(letrec {X#5=S#7} in S#8);E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (app (\ X#5.S#8) T#17[(letrec {E#1} in S#2)])
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= (letrec {X#5=T#17[S#2]} in S#8)
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#11,T#3}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#17[S#2],(\ X#5.[.])),
             (T#17[S#2],(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=(app (\ X#5.S#8) T#17);E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=[.2];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#6;EE#16[X#4,(var X#15)]},
           A#14         |->  [.],
           T#11         |->  (app (\ X#5.S#8) T#17),
           S#7          |->  T#17[S#2]}

and instantiated rules:

                                  (letrec {X#15=(app (\ X#5.S#8) T#17[S#2]);E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=(app (\ X#5.S#8) T#17[(letrec {E#1} in S#2)]);E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=(app (\ X#5.S#8) T#17[S#2]);E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#15=(letrec {X#5=T#17[S#2]} in S#8);E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#1} in A#14[(app (\ X#5.S#8) S#7)])
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#14[(letrec {X#5=S#7} in S#8)]
       ;E#6
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {(A#14[(app (\ X#5.S#8) S#7)],(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=[.];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#14[[.2]];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#6;EE#16[X#4,(var X#15)]},
           T#11         |->  [.],
           S#2          |->  A#14[(app (\ X#5.S#8) S#7)]}

and instantiated rules:

                                  (letrec {X#15=A#14[(app (\ X#5.S#8) S#7)];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=(letrec {E#1} in A#14[(app (\ X#5.S#8) S#7)]);E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#14[(app (\ X#5.S#8) S#7)];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {X#15=A#14[(letrec {X#5=S#7} in S#8)];E#6;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#1
     in
        (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
     )
    ,
     (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
  )

where

   Delta1 = {}
   Delta2 = {E#1}
   Delta3 = {((letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)]),(letrec {E#1} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lbeta3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    and constraints: (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           S#2  |->  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])}

and instantiated rules:

                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {E#1} in (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)]))
    ................................................................................
                                  (letrec {E#6;EE#10[X#4,(app (\ X#5.S#8) S#7)]} in A#9[(var X#4)])
    -SR,lbeta3->                  (letrec {E#6;EE#10[X#4,(letrec {X#5=S#7} in S#8)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#4=(\ X#5.S#7);E#6} in A#10[(letrec {E#1} in (var X#4))])
    ,
     (letrec {X#4=(\ X#5.S#7);E#6} in A#10[(\ X#5.S#7)])
  )

where

   Delta1 = {A#8,T#9,T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {((var X#4),(letrec {E#1} in [.])),
             ((var X#4),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])
    -SR,cp-in1->                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(\ X#5.S#7)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(\ X#5.S#7);E#6} in A#10[[.]]),
           A#8   |->  A#10,
           T#9   |->  A#10[[.]],
           T#11  |->  [.],
           S#2   |->  (var X#4)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#10[(var X#4)])
    -gc1->                        (letrec {X#4=(\ X#5.S#7);E#6} in A#10[(letrec {E#1} in (var X#4))])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#10[(var X#4)])
    -SR,cp-in1->                  (letrec {X#4=(\ X#5.S#7);E#6} in A#10[(\ X#5.S#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#4=(\ X#5.S#7);E#6} in A#10[(letrec {E#1} in A#11[(var X#4)])])
    ,
     (letrec {X#4=(\ X#5.S#7);E#6} in A#10[A#11[(\ X#5.S#7)]])
  )

where

   Delta1 = {A#8,T#9,T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {(A#11[(var X#4)],(letrec {E#1} in [.])),
             ((var X#4),A#10[A#11[[.]]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])
    -SR,cp-in1->                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(\ X#5.S#7)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3  |->  (letrec {X#4=(\ X#5.S#7);E#6} in A#10),
           A#8  |->  A#10[A#11],
           T#9  |->  A#10,
           S#2  |->  A#11[(var X#4)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#10[A#11[(var X#4)]])
    -gc1->                        (letrec {X#4=(\ X#5.S#7);E#6} in A#10[(letrec {E#1} in A#11[(var X#4)])])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#10[A#11[(var X#4)]])
    -SR,cp-in1->                  (letrec {X#4=(\ X#5.S#7);E#6} in A#10[A#11[(\ X#5.S#7)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#7)
       ;E#6
     in
        A#10[(app A#11[(var X#4)] T#12[(letrec {E#1} in S#2)])]
     )
    ,
     (letrec {X#4=(\ X#5.S#7);E#6} in A#10[(app A#11[(\ X#5.S#7)] T#12[S#2])])
  )

where

   Delta1 = {A#8,T#9,T#3}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),A#10[(app A#11[[.]] T#12[S#2])])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])
    -SR,cp-in1->                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(\ X#5.S#7)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3  |->  (letrec {X#4=(\ X#5.S#7);E#6} in A#10[(app A#11[(var X#4)] T#12)]),
           T#9  |->  A#10[(app A#11[(var X#4)] T#12)],
           A#8  |->  A#10[(app A#11 T#12[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#10[(app A#11[(var X#4)] T#12[S#2])])
    -gc1->                        (letrec {X#4=(\ X#5.S#7);E#6} in A#10[(app A#11[(var X#4)] T#12[(letrec {E#1} in S#2)])])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#10[(app A#11[(var X#4)] T#12[S#2])])
    -SR,cp-in1->                  (letrec {X#4=(\ X#5.S#7);E#6} in A#10[(app A#11[(\ X#5.S#7)] T#12[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#4=(\ X#5.S#7);E#6} in (letrec {E#1} in A#8[(var X#4)]))
    ,
     (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(\ X#5.S#7)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {(A#8[(var X#4)],(letrec {E#1} in [.])),
             ((var X#4),A#8[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])
    -SR,cp-in1->                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(\ X#5.S#7)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3  |->  (letrec {X#4=(\ X#5.S#7);E#6} in [.]),
           T#9  |->  [.],
           S#2  |->  A#8[(var X#4)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])
    -gc1->                        (letrec {X#4=(\ X#5.S#7);E#6} in (letrec {E#1} in A#8[(var X#4)]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])
    -SR,cp-in1->                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(\ X#5.S#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#4=(letrec {E#1} in (\ X#5.S#7));E#6} in A#8[(var X#4)])
    ,
     (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(\ X#5.S#7)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {((\ X#5.S#7),(letrec {E#1} in [.])),
             ((var X#4),A#8[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])
    -SR,cp-in1->                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(\ X#5.S#7)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=[.];E#6} in A#8[(var X#4)]),
           X#10  |->  X#4,
           E#11  |->  {E#6},
           T#9   |->  [.],
           S#2   |->  (\ X#5.S#7)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])
    -gc1->                        (letrec {X#4=(letrec {E#1} in (\ X#5.S#7));E#6} in A#8[(var X#4)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])
    -SR,cp-in1->                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(\ X#5.S#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= T#9[(letrec {E#1} in S#2)]
       ;X#4= (\ X#5.S#7)
       ;E#12
     in
        A#8[(var X#4)]
     )
    ,
     (letrec {X#10=T#9[S#2];X#4=(\ X#5.S#7);E#12} in A#8[(\ X#5.S#7)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),A#8[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])
    -SR,cp-in1->                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(\ X#5.S#7)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#10=T#9;X#4=(\ X#5.S#7);E#12} in A#8[(var X#4)]),
           E#6   |->  {X#10=T#9[S#2];E#12},
           E#11  |->  {X#4=(\ X#5.S#7);E#12}}

and instantiated rules:

                                  (letrec {X#10=T#9[S#2];X#4=(\ X#5.S#7);E#12} in A#8[(var X#4)])
    -gc1->                        (letrec {X#10=T#9[(letrec {E#1} in S#2)];X#4=(\ X#5.S#7);E#12} in A#8[(var X#4)])
    ................................................................................
                                  (letrec {X#10=T#9[S#2];X#4=(\ X#5.S#7);E#12} in A#8[(var X#4)])
    -SR,cp-in1->                  (letrec {X#10=T#9[S#2];X#4=(\ X#5.S#7);E#12} in A#8[(\ X#5.S#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#1} in (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)]))
    ,
     (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(\ X#5.S#7)])
  )

where

   Delta1 = {}
   Delta2 = {E#1}
   Delta3 = {((letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)]),(letrec {E#1} in [.])),
             ((var X#4),A#8[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])
    -SR,cp-in1->                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(\ X#5.S#7)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           S#2  |->  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])
    -gc1->                        (letrec {E#1} in (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(var X#4)])
    -SR,cp-in1->                  (letrec {X#4=(\ X#5.S#7);E#6} in A#8[(\ X#5.S#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;E#7
       ;VV#10|X#6,(var X#4)|
     in
        A#12[(letrec {E#1} in (var X#6))]
     )
    ,
     (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[(\ X#5.S#8)])
  )

where

   Delta1 = {A#9,T#11,T#3,A#12}
   Delta2 = {E#1}
   Delta3 = {((var X#6),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#12[[.]]),
             ((var X#4),[.])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#9[[.]]),((var X#4),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[[.]]),
           A#9   |->  A#12,
           T#11  |->  A#12[[.]],
           T#13  |->  [.],
           S#2   |->  (var X#6)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[(letrec {E#1} in (var X#6))])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[(\ X#5.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;E#7
       ;VV#10|X#6,(var X#4)|
     in
        A#12[(letrec {E#1} in A#13[(var X#6)])]
     )
    ,
     (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[A#13[(\ X#5.S#8)]])
  )

where

   Delta1 = {A#9,T#11,T#3,A#12}
   Delta2 = {E#1}
   Delta3 = {(A#13[(var X#6)],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#12[A#13[[.]]]),
             ((var X#4),[.])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#9[[.]]),((var X#4),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12),
           A#9   |->  A#12[A#13],
           T#11  |->  A#12,
           S#2   |->  A#13[(var X#6)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[A#13[(var X#6)]])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[(letrec {E#1} in A#13[(var X#6)])])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[A#13[(var X#6)]])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[A#13[(\ X#5.S#8)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;E#7
       ;VV#10|X#6,(var X#4)|
     in
        A#12[(app A#13[(var X#6)] T#14[(letrec {E#1} in S#2)])]
     )
    ,
     (letrec
        X#4= (\ X#5.S#8)
       ;E#7
       ;VV#10|X#6,(var X#4)|
     in
        A#12[(app A#13[(\ X#5.S#8)] T#14[S#2])]
     )
  )

where

   Delta1 = {A#9,T#11,T#3}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#12[(app A#13[[.]] T#14[S#2])]),
             ((var X#4),[.])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#9[[.]]),((var X#4),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[(app A#13[(var X#6)] T#14)]),
           T#11  |->  A#12[(app A#13[(var X#6)] T#14)],
           A#9   |->  A#12[(app A#13 T#14[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[(app A#13[(var X#6)] T#14[S#2])])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[(app A#13[(var X#6)] T#14[(letrec {E#1} in S#2)])])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[(app A#13[(var X#6)] T#14[S#2])])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#12[(app A#13[(\ X#5.S#8)] T#14[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;E#7
       ;VV#10|X#6,(var X#4)|
     in
        (letrec {E#1} in A#9[(var X#6)])
     )
    ,
     (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {(A#9[(var X#6)],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#9[[.]]),
             ((var X#4),[.])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#9[[.]]),((var X#4),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in [.]),
           T#11  |->  [.],
           S#2   |->  A#9[(var X#6)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in (letrec {E#1} in A#9[(var X#6)]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#1} in (\ X#5.S#8))
       ;E#7
       ;VV#10|X#6,(var X#4)|
     in
        A#9[(var X#6)]
     )
    ,
     (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {((\ X#5.S#8),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#9[[.]]),
             ((var X#4),[.])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#9[[.]]),((var X#4),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=[.];E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)]),
           X#12  |->  X#4,
           E#13  |->  {E#7;VV#10|X#6,(var X#4)|},
           T#11  |->  [.],
           S#2   |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -gc1->                        (letrec {X#4=(letrec {E#1} in (\ X#5.S#8));E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#12= T#11[(letrec {E#1} in S#2)]
       ;X#4= (\ X#5.S#8)
       ;E#14
       ;VV#10|X#6,(var X#4)|
     in
        A#9[(var X#6)]
     )
    ,
     (letrec
        X#12= T#11[S#2]
       ;X#4= (\ X#5.S#8)
       ;E#14
       ;VV#10|X#6,(var X#4)|
     in
        A#9[(\ X#5.S#8)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#9[[.]]),
             ((var X#4),[.])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#9[[.]]),((var X#4),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#12=T#11;X#4=(\ X#5.S#8);E#14;VV#10|X#6,(var X#4)|} in A#9[(var X#6)]),
           E#7   |->  {X#12=T#11[S#2];E#14},
           E#13  |->  {X#4=(\ X#5.S#8);E#14;VV#10|X#6,(var X#4)|}}

and instantiated rules:

                                  (letrec {X#12=T#11[S#2];X#4=(\ X#5.S#8);E#14;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -gc1->                        (letrec {X#12=T#11[(letrec {E#1} in S#2)];X#4=(\ X#5.S#8);E#14;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    ................................................................................
                                  (letrec {X#12=T#11[S#2];X#4=(\ X#5.S#8);E#14;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#12=T#11[S#2];X#4=(\ X#5.S#8);E#14;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#4=(\ X#5.S#8);X#6=(letrec {E#1} in (var X#4));E#7} in A#9[(var X#6)])
    ,
     (letrec {X#4=(\ X#5.S#8);X#6=(var X#4);E#7} in A#9[(\ X#5.S#8)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {((var X#4),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#9[[.]]),
             ((var X#4),[.])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#9[[.]]),((var X#4),[.])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=[.];E#7} in A#9[(var X#6)]),
           VV#10|.1,.2| |-> {[.1]=[.2]},
           X#12         |->  X#6,
           E#13         |->  {X#4=(\ X#5.S#8);E#7},
           T#11         |->  [.],
           S#2          |->  (var X#4)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=(var X#4);E#7} in A#9[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=(letrec {E#1} in (var X#4));E#7} in A#9[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=(var X#4);E#7} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);X#6=(var X#4);E#7} in A#9[(\ X#5.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= (letrec {E#1} in (var X#15))
       ;E#7
       ;VV#16|X#15,(var X#4)|
     in
        A#9[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= (var X#15)
       ;E#7
       ;VV#16|X#15,(var X#4)|
     in
        A#9[(\ X#5.S#8)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {((var X#15),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#9[[.]]),
             ((var X#4),[.])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#9[[.]]),((var X#4),[.])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=[.];E#7;VV#16|X#15,(var X#4)|} in A#9[(var X#6)]),
           VV#10|.1,.2| |-> {[.1]=(var X#15);VV#16|X#15,[.2]|},
           X#12         |->  X#6,
           E#13         |->  {X#4=(\ X#5.S#8);E#7;VV#16|X#15,(var X#4)|},
           T#11         |->  [.],
           S#2          |->  (var X#15)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=(var X#15);E#7;VV#16|X#15,(var X#4)|} in A#9[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=(letrec {E#1} in (var X#15));E#7;VV#16|X#15,(var X#4)|} in A#9[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=(var X#15);E#7;VV#16|X#15,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);X#6=(var X#15);E#7;VV#16|X#15,(var X#4)|} in A#9[(\ X#5.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#1} in (var X#16))
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;VV#17|X#6,(var X#15)|
       ;VV#18|X#16,(var X#4)|
     in
        A#9[(var X#6)]
     )
    ,
     (letrec
        X#15= (var X#16)
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;VV#17|X#6,(var X#15)|
       ;VV#18|X#16,(var X#4)|
     in
        A#9[(\ X#5.S#8)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {((var X#16),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#9[[.]]),
             ((var X#4),[.])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#9[[.]]),((var X#4),[.])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=[.];X#4=(\ X#5.S#8);E#7;VV#17|X#6,(var X#15)|;VV#18|X#16,(var X#4)|} in A#9[(var X#6)]),
           VV#10|.1,.2| |-> {X#15=(var X#16);VV#17|[.1],(var X#15)|;VV#18|X#16,[.2]|},
           X#12         |->  X#15,
           E#13         |->  {X#4=(\ X#5.S#8);E#7;VV#17|X#6,(var X#15)|;VV#18|X#16,(var X#4)|},
           T#11         |->  [.],
           S#2          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#15=(var X#16);X#4=(\ X#5.S#8);E#7;VV#17|X#6,(var X#15)|;VV#18|X#16,(var X#4)|} in A#9[(var X#6)])
    -gc1->                        (letrec {X#15=(letrec {E#1} in (var X#16));X#4=(\ X#5.S#8);E#7;VV#17|X#6,(var X#15)|;VV#18|X#16,(var X#4)|} in A#9[(var X#6)])
    ................................................................................
                                  (letrec {X#15=(var X#16);X#4=(\ X#5.S#8);E#7;VV#17|X#6,(var X#15)|;VV#18|X#16,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#15=(var X#16);X#4=(\ X#5.S#8);E#7;VV#17|X#6,(var X#15)|;VV#18|X#16,(var X#4)|} in A#9[(\ X#5.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#1} in (var X#4))
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;VV#16|X#6,(var X#15)|
     in
        A#9[(var X#6)]
     )
    ,
     (letrec
        X#15= (var X#4)
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;VV#16|X#6,(var X#15)|
     in
        A#9[(\ X#5.S#8)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1}
   Delta3 = {((var X#4),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#9[[.]]),
             ((var X#4),[.])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#9[[.]]),((var X#4),[.])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=[.];X#4=(\ X#5.S#8);E#7;VV#16|X#6,(var X#15)|} in A#9[(var X#6)]),
           VV#10|.1,.2| |-> {X#15=[.2];VV#16|[.1],(var X#15)|},
           X#12         |->  X#15,
           E#13         |->  {X#4=(\ X#5.S#8);E#7;VV#16|X#6,(var X#15)|},
           T#11         |->  [.],
           S#2          |->  (var X#4)}

and instantiated rules:

                                  (letrec {X#15=(var X#4);X#4=(\ X#5.S#8);E#7;VV#16|X#6,(var X#15)|} in A#9[(var X#6)])
    -gc1->                        (letrec {X#15=(letrec {E#1} in (var X#4));X#4=(\ X#5.S#8);E#7;VV#16|X#6,(var X#15)|} in A#9[(var X#6)])
    ................................................................................
                                  (letrec {X#15=(var X#4);X#4=(\ X#5.S#8);E#7;VV#16|X#6,(var X#15)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#15=(var X#4);X#4=(\ X#5.S#8);E#7;VV#16|X#6,(var X#15)|} in A#9[(\ X#5.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#1
     in
        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
     )
    ,
     (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#1}
   Delta3 = {((letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)]),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#9[[.]]),
             ((var X#4),[.])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-in2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#9[[.]]),((var X#4),[.])}


and found solution:

    Sol = {T#3  |->  [.],
           S#2  |->  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -gc1->                        (letrec {E#1} in (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(var X#6)])
    -SR,cp-in2->                  (letrec {X#4=(\ X#5.S#8);E#7;VV#10|X#6,(var X#4)|} in A#9[(\ X#5.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;E#7
       ;EE#11[X#6,A#9[(var X#4)]]
     in
        A#13[(letrec {E#1} in (var X#6))]
     )
    ,
     (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#13[(var X#6)])
  )

where

   Delta1 = {A#10,T#12,T#3,A#9,A#13}
   Delta2 = {E#1}
   Delta3 = {((var X#6),(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#13[[.]]),
             ((var X#6),A#13[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#13[[.]]),
           A#10  |->  A#13,
           T#12  |->  A#13[[.]],
           T#14  |->  [.],
           S#2   |->  (var X#6)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#13[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#13[(letrec {E#1} in (var X#6))])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#13[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#13[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;E#7
       ;EE#11[X#6,A#9[(var X#4)]]
     in
        A#13[(letrec {E#1} in A#14[(var X#6)])]
     )
    ,
     (letrec
        X#4= (\ X#5.S#8)
       ;E#7
       ;EE#11[X#6,A#9[(\ X#5.S#8)]]
     in
        A#13[A#14[(var X#6)]]
     )
  )

where

   Delta1 = {A#10,T#12,T#3,A#9,A#13}
   Delta2 = {E#1}
   Delta3 = {(A#14[(var X#6)],(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#13[A#14[[.]]]),
             ((var X#6),A#13[A#14[[.]]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#13),
           A#10  |->  A#13[A#14],
           T#12  |->  A#13,
           S#2   |->  A#14[(var X#6)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#13[A#14[(var X#6)]])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#13[(letrec {E#1} in A#14[(var X#6)])])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#13[A#14[(var X#6)]])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#13[A#14[(var X#6)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;E#7
       ;EE#11[X#6,A#9[(var X#4)]]
     in
        A#13[(app A#14[(var X#6)] T#15[(letrec {E#1} in S#2)])]
     )
    ,
     (letrec
        X#4= (\ X#5.S#8)
       ;E#7
       ;EE#11[X#6,A#9[(\ X#5.S#8)]]
     in
        A#13[(app A#14[(var X#6)] T#15[S#2])]
     )
  )

where

   Delta1 = {A#10,T#12,T#3,A#9}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#13[(app A#14[[.]] T#15[S#2])]),
             ((var X#6),A#13[(app A#14[[.]] T#15[S#2])])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#13[(app A#14[(var X#6)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#6)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#13[(app A#14[(var X#6)] T#15[S#2])])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#13[(app A#14[(var X#6)] T#15[(letrec {E#1} in S#2)])])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#13[(app A#14[(var X#6)] T#15[S#2])])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#13[(app A#14[(var X#6)] T#15[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;E#7
       ;EE#11[X#6,A#9[(var X#4)]]
     in
        (letrec {E#1} in A#10[(var X#6)])
     )
    ,
     (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
  )

where

   Delta1 = {T#3,A#9}
   Delta2 = {E#1}
   Delta3 = {(A#10[(var X#6)],(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in [.]),
           T#12  |->  [.],
           S#2   |->  A#10[(var X#6)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in (letrec {E#1} in A#10[(var X#6)]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#1} in (\ X#5.S#8))
       ;E#7
       ;EE#11[X#6,A#9[(var X#4)]]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
  )

where

   Delta1 = {T#3,A#9}
   Delta2 = {E#1}
   Delta3 = {((\ X#5.S#8),(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=[.];E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)]),
           X#13  |->  X#4,
           E#14  |->  {E#7;EE#11[X#6,A#9[(var X#4)]]},
           T#12  |->  [.],
           S#2   |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(letrec {E#1} in (\ X#5.S#8));E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {E#1} in S#2)]
       ;X#4= (\ X#5.S#8)
       ;E#15
       ;EE#11[X#6,A#9[(var X#4)]]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#13= T#12[S#2]
       ;X#4= (\ X#5.S#8)
       ;E#15
       ;EE#11[X#6,A#9[(\ X#5.S#8)]]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#3,A#9}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#13=T#12;X#4=(\ X#5.S#8);E#15;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)]),
           E#7   |->  {X#13=T#12[S#2];E#15},
           E#14  |->  {X#4=(\ X#5.S#8);E#15;EE#11[X#6,A#9[(var X#4)]]}}

and instantiated rules:

                                  (letrec {X#13=T#12[S#2];X#4=(\ X#5.S#8);E#15;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#13=T#12[(letrec {E#1} in S#2)];X#4=(\ X#5.S#8);E#15;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#13=T#12[S#2];X#4=(\ X#5.S#8);E#15;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#13=T#12[S#2];X#4=(\ X#5.S#8);E#15;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#16[A#18[(letrec {E#1} in (var X#4))]]
       ;E#7
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18[(\ X#5.S#8)]];E#7} in A#10[(var X#6)])
  )

where

   Delta1 = {T#17,A#15,T#12,T#3,A#9,A#16,A#18}
   Delta2 = {E#1}
   Delta3 = {((var X#4),(letrec {E#1} in [.])),
             ((var X#4),A#18[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18[[.]]];E#7} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#4=(\ X#5.S#8);E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[A#18[[.]]],
           A#9          |->  A#18,
           T#17         |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  (var X#4)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18[(var X#4)]];E#7} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18[(letrec {E#1} in (var X#4))]];E#7} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18[(var X#4)]];E#7} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18[(\ X#5.S#8)]];E#7} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#16[A#18[(letrec {E#1} in A#19[(var X#4)])]]
       ;E#7
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#16[A#18[A#19[(\ X#5.S#8)]]]
       ;E#7
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#17,A#15,T#12,T#3,A#9,A#16,A#18}
   Delta2 = {E#1}
   Delta3 = {(A#19[(var X#4)],(letrec {E#1} in [.])),
             ((var X#4),A#18[A#19[[.]]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18];E#7} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#4=(\ X#5.S#8);E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[A#18],
           A#9          |->  A#18[A#19],
           T#17         |->  A#18,
           S#2          |->  A#19[(var X#4)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18[A#19[(var X#4)]]];E#7} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18[(letrec {E#1} in A#19[(var X#4)])]];E#7} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18[A#19[(var X#4)]]];E#7} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18[A#19[(\ X#5.S#8)]]];E#7} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#16[A#18[(app A#19[(var X#4)] T#20[(letrec {E#1} in S#2)])]]
       ;E#7
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#16[A#18[(app A#19[(\ X#5.S#8)] T#20[S#2])]]
       ;E#7
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#17,A#15,T#12,T#3,A#9,A#16}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),A#18[(app A#19[[.]] T#20[S#2])]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18[(app A#19[(var X#4)] T#20)]];E#7} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#4=(\ X#5.S#8);E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[A#18[(app A#19[(var X#4)] T#20)]],
           T#17         |->  A#18[(app A#19[(var X#4)] T#20)],
           A#9          |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18[(app A#19[(var X#4)] T#20[S#2])]];E#7} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18[(app A#19[(var X#4)] T#20[(letrec {E#1} in S#2)])]];E#7} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18[(app A#19[(var X#4)] T#20[S#2])]];E#7} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#18[(app A#19[(\ X#5.S#8)] T#20[S#2])]];E#7} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#16[(letrec {E#1} in A#9[(var X#4)])]
       ;E#7
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#9[(\ X#5.S#8)]];E#7} in A#10[(var X#6)])
  )

where

   Delta1 = {A#15,T#12,T#3,A#9,A#16}
   Delta2 = {E#1}
   Delta3 = {(A#9[(var X#4)],(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=A#16[[.]];E#7} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#4=(\ X#5.S#8);E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[[.]],
           T#17         |->  [.],
           S#2          |->  A#9[(var X#4)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#9[(var X#4)]];E#7} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=A#16[(letrec {E#1} in A#9[(var X#4)])];E#7} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#9[(var X#4)]];E#7} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#9[(\ X#5.S#8)]];E#7} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#16[(letrec {E#1} in A#17[A#9[(var X#4)]])]
       ;E#7
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#16[A#17[A#9[(\ X#5.S#8)]]]
       ;E#7
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#9,A#16}
   Delta2 = {E#1}
   Delta3 = {(A#17[A#9[(var X#4)]],(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=A#16;E#7} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#17[[.2]]]},
           X#13         |->  X#6,
           E#14         |->  {X#4=(\ X#5.S#8);E#7},
           A#15         |->  A#16[A#17],
           T#12         |->  A#16,
           S#2          |->  A#17[A#9[(var X#4)]]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#17[A#9[(var X#4)]]];E#7} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=A#16[(letrec {E#1} in A#17[A#9[(var X#4)]])];E#7} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#17[A#9[(var X#4)]]];E#7} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#17[A#9[(\ X#5.S#8)]]];E#7} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#16[(app A#17[A#9[(var X#4)]] T#18[(letrec {E#1} in S#2)])]
       ;E#7
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#16[(app A#17[A#9[(\ X#5.S#8)]] T#18[S#2])]
       ;E#7
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#9}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=A#16[(app A#17[A#9[(var X#4)]] T#18)];E#7} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[S#2])]},
           X#13         |->  X#6,
           E#14         |->  {X#4=(\ X#5.S#8);E#7},
           T#12         |->  A#16[(app A#17[A#9[(var X#4)]] T#18)],
           A#15         |->  A#16[(app A#17 T#18[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[(app A#17[A#9[(var X#4)]] T#18[S#2])];E#7} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=A#16[(app A#17[A#9[(var X#4)]] T#18[(letrec {E#1} in S#2)])];E#7} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[(app A#17[A#9[(var X#4)]] T#18[S#2])];E#7} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);X#6=A#16[(app A#17[A#9[(\ X#5.S#8)]] T#18[S#2])];E#7} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#16[(letrec {E#1} in (var X#4))]
       ;E#7
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#4=(\ X#5.S#8);X#6=A#16[(\ X#5.S#8)];E#7} in A#10[(var X#6)])
  )

where

   Delta1 = {T#12,T#3,A#9,A#16}
   Delta2 = {E#1}
   Delta3 = {((var X#4),(letrec {E#1} in [.])),
             ((var X#4),A#16[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=A#16[[.]];E#7} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#6,
           E#14         |->  {X#4=(\ X#5.S#8);E#7},
           A#15         |->  [.],
           A#9          |->  A#16,
           T#12         |->  A#16[[.]],
           T#17         |->  [.],
           S#2          |->  (var X#4)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[(var X#4)];E#7} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=A#16[(letrec {E#1} in (var X#4))];E#7} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[(var X#4)];E#7} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);X#6=A#16[(\ X#5.S#8)];E#7} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#16[(letrec {E#1} in A#17[(var X#4)])]
       ;E#7
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#17[(\ X#5.S#8)]];E#7} in A#10[(var X#6)])
  )

where

   Delta1 = {T#12,T#3,A#9,A#16}
   Delta2 = {E#1}
   Delta3 = {(A#17[(var X#4)],(letrec {E#1} in [.])),
             ((var X#4),A#16[A#17[[.]]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=A#16;E#7} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#6,
           E#14         |->  {X#4=(\ X#5.S#8);E#7},
           A#15         |->  [.],
           A#9          |->  A#16[A#17],
           T#12         |->  A#16,
           S#2          |->  A#17[(var X#4)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#17[(var X#4)]];E#7} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=A#16[(letrec {E#1} in A#17[(var X#4)])];E#7} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#17[(var X#4)]];E#7} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);X#6=A#16[A#17[(\ X#5.S#8)]];E#7} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#16[(app A#17[(var X#4)] T#18[(letrec {E#1} in S#2)])]
       ;E#7
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#16[(app A#17[(\ X#5.S#8)] T#18[S#2])]
       ;E#7
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#12,T#3,A#9}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),A#16[(app A#17[[.]] T#18[S#2])]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=A#16[(app A#17[(var X#4)] T#18)];E#7} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#6,
           E#14         |->  {X#4=(\ X#5.S#8);E#7},
           A#15         |->  [.],
           T#12         |->  A#16[(app A#17[(var X#4)] T#18)],
           A#9          |->  A#16[(app A#17 T#18[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[(app A#17[(var X#4)] T#18[S#2])];E#7} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=A#16[(app A#17[(var X#4)] T#18[(letrec {E#1} in S#2)])];E#7} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=A#16[(app A#17[(var X#4)] T#18[S#2])];E#7} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);X#6=A#16[(app A#17[(\ X#5.S#8)] T#18[S#2])];E#7} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= (letrec {E#1} in A#15[A#9[(var X#4)]])
       ;E#7
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#4=(\ X#5.S#8);X#6=A#15[A#9[(\ X#5.S#8)]];E#7} in A#10[(var X#6)])
  )

where

   Delta1 = {T#3,A#9}
   Delta2 = {E#1}
   Delta3 = {(A#15[A#9[(var X#4)]],(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=[.];E#7} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#4=(\ X#5.S#8);E#7},
           T#12         |->  [.],
           S#2          |->  A#15[A#9[(var X#4)]]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=A#15[A#9[(var X#4)]];E#7} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=(letrec {E#1} in A#15[A#9[(var X#4)]]);E#7} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=A#15[A#9[(var X#4)]];E#7} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);X#6=A#15[A#9[(\ X#5.S#8)]];E#7} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#18[(letrec {E#1} in (var X#16))]
       ;E#7
       ;EE#17[X#16,A#9[(var X#4)]]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#18[(var X#16)]
       ;E#7
       ;EE#17[X#16,A#9[(\ X#5.S#8)]]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#9,A#18}
   Delta2 = {E#1}
   Delta3 = {((var X#16),(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=A#18[[.]];E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(var X#16)];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#17[X#16,A#9[(var X#4)]]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=A#18[(var X#16)];E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=A#18[(letrec {E#1} in (var X#16))];E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=A#18[(var X#16)];E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);X#6=A#18[(var X#16)];E#7;EE#17[X#16,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#18[(letrec {E#1} in A#19[(var X#16)])]
       ;E#7
       ;EE#17[X#16,A#9[(var X#4)]]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#18[A#19[(var X#16)]]
       ;E#7
       ;EE#17[X#16,A#9[(\ X#5.S#8)]]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#9,A#18}
   Delta2 = {E#1}
   Delta3 = {(A#19[(var X#16)],(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=A#18;E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#19[(var X#16)]];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#17[X#16,A#9[(var X#4)]]},
           A#15         |->  A#18[A#19],
           T#12         |->  A#18,
           S#2          |->  A#19[(var X#16)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=A#18[A#19[(var X#16)]];E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=A#18[(letrec {E#1} in A#19[(var X#16)])];E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=A#18[A#19[(var X#16)]];E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);X#6=A#18[A#19[(var X#16)]];E#7;EE#17[X#16,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#2)])]
       ;E#7
       ;EE#17[X#16,A#9[(var X#4)]]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#18[(app A#19[(var X#16)] T#20[S#2])]
       ;E#7
       ;EE#17[X#16,A#9[(\ X#5.S#8)]]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#9}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=A#18[(app A#19[(var X#16)] T#20)];E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[S#2])];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#17[X#16,A#9[(var X#4)]]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=A#18[(app A#19[(var X#16)] T#20[S#2])];E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#2)])];E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=A#18[(app A#19[(var X#16)] T#20[S#2])];E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);X#6=A#18[(app A#19[(var X#16)] T#20[S#2])];E#7;EE#17[X#16,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= (letrec {E#1} in A#15[(var X#16)])
       ;E#7
       ;EE#17[X#16,A#9[(var X#4)]]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#8)
       ;X#6= A#15[(var X#16)]
       ;E#7
       ;EE#17[X#16,A#9[(\ X#5.S#8)]]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#3,A#9}
   Delta2 = {E#1}
   Delta3 = {(A#15[(var X#16)],(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#8);X#6=[.];E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#15[(var X#16)];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#17[X#16,A#9[(var X#4)]]},
           T#12         |->  [.],
           S#2          |->  A#15[(var X#16)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);X#6=A#15[(var X#16)];E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#8);X#6=(letrec {E#1} in A#15[(var X#16)]);E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);X#6=A#15[(var X#16)];E#7;EE#17[X#16,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);X#6=A#15[(var X#16)];E#7;EE#17[X#16,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {E#1} in (var X#17))]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,A#9[(var X#4)]]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[(var X#17)]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,A#9[(\ X#5.S#8)]]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#9,A#20}
   Delta2 = {E#1}
   Delta3 = {((var X#17),(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20[[.]];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]},
           A#15         |->  A#20,
           T#12         |->  A#20[[.]],
           T#21         |->  [.],
           S#2          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#16=A#20[(var X#17)];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#16=A#20[(letrec {E#1} in (var X#17))];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[(var X#17)];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#16=A#20[(var X#17)];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {E#1} in A#21[(var X#17)])]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,A#9[(var X#4)]]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[A#21[(var X#17)]]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,A#9[(\ X#5.S#8)]]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#9,A#20}
   Delta2 = {E#1}
   Delta3 = {(A#21[(var X#17)],(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20;X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#21[(var X#17)]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]},
           A#15         |->  A#20[A#21],
           T#12         |->  A#20,
           S#2          |->  A#21[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#21[(var X#17)]];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#16=A#20[(letrec {E#1} in A#21[(var X#17)])];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[A#21[(var X#17)]];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#16=A#20[A#21[(var X#17)]];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#2)])]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,A#9[(var X#4)]]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[S#2])]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,A#9[(\ X#5.S#8)]]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#9}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#2)])];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {E#1} in A#15[(var X#17)])
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,A#9[(var X#4)]]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#15[(var X#17)]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,A#9[(\ X#5.S#8)]]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#3,A#9}
   Delta2 = {E#1}
   Delta3 = {(A#15[(var X#17)],(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#15[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]},
           T#12         |->  [.],
           S#2          |->  A#15[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#15[(var X#17)];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#16=(letrec {E#1} in A#15[(var X#17)]);X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#15[(var X#17)];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#16=A#15[(var X#17)];X#4=(\ X#5.S#8);E#7;EE#18[X#6,(var X#16)];EE#19[X#17,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[A#20[(letrec {E#1} in (var X#4))]]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[A#20[(\ X#5.S#8)]]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#3,A#9,A#18,A#20}
   Delta2 = {E#1}
   Delta3 = {((var X#4),(letrec {E#1} in [.])),
             ((var X#4),A#20[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[A#20[[.]]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[A#20[[.]]],
           A#9          |->  A#20,
           T#19         |->  A#20[[.]],
           T#21         |->  [.],
           S#2          |->  (var X#4)}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[(var X#4)]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#16=A#18[A#20[(letrec {E#1} in (var X#4))]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[(var X#4)]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#16=A#18[A#20[(\ X#5.S#8)]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[A#20[(letrec {E#1} in A#21[(var X#4)])]]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[A#20[A#21[(\ X#5.S#8)]]]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#3,A#9,A#18,A#20}
   Delta2 = {E#1}
   Delta3 = {(A#21[(var X#4)],(letrec {E#1} in [.])),
             ((var X#4),A#20[A#21[[.]]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[A#20];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[A#20],
           A#9          |->  A#20[A#21],
           T#19         |->  A#20,
           S#2          |->  A#21[(var X#4)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[A#21[(var X#4)]]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#16=A#18[A#20[(letrec {E#1} in A#21[(var X#4)])]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[A#21[(var X#4)]]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#16=A#18[A#20[A#21[(\ X#5.S#8)]]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[A#20[(app A#21[(var X#4)] T#22[(letrec {E#1} in S#2)])]]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[A#20[(app A#21[(\ X#5.S#8)] T#22[S#2])]]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#3,A#9,A#18}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),A#20[(app A#21[[.]] T#22[S#2])]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[A#20[(app A#21[(var X#4)] T#22)]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[A#20[(app A#21[(var X#4)] T#22)]],
           T#19         |->  A#20[(app A#21[(var X#4)] T#22)],
           A#9          |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[(app A#21[(var X#4)] T#22[S#2])]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#16=A#18[A#20[(app A#21[(var X#4)] T#22[(letrec {E#1} in S#2)])]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[(app A#21[(var X#4)] T#22[S#2])]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#16=A#18[A#20[(app A#21[(\ X#5.S#8)] T#22[S#2])]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {E#1} in A#9[(var X#4)])]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[A#9[(\ X#5.S#8)]]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#9,A#18}
   Delta2 = {E#1}
   Delta3 = {(A#9[(var X#4)],(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[[.]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  A#9[(var X#4)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#9[(var X#4)]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#16=A#18[(letrec {E#1} in A#9[(var X#4)])];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[A#9[(var X#4)]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#16=A#18[A#9[(\ X#5.S#8)]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {E#1} in A#19[A#9[(var X#4)]])]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[A#19[A#9[(\ X#5.S#8)]]]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#9,A#18}
   Delta2 = {E#1}
   Delta3 = {(A#19[A#9[(var X#4)]],(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#19[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]},
           A#15         |->  A#18[A#19],
           T#12         |->  A#18,
           S#2          |->  A#19[A#9[(var X#4)]]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#19[A#9[(var X#4)]]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#16=A#18[(letrec {E#1} in A#19[A#9[(var X#4)]])];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[A#19[A#9[(var X#4)]]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#16=A#18[A#19[A#9[(\ X#5.S#8)]]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[A#9[(var X#4)]] T#20[(letrec {E#1} in S#2)])]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[A#9[(\ X#5.S#8)]] T#20[S#2])]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#9}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[(app A#19[A#9[(var X#4)]] T#20)];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[S#2])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]},
           T#12         |->  A#18[(app A#19[A#9[(var X#4)]] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[A#9[(var X#4)]] T#20[S#2])];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#16=A#18[(app A#19[A#9[(var X#4)]] T#20[(letrec {E#1} in S#2)])];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[A#9[(var X#4)]] T#20[S#2])];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#16=A#18[(app A#19[A#9[(\ X#5.S#8)]] T#20[S#2])];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {E#1} in (var X#4))]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[(\ X#5.S#8)]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#12,T#3,A#9,A#18}
   Delta2 = {E#1}
   Delta3 = {((var X#4),(letrec {E#1} in [.])),
             ((var X#4),A#18[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[[.]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]},
           A#15         |->  [.],
           A#9          |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  (var X#4)}

and instantiated rules:

                                  (letrec {X#16=A#18[(var X#4)];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#16=A#18[(letrec {E#1} in (var X#4))];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[(var X#4)];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#16=A#18[(\ X#5.S#8)];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {E#1} in A#19[(var X#4)])]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[A#19[(\ X#5.S#8)]]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#12,T#3,A#9,A#18}
   Delta2 = {E#1}
   Delta3 = {(A#19[(var X#4)],(letrec {E#1} in [.])),
             ((var X#4),A#18[A#19[[.]]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]},
           A#15         |->  [.],
           A#9          |->  A#18[A#19],
           T#12         |->  A#18,
           S#2          |->  A#19[(var X#4)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#19[(var X#4)]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#16=A#18[(letrec {E#1} in A#19[(var X#4)])];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[A#19[(var X#4)]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#16=A#18[A#19[(\ X#5.S#8)]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(var X#4)] T#20[(letrec {E#1} in S#2)])]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(\ X#5.S#8)] T#20[S#2])]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#12,T#3,A#9}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),A#18[(app A#19[[.]] T#20[S#2])]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[(app A#19[(var X#4)] T#20)];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  A#18[(app A#19[(var X#4)] T#20)],
           A#9          |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(var X#4)] T#20[S#2])];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#16=A#18[(app A#19[(var X#4)] T#20[(letrec {E#1} in S#2)])];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(var X#4)] T#20[S#2])];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#16=A#18[(app A#19[(\ X#5.S#8)] T#20[S#2])];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {E#1} in A#15[A#9[(var X#4)]])
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#15[A#9[(\ X#5.S#8)]]
       ;X#4= (\ X#5.S#8)
       ;E#7
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#3,A#9}
   Delta2 = {E#1}
   Delta3 = {(A#15[A#9[(var X#4)]],(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#15[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]},
           T#12         |->  [.],
           S#2          |->  A#15[A#9[(var X#4)]]}

and instantiated rules:

                                  (letrec {X#16=A#15[A#9[(var X#4)]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -gc1->                        (letrec {X#16=(letrec {E#1} in A#15[A#9[(var X#4)]]);X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#15[A#9[(var X#4)]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#16=A#15[A#9[(\ X#5.S#8)]];X#4=(\ X#5.S#8);E#7;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#1
     in
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
     )
    ,
     (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
  )

where

   Delta1 = {A#9}
   Delta2 = {E#1}
   Delta3 = {((letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)]),(letrec {E#1} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    and constraints: A#9/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}
      Delta1=  {A#9}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),A#9[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           S#2  |->  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -gc1->                        (letrec {E#1} in (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(var X#4)]]} in A#10[(var X#6)])
    -SR,cp-e1->                   (letrec {X#4=(\ X#5.S#8);E#7;EE#11[X#6,A#9[(\ X#5.S#8)]]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;E#8
       ;EE#12[X#6,A#10[(var X#7)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#15[(letrec {E#1} in (var X#6))]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;E#8
       ;EE#12[X#6,A#10[(\ X#5.S#9)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#15[(var X#6)]
     )
  )

where

   Delta1 = {A#11,T#14,T#3,A#10,A#15}
   Delta2 = {E#1}
   Delta3 = {((var X#6),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#15[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#15[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#15[[.]]),
           A#11  |->  A#15,
           T#14  |->  A#15[[.]],
           T#16  |->  [.],
           S#2   |->  (var X#6)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#15[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#15[(letrec {E#1} in (var X#6))])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#15[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#15[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;E#8
       ;EE#12[X#6,A#10[(var X#7)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#15[(letrec {E#1} in A#16[(var X#6)])]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;E#8
       ;EE#12[X#6,A#10[(\ X#5.S#9)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#15[A#16[(var X#6)]]
     )
  )

where

   Delta1 = {A#11,T#14,T#3,A#10,A#15}
   Delta2 = {E#1}
   Delta3 = {(A#16[(var X#6)],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#15[A#16[[.]]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#15[A#16[[.]]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#15),
           A#11  |->  A#15[A#16],
           T#14  |->  A#15,
           S#2   |->  A#16[(var X#6)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#15[A#16[(var X#6)]])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#15[(letrec {E#1} in A#16[(var X#6)])])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#15[A#16[(var X#6)]])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#15[A#16[(var X#6)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;E#8
       ;EE#12[X#6,A#10[(var X#7)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#15[(app A#16[(var X#6)] T#17[(letrec {E#1} in S#2)])]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;E#8
       ;EE#12[X#6,A#10[(\ X#5.S#9)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#15[(app A#16[(var X#6)] T#17[S#2])]
     )
  )

where

   Delta1 = {A#11,T#14,T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#15[(app A#16[[.]] T#17[S#2])]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#15[(app A#16[[.]] T#17[S#2])])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#15[(app A#16[(var X#6)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#6)] T#17)],
           A#11  |->  A#15[(app A#16 T#17[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#15[(app A#16[(var X#6)] T#17[S#2])])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#15[(app A#16[(var X#6)] T#17[(letrec {E#1} in S#2)])])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#15[(app A#16[(var X#6)] T#17[S#2])])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#15[(app A#16[(var X#6)] T#17[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;E#8
       ;EE#12[X#6,A#10[(var X#7)]]
       ;VV#13|X#7,(var X#4)|
     in
        (letrec {E#1} in A#11[(var X#6)])
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;E#8
       ;EE#12[X#6,A#10[(\ X#5.S#9)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {(A#11[(var X#6)],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in [.]),
           T#14  |->  [.],
           S#2   |->  A#11[(var X#6)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in (letrec {E#1} in A#11[(var X#6)]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#1} in (\ X#5.S#9))
       ;E#8
       ;EE#12[X#6,A#10[(var X#7)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;E#8
       ;EE#12[X#6,A#10[(\ X#5.S#9)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {((\ X#5.S#9),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=[.];E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           X#15  |->  X#4,
           E#16  |->  {E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|},
           T#14  |->  [.],
           S#2   |->  (\ X#5.S#9)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(letrec {E#1} in (\ X#5.S#9));E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {E#1} in S#2)]
       ;X#4= (\ X#5.S#9)
       ;E#17
       ;EE#12[X#6,A#10[(var X#7)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#15= T#14[S#2]
       ;X#4= (\ X#5.S#9)
       ;E#17
       ;EE#12[X#6,A#10[(\ X#5.S#9)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#15=T#14;X#4=(\ X#5.S#9);E#17;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           E#8   |->  {X#15=T#14[S#2];E#17},
           E#16  |->  {X#4=(\ X#5.S#9);E#17;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|}}

and instantiated rules:

                                  (letrec {X#15=T#14[S#2];X#4=(\ X#5.S#9);E#17;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#15=T#14[(letrec {E#1} in S#2)];X#4=(\ X#5.S#9);E#17;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#15=T#14[S#2];X#4=(\ X#5.S#9);E#17;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#15=T#14[S#2];X#4=(\ X#5.S#9);E#17;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#7= (letrec {E#1} in (var X#4))
       ;E#8
       ;EE#12[X#6,A#10[(var X#7)]]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#7= (var X#4)
       ;E#8
       ;EE#12[X#6,A#10[(\ X#5.S#9)]]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {((var X#4),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#7=[.];E#8;EE#12[X#6,A#10[(var X#7)]]} in A#11[(var X#6)]),
           VV#13|.1,.2| |-> {[.1]=[.2]},
           X#15         |->  X#7,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]]},
           T#14         |->  [.],
           S#2          |->  (var X#4)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#7=(var X#4);E#8;EE#12[X#6,A#10[(var X#7)]]} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#7=(letrec {E#1} in (var X#4));E#8;EE#12[X#6,A#10[(var X#7)]]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#7=(var X#4);E#8;EE#12[X#6,A#10[(var X#7)]]} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#7=(var X#4);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#7= (letrec {E#1} in (var X#18))
       ;E#8
       ;EE#12[X#6,A#10[(var X#7)]]
       ;VV#19|X#18,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#7= (var X#18)
       ;E#8
       ;EE#12[X#6,A#10[(\ X#5.S#9)]]
       ;VV#19|X#18,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {((var X#18),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#7=[.];E#8;EE#12[X#6,A#10[(var X#7)]];VV#19|X#18,(var X#4)|} in A#11[(var X#6)]),
           VV#13|.1,.2| |-> {[.1]=(var X#18);VV#19|X#18,[.2]|},
           X#15         |->  X#7,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#19|X#18,(var X#4)|},
           T#14         |->  [.],
           S#2          |->  (var X#18)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#7=(var X#18);E#8;EE#12[X#6,A#10[(var X#7)]];VV#19|X#18,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#7=(letrec {E#1} in (var X#18));E#8;EE#12[X#6,A#10[(var X#7)]];VV#19|X#18,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#7=(var X#18);E#8;EE#12[X#6,A#10[(var X#7)]];VV#19|X#18,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#7=(var X#18);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#19|X#18,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {E#1} in (var X#19))
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#12[X#6,A#10[(var X#7)]]
       ;VV#20|X#7,(var X#18)|
       ;VV#21|X#19,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= (var X#19)
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#12[X#6,A#10[(\ X#5.S#9)]]
       ;VV#20|X#7,(var X#18)|
       ;VV#21|X#19,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {((var X#19),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=[.];X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#20|X#7,(var X#18)|;VV#21|X#19,(var X#4)|} in A#11[(var X#6)]),
           VV#13|.1,.2| |-> {X#18=(var X#19);VV#20|[.1],(var X#18)|;VV#21|X#19,[.2]|},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#20|X#7,(var X#18)|;VV#21|X#19,(var X#4)|},
           T#14         |->  [.],
           S#2          |->  (var X#19)}

and instantiated rules:

                                  (letrec {X#18=(var X#19);X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#20|X#7,(var X#18)|;VV#21|X#19,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=(letrec {E#1} in (var X#19));X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#20|X#7,(var X#18)|;VV#21|X#19,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=(var X#19);X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#20|X#7,(var X#18)|;VV#21|X#19,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=(var X#19);X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#20|X#7,(var X#18)|;VV#21|X#19,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {E#1} in (var X#4))
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#12[X#6,A#10[(var X#7)]]
       ;VV#19|X#7,(var X#18)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= (var X#4)
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#12[X#6,A#10[(\ X#5.S#9)]]
       ;VV#19|X#7,(var X#18)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {((var X#4),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=[.];X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#19|X#7,(var X#18)|} in A#11[(var X#6)]),
           VV#13|.1,.2| |-> {X#18=[.2];VV#19|[.1],(var X#18)|},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#19|X#7,(var X#18)|},
           T#14         |->  [.],
           S#2          |->  (var X#4)}

and instantiated rules:

                                  (letrec {X#18=(var X#4);X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#19|X#7,(var X#18)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=(letrec {E#1} in (var X#4));X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#19|X#7,(var X#18)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=(var X#4);X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#19|X#7,(var X#18)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=(var X#4);X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#19|X#7,(var X#18)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[A#20[(letrec {E#1} in (var X#7))]]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[A#20[(\ X#5.S#9)]]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#19,A#17,T#14,T#3,A#10,A#18,A#20}
   Delta2 = {E#1}
   Delta3 = {((var X#7),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#20[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#20[[.]]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#6,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;VV#13|X#7,(var X#4)|},
           A#17         |->  A#18,
           T#14         |->  A#18[A#20[[.]]],
           A#10         |->  A#20,
           T#19         |->  A#20[[.]],
           T#21         |->  [.],
           S#2          |->  (var X#7)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#20[(var X#7)]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#20[(letrec {E#1} in (var X#7))]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#20[(var X#7)]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#20[(\ X#5.S#9)]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[A#20[(letrec {E#1} in A#21[(var X#7)])]]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[A#20[A#21[(\ X#5.S#9)]]]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#19,A#17,T#14,T#3,A#10,A#18,A#20}
   Delta2 = {E#1}
   Delta3 = {(A#21[(var X#7)],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#20[A#21[[.]]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#20];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#6,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;VV#13|X#7,(var X#4)|},
           A#17         |->  A#18,
           T#14         |->  A#18[A#20],
           A#10         |->  A#20[A#21],
           T#19         |->  A#20,
           S#2          |->  A#21[(var X#7)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#20[A#21[(var X#7)]]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#20[(letrec {E#1} in A#21[(var X#7)])]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#20[A#21[(var X#7)]]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#20[A#21[(\ X#5.S#9)]]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[A#20[(app A#21[(var X#7)] T#22[(letrec {E#1} in S#2)])]]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[A#20[(app A#21[(\ X#5.S#9)] T#22[S#2])]]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#19,A#17,T#14,T#3,A#10,A#18}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#20[(app A#21[[.]] T#22[S#2])]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#20[(app A#21[(var X#7)] T#22)]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#6,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;VV#13|X#7,(var X#4)|},
           A#17         |->  A#18,
           T#14         |->  A#18[A#20[(app A#21[(var X#7)] T#22)]],
           T#19         |->  A#20[(app A#21[(var X#7)] T#22)],
           A#10         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#20[(app A#21[(var X#7)] T#22[S#2])]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#20[(app A#21[(var X#7)] T#22[(letrec {E#1} in S#2)])]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#20[(app A#21[(var X#7)] T#22[S#2])]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#20[(app A#21[(\ X#5.S#9)] T#22[S#2])]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[(letrec {E#1} in A#10[(var X#7)])]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[A#10[(\ X#5.S#9)]]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#17,T#14,T#3,A#10,A#18}
   Delta2 = {E#1}
   Delta3 = {(A#10[(var X#7)],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#6=A#18[[.]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#6,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;VV#13|X#7,(var X#4)|},
           A#17         |->  A#18,
           T#14         |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  A#10[(var X#7)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#10[(var X#7)]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#6=A#18[(letrec {E#1} in A#10[(var X#7)])];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#10[(var X#7)]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#10[(\ X#5.S#9)]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[(letrec {E#1} in A#19[A#10[(var X#7)]])]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[A#19[A#10[(\ X#5.S#9)]]]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#17,T#14,T#3,A#10,A#18}
   Delta2 = {E#1}
   Delta3 = {(A#19[A#10[(var X#7)]],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#6=A#18;E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#18[A#19[[.2]]]},
           X#15         |->  X#6,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;VV#13|X#7,(var X#4)|},
           A#17         |->  A#18[A#19],
           T#14         |->  A#18,
           S#2          |->  A#19[A#10[(var X#7)]]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#19[A#10[(var X#7)]]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#6=A#18[(letrec {E#1} in A#19[A#10[(var X#7)]])];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#19[A#10[(var X#7)]]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#19[A#10[(\ X#5.S#9)]]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[(app A#19[A#10[(var X#7)]] T#20[(letrec {E#1} in S#2)])]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[(app A#19[A#10[(\ X#5.S#9)]] T#20[S#2])]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#17,T#14,T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#6=A#18[(app A#19[A#10[(var X#7)]] T#20)];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] T#20[S#2])]},
           X#15         |->  X#6,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;VV#13|X#7,(var X#4)|},
           T#14         |->  A#18[(app A#19[A#10[(var X#7)]] T#20)],
           A#17         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[(app A#19[A#10[(var X#7)]] T#20[S#2])];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#6=A#18[(app A#19[A#10[(var X#7)]] T#20[(letrec {E#1} in S#2)])];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[(app A#19[A#10[(var X#7)]] T#20[S#2])];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#6=A#18[(app A#19[A#10[(\ X#5.S#9)]] T#20[S#2])];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[(letrec {E#1} in (var X#7))]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[(\ X#5.S#9)]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#14,T#3,A#10,A#18}
   Delta2 = {E#1}
   Delta3 = {((var X#7),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#18[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#6=A#18[[.]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#6,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;VV#13|X#7,(var X#4)|},
           A#17         |->  [.],
           A#10         |->  A#18,
           T#14         |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  (var X#7)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[(var X#7)];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#6=A#18[(letrec {E#1} in (var X#7))];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[(var X#7)];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#6=A#18[(\ X#5.S#9)];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[(letrec {E#1} in A#19[(var X#7)])]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[A#19[(\ X#5.S#9)]]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#14,T#3,A#10,A#18}
   Delta2 = {E#1}
   Delta3 = {(A#19[(var X#7)],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#18[A#19[[.]]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#6=A#18;E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#6,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;VV#13|X#7,(var X#4)|},
           A#17         |->  [.],
           A#10         |->  A#18[A#19],
           T#14         |->  A#18,
           S#2          |->  A#19[(var X#7)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#19[(var X#7)]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#6=A#18[(letrec {E#1} in A#19[(var X#7)])];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#19[(var X#7)]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#6=A#18[A#19[(\ X#5.S#9)]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[(app A#19[(var X#7)] T#20[(letrec {E#1} in S#2)])]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#18[(app A#19[(\ X#5.S#9)] T#20[S#2])]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#14,T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#18[(app A#19[[.]] T#20[S#2])]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#6=A#18[(app A#19[(var X#7)] T#20)];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#6,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;VV#13|X#7,(var X#4)|},
           A#17         |->  [.],
           T#14         |->  A#18[(app A#19[(var X#7)] T#20)],
           A#10         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[(app A#19[(var X#7)] T#20[S#2])];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#6=A#18[(app A#19[(var X#7)] T#20[(letrec {E#1} in S#2)])];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#6=A#18[(app A#19[(var X#7)] T#20[S#2])];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#6=A#18[(app A#19[(\ X#5.S#9)] T#20[S#2])];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= (letrec {E#1} in A#17[A#10[(var X#7)]])
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#17[A#10[(\ X#5.S#9)]]
       ;E#8
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {(A#17[A#10[(var X#7)]],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#6=[.];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#15         |->  X#6,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;VV#13|X#7,(var X#4)|},
           T#14         |->  [.],
           S#2          |->  A#17[A#10[(var X#7)]]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#6=A#17[A#10[(var X#7)]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#6=(letrec {E#1} in A#17[A#10[(var X#7)]]);E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#6=A#17[A#10[(var X#7)]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#6=A#17[A#10[(\ X#5.S#9)]];E#8;VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#20[(letrec {E#1} in (var X#18))]
       ;E#8
       ;EE#19[X#18,A#10[(var X#7)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#20[(var X#18)]
       ;E#8
       ;EE#19[X#18,A#10[(\ X#5.S#9)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#17,T#14,T#3,A#10,A#20}
   Delta2 = {E#1}
   Delta3 = {((var X#18),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#6=A#20[[.]];E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#20[(var X#18)];EE#19[X#18,[.2]]},
           X#15         |->  X#6,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|},
           A#17         |->  A#20,
           T#14         |->  A#20[[.]],
           T#21         |->  [.],
           S#2          |->  (var X#18)}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#6=A#20[(var X#18)];E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#6=A#20[(letrec {E#1} in (var X#18))];E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#6=A#20[(var X#18)];E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#6=A#20[(var X#18)];E#8;EE#19[X#18,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#20[(letrec {E#1} in A#21[(var X#18)])]
       ;E#8
       ;EE#19[X#18,A#10[(var X#7)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#20[A#21[(var X#18)]]
       ;E#8
       ;EE#19[X#18,A#10[(\ X#5.S#9)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#17,T#14,T#3,A#10,A#20}
   Delta2 = {E#1}
   Delta3 = {(A#21[(var X#18)],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#6=A#20;E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#20[A#21[(var X#18)]];EE#19[X#18,[.2]]},
           X#15         |->  X#6,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|},
           A#17         |->  A#20[A#21],
           T#14         |->  A#20,
           S#2          |->  A#21[(var X#18)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#6=A#20[A#21[(var X#18)]];E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#6=A#20[(letrec {E#1} in A#21[(var X#18)])];E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#6=A#20[A#21[(var X#18)]];E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#6=A#20[A#21[(var X#18)]];E#8;EE#19[X#18,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#20[(app A#21[(var X#18)] T#22[(letrec {E#1} in S#2)])]
       ;E#8
       ;EE#19[X#18,A#10[(var X#7)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#20[(app A#21[(var X#18)] T#22[S#2])]
       ;E#8
       ;EE#19[X#18,A#10[(\ X#5.S#9)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#17,T#14,T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#6=A#20[(app A#21[(var X#18)] T#22)];E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] T#22[S#2])];EE#19[X#18,[.2]]},
           X#15         |->  X#6,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|},
           T#14         |->  A#20[(app A#21[(var X#18)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#6=A#20[(app A#21[(var X#18)] T#22[S#2])];E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#6=A#20[(app A#21[(var X#18)] T#22[(letrec {E#1} in S#2)])];E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#6=A#20[(app A#21[(var X#18)] T#22[S#2])];E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#6=A#20[(app A#21[(var X#18)] T#22[S#2])];E#8;EE#19[X#18,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= (letrec {E#1} in A#17[(var X#18)])
       ;E#8
       ;EE#19[X#18,A#10[(var X#7)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;X#6= A#17[(var X#18)]
       ;E#8
       ;EE#19[X#18,A#10[(\ X#5.S#9)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {(A#17[(var X#18)],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(\ X#5.S#9);X#6=[.];E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[(var X#18)];EE#19[X#18,[.2]]},
           X#15         |->  X#6,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|},
           T#14         |->  [.],
           S#2          |->  A#17[(var X#18)]}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);X#6=A#17[(var X#18)];E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#4=(\ X#5.S#9);X#6=(letrec {E#1} in A#17[(var X#18)]);E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);X#6=A#17[(var X#18)];E#8;EE#19[X#18,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);X#6=A#17[(var X#18)];E#8;EE#19[X#18,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(letrec {E#1} in (var X#19))]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#20[X#6,(var X#18)]
       ;EE#21[X#19,A#10[(var X#7)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= A#22[(var X#19)]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#20[X#6,(var X#18)]
       ;EE#21[X#19,A#10[(\ X#5.S#9)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#17,T#14,T#3,A#10,A#22}
   Delta2 = {E#1}
   Delta3 = {((var X#19),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=A#22[[.]];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#18=A#22[(var X#19)];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|},
           A#17         |->  A#22,
           T#14         |->  A#22[[.]],
           T#23         |->  [.],
           S#2          |->  (var X#19)}

and instantiated rules:

                                  (letrec {X#18=A#22[(var X#19)];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=A#22[(letrec {E#1} in (var X#19))];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=A#22[(var X#19)];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=A#22[(var X#19)];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(letrec {E#1} in A#23[(var X#19)])]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#20[X#6,(var X#18)]
       ;EE#21[X#19,A#10[(var X#7)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= A#22[A#23[(var X#19)]]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#20[X#6,(var X#18)]
       ;EE#21[X#19,A#10[(\ X#5.S#9)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#17,T#14,T#3,A#10,A#22}
   Delta2 = {E#1}
   Delta3 = {(A#23[(var X#19)],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=A#22;X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#18=A#22[A#23[(var X#19)]];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|},
           A#17         |->  A#22[A#23],
           T#14         |->  A#22,
           S#2          |->  A#23[(var X#19)]}

and instantiated rules:

                                  (letrec {X#18=A#22[A#23[(var X#19)]];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=A#22[(letrec {E#1} in A#23[(var X#19)])];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=A#22[A#23[(var X#19)]];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=A#22[A#23[(var X#19)]];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {E#1} in S#2)])]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#20[X#6,(var X#18)]
       ;EE#21[X#19,A#10[(var X#7)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[S#2])]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#20[X#6,(var X#18)]
       ;EE#21[X#19,A#10[(\ X#5.S#9)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#17,T#14,T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24)];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] T#24[S#2])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|},
           T#14         |->  A#22[(app A#23[(var X#19)] T#24)],
           A#17         |->  A#22[(app A#23 T#24[S#2])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[S#2])];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {E#1} in S#2)])];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[S#2])];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[S#2])];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {E#1} in A#17[(var X#19)])
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#20[X#6,(var X#18)]
       ;EE#21[X#19,A#10[(var X#7)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= A#17[(var X#19)]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#20[X#6,(var X#18)]
       ;EE#21[X#19,A#10[(\ X#5.S#9)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {(A#17[(var X#19)],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=[.];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#18=A#17[(var X#19)];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|},
           T#14         |->  [.],
           S#2          |->  A#17[(var X#19)]}

and instantiated rules:

                                  (letrec {X#18=A#17[(var X#19)];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=(letrec {E#1} in A#17[(var X#19)]);X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=A#17[(var X#19)];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=A#17[(var X#19)];X#4=(\ X#5.S#9);E#8;EE#20[X#6,(var X#18)];EE#21[X#19,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[A#22[(letrec {E#1} in (var X#7))]]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= A#20[A#22[(\ X#5.S#9)]]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#21,A#17,T#14,T#3,A#10,A#20,A#22}
   Delta2 = {E#1}
   Delta3 = {((var X#7),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#22[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=A#20[A#22[[.]]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|},
           A#17         |->  A#20,
           T#14         |->  A#20[A#22[[.]]],
           A#10         |->  A#22,
           T#21         |->  A#22[[.]],
           T#23         |->  [.],
           S#2          |->  (var X#7)}

and instantiated rules:

                                  (letrec {X#18=A#20[A#22[(var X#7)]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=A#20[A#22[(letrec {E#1} in (var X#7))]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=A#20[A#22[(var X#7)]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=A#20[A#22[(\ X#5.S#9)]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[A#22[(letrec {E#1} in A#23[(var X#7)])]]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= A#20[A#22[A#23[(\ X#5.S#9)]]]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#21,A#17,T#14,T#3,A#10,A#20,A#22}
   Delta2 = {E#1}
   Delta3 = {(A#23[(var X#7)],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#22[A#23[[.]]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=A#20[A#22];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|},
           A#17         |->  A#20,
           T#14         |->  A#20[A#22],
           A#10         |->  A#22[A#23],
           T#21         |->  A#22,
           S#2          |->  A#23[(var X#7)]}

and instantiated rules:

                                  (letrec {X#18=A#20[A#22[A#23[(var X#7)]]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=A#20[A#22[(letrec {E#1} in A#23[(var X#7)])]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=A#20[A#22[A#23[(var X#7)]]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=A#20[A#22[A#23[(\ X#5.S#9)]]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[A#22[(app A#23[(var X#7)] T#24[(letrec {E#1} in S#2)])]]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= A#20[A#22[(app A#23[(\ X#5.S#9)] T#24[S#2])]]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#21,A#17,T#14,T#3,A#10,A#20}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#22[(app A#23[[.]] T#24[S#2])]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=A#20[A#22[(app A#23[(var X#7)] T#24)]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|},
           A#17         |->  A#20,
           T#14         |->  A#20[A#22[(app A#23[(var X#7)] T#24)]],
           T#21         |->  A#22[(app A#23[(var X#7)] T#24)],
           A#10         |->  A#22[(app A#23 T#24[S#2])]}

and instantiated rules:

                                  (letrec {X#18=A#20[A#22[(app A#23[(var X#7)] T#24[S#2])]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=A#20[A#22[(app A#23[(var X#7)] T#24[(letrec {E#1} in S#2)])]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=A#20[A#22[(app A#23[(var X#7)] T#24[S#2])]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=A#20[A#22[(app A#23[(\ X#5.S#9)] T#24[S#2])]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(letrec {E#1} in A#10[(var X#7)])]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= A#20[A#10[(\ X#5.S#9)]]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#17,T#14,T#3,A#10,A#20}
   Delta2 = {E#1}
   Delta3 = {(A#10[(var X#7)],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=A#20[[.]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|},
           A#17         |->  A#20,
           T#14         |->  A#20[[.]],
           T#21         |->  [.],
           S#2          |->  A#10[(var X#7)]}

and instantiated rules:

                                  (letrec {X#18=A#20[A#10[(var X#7)]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=A#20[(letrec {E#1} in A#10[(var X#7)])];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=A#20[A#10[(var X#7)]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=A#20[A#10[(\ X#5.S#9)]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(letrec {E#1} in A#21[A#10[(var X#7)]])]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= A#20[A#21[A#10[(\ X#5.S#9)]]]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#17,T#14,T#3,A#10,A#20}
   Delta2 = {E#1}
   Delta3 = {(A#21[A#10[(var X#7)]],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=A#20;X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#18=A#20[A#21[[.2]]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|},
           A#17         |->  A#20[A#21],
           T#14         |->  A#20,
           S#2          |->  A#21[A#10[(var X#7)]]}

and instantiated rules:

                                  (letrec {X#18=A#20[A#21[A#10[(var X#7)]]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=A#20[(letrec {E#1} in A#21[A#10[(var X#7)]])];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=A#20[A#21[A#10[(var X#7)]]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=A#20[A#21[A#10[(\ X#5.S#9)]]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[A#10[(var X#7)]] T#22[(letrec {E#1} in S#2)])]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[A#10[(\ X#5.S#9)]] T#22[S#2])]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#17,T#14,T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=A#20[(app A#21[A#10[(var X#7)]] T#22)];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] T#22[S#2])];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|},
           T#14         |->  A#20[(app A#21[A#10[(var X#7)]] T#22)],
           A#17         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[A#10[(var X#7)]] T#22[S#2])];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=A#20[(app A#21[A#10[(var X#7)]] T#22[(letrec {E#1} in S#2)])];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[A#10[(var X#7)]] T#22[S#2])];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=A#20[(app A#21[A#10[(\ X#5.S#9)]] T#22[S#2])];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(letrec {E#1} in (var X#7))]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= A#20[(\ X#5.S#9)]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#14,T#3,A#10,A#20}
   Delta2 = {E#1}
   Delta3 = {((var X#7),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#20[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=A#20[[.]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|},
           A#17         |->  [.],
           A#10         |->  A#20,
           T#14         |->  A#20[[.]],
           T#21         |->  [.],
           S#2          |->  (var X#7)}

and instantiated rules:

                                  (letrec {X#18=A#20[(var X#7)];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=A#20[(letrec {E#1} in (var X#7))];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=A#20[(var X#7)];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=A#20[(\ X#5.S#9)];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(letrec {E#1} in A#21[(var X#7)])]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= A#20[A#21[(\ X#5.S#9)]]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#14,T#3,A#10,A#20}
   Delta2 = {E#1}
   Delta3 = {(A#21[(var X#7)],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#20[A#21[[.]]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=A#20;X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|},
           A#17         |->  [.],
           A#10         |->  A#20[A#21],
           T#14         |->  A#20,
           S#2          |->  A#21[(var X#7)]}

and instantiated rules:

                                  (letrec {X#18=A#20[A#21[(var X#7)]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=A#20[(letrec {E#1} in A#21[(var X#7)])];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=A#20[A#21[(var X#7)]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=A#20[A#21[(\ X#5.S#9)]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(var X#7)] T#22[(letrec {E#1} in S#2)])]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(\ X#5.S#9)] T#22[S#2])]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#14,T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#20[(app A#21[[.]] T#22[S#2])]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=A#20[(app A#21[(var X#7)] T#22)];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|},
           A#17         |->  [.],
           T#14         |->  A#20[(app A#21[(var X#7)] T#22)],
           A#10         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(var X#7)] T#22[S#2])];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=A#20[(app A#21[(var X#7)] T#22[(letrec {E#1} in S#2)])];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(var X#7)] T#22[S#2])];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=A#20[(app A#21[(\ X#5.S#9)] T#22[S#2])];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= (letrec {E#1} in A#17[A#10[(var X#7)]])
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#18= A#17[A#10[(\ X#5.S#9)]]
       ;X#4= (\ X#5.S#9)
       ;E#8
       ;EE#19[X#6,(var X#18)]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {E#1}
   Delta3 = {(A#17[A#10[(var X#7)]],(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#18=[.];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#18=A#17[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|},
           T#14         |->  [.],
           S#2          |->  A#17[A#10[(var X#7)]]}

and instantiated rules:

                                  (letrec {X#18=A#17[A#10[(var X#7)]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {X#18=(letrec {E#1} in A#17[A#10[(var X#7)]]);X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#18=A#17[A#10[(var X#7)]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#18=A#17[A#10[(\ X#5.S#9)]];X#4=(\ X#5.S#9);E#8;EE#19[X#6,(var X#18)];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#1
     in
        (letrec
           X#4= (\ X#5.S#9)
          ;E#8
          ;EE#12[X#6,A#10[(var X#7)]]
          ;VV#13|X#7,(var X#4)|
        in
           A#11[(var X#6)]
        )
     )
    ,
     (letrec
        X#4= (\ X#5.S#9)
       ;E#8
       ;EE#12[X#6,A#10[(\ X#5.S#9)]]
       ;VV#13|X#7,(var X#4)|
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#10}
   Delta2 = {E#1}
   Delta3 = {((letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]),(letrec {E#1} in [.])),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#7),A#10[[.]]),
             ((var X#4),[.]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,cp-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}
      Delta1=  {A#10}
      Delta2=  {E#1}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),[.]),((var X#6),A#11[[.]]),((var X#7),A#10[[.]]),((var X#4),[.]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           S#2  |->  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])}

and instantiated rules:

                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -gc1->                        (letrec {E#1} in (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)]))
    ................................................................................
                                  (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(var X#7)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    -SR,cp-e2->                   (letrec {X#4=(\ X#5.S#9);E#8;EE#12[X#6,A#10[(\ X#5.S#9)]];VV#13|X#7,(var X#4)|} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#4} in (letrec {E#5} in T#8[(letrec {E#1} in S#2)]))
    ,
     (letrec {E#4;E#5} in T#8[S#2])
  )

where

   Delta1 = {T#7,T#3}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             [{E#4},(letrec {E#5} in [.])]}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-in1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in (letrec {E#5} in S#6))
    -SR,llet-in1->                (letrec {E#4;E#5} in S#6)
    and constraints: E#4/= {}, E#5/= {}, ({E#4},(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in (letrec {E#5} in S#6))}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),[{E#4},(letrec {E#5} in [.])]}


and found solution:

    Sol = {T#3  |->  (letrec {E#4} in (letrec {E#5} in T#8)),
           T#7  |->  (letrec {E#5} in T#8),
           S#6  |->  T#8[S#2]}

and instantiated rules:

                                  (letrec {E#4} in (letrec {E#5} in T#8[S#2]))
    -gc1->                        (letrec {E#4} in (letrec {E#5} in T#8[(letrec {E#1} in S#2)]))
    ................................................................................
                                  (letrec {E#4} in (letrec {E#5} in T#8[S#2]))
    -SR,llet-in1->                (letrec {E#4;E#5} in T#8[S#2])
    

================================================================================
Critical Pair:

  (
     (letrec {E#4} in (letrec {X#9=T#8[(letrec {E#1} in S#2)];E#11} in S#6))
    ,
     (letrec {X#9=T#8[S#2];E#11;E#4} in S#6)
  )

where

   Delta1 = {T#7,T#3}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             [{E#4},(letrec {X#9=T#8[S#2];E#11} in [.])]}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-in1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in (letrec {E#5} in S#6))
    -SR,llet-in1->                (letrec {E#4;E#5} in S#6)
    and constraints: E#4/= {}, E#5/= {}, ({E#4},(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in (letrec {E#5} in S#6))}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),[{E#4},(letrec {E#5} in [.])]}


and found solution:

    Sol = {T#3   |->  (letrec {E#4} in (letrec {X#9=T#8;E#11} in S#6)),
           T#7   |->  (letrec {X#9=T#8;E#11} in S#6),
           E#5   |->  {X#9=T#8[S#2];E#11},
           E#10  |->  {E#11}}

and instantiated rules:

                                  (letrec {E#4} in (letrec {X#9=T#8[S#2];E#11} in S#6))
    -gc1->                        (letrec {E#4} in (letrec {X#9=T#8[(letrec {E#1} in S#2)];E#11} in S#6))
    ................................................................................
                                  (letrec {E#4} in (letrec {X#9=T#8[S#2];E#11} in S#6))
    -SR,llet-in1->                (letrec {X#9=T#8[S#2];E#11;E#4} in S#6)
    

================================================================================
Critical Pair:

  (
     (letrec {E#4} in (letrec {E#1} in (letrec {E#5} in S#6)))
    ,
     (letrec {E#4;E#5} in S#6)
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {((letrec {E#5} in S#6),(letrec {E#1} in [.])),
             [{E#4},(letrec {E#5} in [.])]}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-in1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in (letrec {E#5} in S#6))
    -SR,llet-in1->                (letrec {E#4;E#5} in S#6)
    and constraints: E#4/= {}, E#5/= {}, ({E#4},(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in (letrec {E#5} in S#6))}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),[{E#4},(letrec {E#5} in [.])]}


and found solution:

    Sol = {T#3  |->  (letrec {E#4} in [.]),
           T#7  |->  [.],
           S#2  |->  (letrec {E#5} in S#6)}

and instantiated rules:

                                  (letrec {E#4} in (letrec {E#5} in S#6))
    -gc1->                        (letrec {E#4} in (letrec {E#1} in (letrec {E#5} in S#6)))
    ................................................................................
                                  (letrec {E#4} in (letrec {E#5} in S#6))
    -SR,llet-in1->                (letrec {E#4;E#5} in S#6)
    

================================================================================
Critical Pair:

  (
     (letrec {X#8=T#7[(letrec {E#1} in S#2)];E#10} in (letrec {E#5} in S#6))
    ,
     (letrec {X#8=T#7[S#2];E#10;E#5} in S#6)
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             [{X#8=T#7[S#2];E#10},(letrec {E#5} in [.])]}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-in1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in (letrec {E#5} in S#6))
    -SR,llet-in1->                (letrec {E#4;E#5} in S#6)
    and constraints: E#4/= {}, E#5/= {}, ({E#4},(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in (letrec {E#5} in S#6))}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),[{E#4},(letrec {E#5} in [.])]}


and found solution:

    Sol = {T#3  |->  (letrec {X#8=T#7;E#10} in (letrec {E#5} in S#6)),
           E#4  |->  {X#8=T#7[S#2];E#10},
           E#9  |->  {E#10}}

and instantiated rules:

                                  (letrec {X#8=T#7[S#2];E#10} in (letrec {E#5} in S#6))
    -gc1->                        (letrec {X#8=T#7[(letrec {E#1} in S#2)];E#10} in (letrec {E#5} in S#6))
    ................................................................................
                                  (letrec {X#8=T#7[S#2];E#10} in (letrec {E#5} in S#6))
    -SR,llet-in1->                (letrec {X#8=T#7[S#2];E#10;E#5} in S#6)
    

================================================================================
Critical Pair:

  (
     (letrec {E#1} in (letrec {E#4} in (letrec {E#5} in S#6)))
    ,
     (letrec {E#4;E#5} in S#6)
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {((letrec {E#4} in (letrec {E#5} in S#6)),(letrec {E#1} in [.])),
             [{E#4},(letrec {E#5} in [.])]}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-in1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in (letrec {E#5} in S#6))
    -SR,llet-in1->                (letrec {E#4;E#5} in S#6)
    and constraints: E#4/= {}, E#5/= {}, ({E#4},(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in (letrec {E#5} in S#6))}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),[{E#4},(letrec {E#5} in [.])]}


and found solution:

    Sol = {T#3  |->  [.],
           S#2  |->  (letrec {E#4} in (letrec {E#5} in S#6))}

and instantiated rules:

                                  (letrec {E#4} in (letrec {E#5} in S#6))
    -gc1->                        (letrec {E#1} in (letrec {E#4} in (letrec {E#5} in S#6)))
    ................................................................................
                                  (letrec {E#4} in (letrec {E#5} in S#6))
    -SR,llet-in1->                (letrec {E#4;E#5} in S#6)
    

================================================================================
Critical Pair:

  (
     (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#10[(letrec {E#1} in (var X#4))])
    ,
     (letrec {X#4=S#7;E#5;E#6} in A#10[(var X#4)])
  )

where

   Delta1 = {A#8,T#9,T#3,A#10}
   Delta2 = {E#1,E#5}
   Delta3 = {((var X#4),(letrec {E#1} in [.])),
             (A#10[(var X#4)],(letrec {E#5} in [.])),
             [{E#6},(letrec {E#5} in [.])],
             ((var X#4),A#10[[.]]),
             ((var X#4),A#10[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])
    -SR,llet-e1->                 (letrec {X#4=S#7;E#5;E#6} in A#8[(var X#4)])
    and constraints: E#5/= {}, (A#8[(var X#4)],(letrec {E#5} in [.])), ({E#6},(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(A#8[(var X#4)],(letrec {E#5} in [.])),[{E#6},(letrec {E#5} in [.])],((var X#4),A#8[[.]]),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#10[[.]]),
           A#8   |->  A#10,
           T#9   |->  A#10[[.]],
           T#11  |->  [.],
           S#2   |->  (var X#4)}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#10[(var X#4)])
    -gc1->                        (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#10[(letrec {E#1} in (var X#4))])
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#10[(var X#4)])
    -SR,llet-e1->                 (letrec {X#4=S#7;E#5;E#6} in A#10[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#5} in S#7)
       ;E#6
     in
        A#10[(letrec {E#1} in A#11[(var X#4)])]
     )
    ,
     (letrec {X#4=S#7;E#5;E#6} in A#10[A#11[(var X#4)]])
  )

where

   Delta1 = {A#8,T#9,T#3,A#10}
   Delta2 = {E#1,E#5}
   Delta3 = {(A#11[(var X#4)],(letrec {E#1} in [.])),
             (A#10[A#11[(var X#4)]],(letrec {E#5} in [.])),
             [{E#6},(letrec {E#5} in [.])],
             ((var X#4),A#10[A#11[[.]]]),
             ((var X#4),A#10[A#11[[.]]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])
    -SR,llet-e1->                 (letrec {X#4=S#7;E#5;E#6} in A#8[(var X#4)])
    and constraints: E#5/= {}, (A#8[(var X#4)],(letrec {E#5} in [.])), ({E#6},(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(A#8[(var X#4)],(letrec {E#5} in [.])),[{E#6},(letrec {E#5} in [.])],((var X#4),A#8[[.]]),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3  |->  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#10),
           A#8  |->  A#10[A#11],
           T#9  |->  A#10,
           S#2  |->  A#11[(var X#4)]}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#10[A#11[(var X#4)]])
    -gc1->                        (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#10[(letrec {E#1} in A#11[(var X#4)])])
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#10[A#11[(var X#4)]])
    -SR,llet-e1->                 (letrec {X#4=S#7;E#5;E#6} in A#10[A#11[(var X#4)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#5} in S#7)
       ;E#6
     in
        A#10[(app A#11[(var X#4)] T#12[(letrec {E#1} in S#2)])]
     )
    ,
     (letrec {X#4=S#7;E#5;E#6} in A#10[(app A#11[(var X#4)] T#12[S#2])])
  )

where

   Delta1 = {A#8,T#9,T#3}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (A#10[(app A#11[(var X#4)] T#12[S#2])],(letrec {E#5} in [.])),
             [{E#6},(letrec {E#5} in [.])],
             ((var X#4),A#10[(app A#11[[.]] T#12[S#2])]),
             ((var X#4),A#10[(app A#11[[.]] T#12[S#2])])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])
    -SR,llet-e1->                 (letrec {X#4=S#7;E#5;E#6} in A#8[(var X#4)])
    and constraints: E#5/= {}, (A#8[(var X#4)],(letrec {E#5} in [.])), ({E#6},(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(A#8[(var X#4)],(letrec {E#5} in [.])),[{E#6},(letrec {E#5} in [.])],((var X#4),A#8[[.]]),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3  |->  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#10[(app A#11[(var X#4)] T#12)]),
           T#9  |->  A#10[(app A#11[(var X#4)] T#12)],
           A#8  |->  A#10[(app A#11 T#12[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#10[(app A#11[(var X#4)] T#12[S#2])])
    -gc1->                        (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#10[(app A#11[(var X#4)] T#12[(letrec {E#1} in S#2)])])
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#10[(app A#11[(var X#4)] T#12[S#2])])
    -SR,llet-e1->                 (letrec {X#4=S#7;E#5;E#6} in A#10[(app A#11[(var X#4)] T#12[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#4=(letrec {E#5} in S#7);E#6} in (letrec {E#1} in A#8[(var X#4)]))
    ,
     (letrec {X#4=S#7;E#5;E#6} in A#8[(var X#4)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#5}
   Delta3 = {(A#8[(var X#4)],(letrec {E#1} in [.])),
             (A#8[(var X#4)],(letrec {E#5} in [.])),
             [{E#6},(letrec {E#5} in [.])],
             ((var X#4),A#8[[.]]),
             ((var X#4),A#8[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])
    -SR,llet-e1->                 (letrec {X#4=S#7;E#5;E#6} in A#8[(var X#4)])
    and constraints: E#5/= {}, (A#8[(var X#4)],(letrec {E#5} in [.])), ({E#6},(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(A#8[(var X#4)],(letrec {E#5} in [.])),[{E#6},(letrec {E#5} in [.])],((var X#4),A#8[[.]]),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3  |->  (letrec {X#4=(letrec {E#5} in S#7);E#6} in [.]),
           T#9  |->  [.],
           S#2  |->  A#8[(var X#4)]}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])
    -gc1->                        (letrec {X#4=(letrec {E#5} in S#7);E#6} in (letrec {E#1} in A#8[(var X#4)]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])
    -SR,llet-e1->                 (letrec {X#4=S#7;E#5;E#6} in A#8[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#5} in T#12[(letrec {E#1} in S#2)])
       ;E#6
     in
        A#8[(var X#4)]
     )
    ,
     (letrec {X#4=T#12[S#2];E#5;E#6} in A#8[(var X#4)])
  )

where

   Delta1 = {T#9,T#3}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (A#8[(var X#4)],(letrec {E#5} in [.])),
             [{E#6},(letrec {E#5} in [.])],
             ((var X#4),A#8[[.]]),
             ((var X#4),A#8[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])
    -SR,llet-e1->                 (letrec {X#4=S#7;E#5;E#6} in A#8[(var X#4)])
    and constraints: E#5/= {}, (A#8[(var X#4)],(letrec {E#5} in [.])), ({E#6},(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(A#8[(var X#4)],(letrec {E#5} in [.])),[{E#6},(letrec {E#5} in [.])],((var X#4),A#8[[.]]),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(letrec {E#5} in T#12);E#6} in A#8[(var X#4)]),
           X#10  |->  X#4,
           E#11  |->  {E#6},
           T#9   |->  (letrec {E#5} in T#12),
           S#7   |->  T#12[S#2]}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#5} in T#12[S#2]);E#6} in A#8[(var X#4)])
    -gc1->                        (letrec {X#4=(letrec {E#5} in T#12[(letrec {E#1} in S#2)]);E#6} in A#8[(var X#4)])
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in T#12[S#2]);E#6} in A#8[(var X#4)])
    -SR,llet-e1->                 (letrec {X#4=T#12[S#2];E#5;E#6} in A#8[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {X#13=T#12[(letrec {E#1} in S#2)];E#15} in S#7)
       ;E#6
     in
        A#8[(var X#4)]
     )
    ,
     (letrec {X#13=T#12[S#2];X#4=S#7;E#15;E#6} in A#8[(var X#4)])
  )

where

   Delta1 = {T#9,T#3}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (A#8[(var X#4)],(letrec {X#13=T#12[S#2];E#15} in [.])),
             [{E#6},(letrec {X#13=T#12[S#2];E#15} in [.])],
             ((var X#4),A#8[[.]]),
             ((var X#4),A#8[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])
    -SR,llet-e1->                 (letrec {X#4=S#7;E#5;E#6} in A#8[(var X#4)])
    and constraints: E#5/= {}, (A#8[(var X#4)],(letrec {E#5} in [.])), ({E#6},(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(A#8[(var X#4)],(letrec {E#5} in [.])),[{E#6},(letrec {E#5} in [.])],((var X#4),A#8[[.]]),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(letrec {X#13=T#12;E#15} in S#7);E#6} in A#8[(var X#4)]),
           X#10  |->  X#4,
           E#11  |->  {E#6},
           T#9   |->  (letrec {X#13=T#12;E#15} in S#7),
           E#5   |->  {X#13=T#12[S#2];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {X#4=(letrec {X#13=T#12[S#2];E#15} in S#7);E#6} in A#8[(var X#4)])
    -gc1->                        (letrec {X#4=(letrec {X#13=T#12[(letrec {E#1} in S#2)];E#15} in S#7);E#6} in A#8[(var X#4)])
    ................................................................................
                                  (letrec {X#4=(letrec {X#13=T#12[S#2];E#15} in S#7);E#6} in A#8[(var X#4)])
    -SR,llet-e1->                 (letrec {X#13=T#12[S#2];X#4=S#7;E#15;E#6} in A#8[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#4=(letrec {E#1} in (letrec {E#5} in S#7));E#6} in A#8[(var X#4)])
    ,
     (letrec {X#4=S#7;E#5;E#6} in A#8[(var X#4)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#5}
   Delta3 = {((letrec {E#5} in S#7),(letrec {E#1} in [.])),
             (A#8[(var X#4)],(letrec {E#5} in [.])),
             [{E#6},(letrec {E#5} in [.])],
             ((var X#4),A#8[[.]]),
             ((var X#4),A#8[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])
    -SR,llet-e1->                 (letrec {X#4=S#7;E#5;E#6} in A#8[(var X#4)])
    and constraints: E#5/= {}, (A#8[(var X#4)],(letrec {E#5} in [.])), ({E#6},(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(A#8[(var X#4)],(letrec {E#5} in [.])),[{E#6},(letrec {E#5} in [.])],((var X#4),A#8[[.]]),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=[.];E#6} in A#8[(var X#4)]),
           X#10  |->  X#4,
           E#11  |->  {E#6},
           T#9   |->  [.],
           S#2   |->  (letrec {E#5} in S#7)}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])
    -gc1->                        (letrec {X#4=(letrec {E#1} in (letrec {E#5} in S#7));E#6} in A#8[(var X#4)])
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])
    -SR,llet-e1->                 (letrec {X#4=S#7;E#5;E#6} in A#8[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= T#9[(letrec {E#1} in S#2)]
       ;X#4= (letrec {E#5} in S#7)
       ;E#12
     in
        A#8[(var X#4)]
     )
    ,
     (letrec {X#10=T#9[S#2];X#4=S#7;E#12;E#5} in A#8[(var X#4)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (A#8[(var X#4)],(letrec {E#5} in [.])),
             [{X#10=T#9[S#2];E#12},(letrec {E#5} in [.])],
             ((var X#4),A#8[[.]]),
             ((var X#4),A#8[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])
    -SR,llet-e1->                 (letrec {X#4=S#7;E#5;E#6} in A#8[(var X#4)])
    and constraints: E#5/= {}, (A#8[(var X#4)],(letrec {E#5} in [.])), ({E#6},(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(A#8[(var X#4)],(letrec {E#5} in [.])),[{E#6},(letrec {E#5} in [.])],((var X#4),A#8[[.]]),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#10=T#9;X#4=(letrec {E#5} in S#7);E#12} in A#8[(var X#4)]),
           E#6   |->  {X#10=T#9[S#2];E#12},
           E#11  |->  {X#4=(letrec {E#5} in S#7);E#12}}

and instantiated rules:

                                  (letrec {X#10=T#9[S#2];X#4=(letrec {E#5} in S#7);E#12} in A#8[(var X#4)])
    -gc1->                        (letrec {X#10=T#9[(letrec {E#1} in S#2)];X#4=(letrec {E#5} in S#7);E#12} in A#8[(var X#4)])
    ................................................................................
                                  (letrec {X#10=T#9[S#2];X#4=(letrec {E#5} in S#7);E#12} in A#8[(var X#4)])
    -SR,llet-e1->                 (letrec {X#10=T#9[S#2];X#4=S#7;E#12;E#5} in A#8[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#1} in (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)]))
    ,
     (letrec {X#4=S#7;E#5;E#6} in A#8[(var X#4)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#5}
   Delta3 = {((letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)]),(letrec {E#1} in [.])),
             (A#8[(var X#4)],(letrec {E#5} in [.])),
             [{E#6},(letrec {E#5} in [.])],
             ((var X#4),A#8[[.]]),
             ((var X#4),A#8[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])
    -SR,llet-e1->                 (letrec {X#4=S#7;E#5;E#6} in A#8[(var X#4)])
    and constraints: E#5/= {}, (A#8[(var X#4)],(letrec {E#5} in [.])), ({E#6},(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(A#8[(var X#4)],(letrec {E#5} in [.])),[{E#6},(letrec {E#5} in [.])],((var X#4),A#8[[.]]),((var X#4),A#8[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           S#2  |->  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])
    -gc1->                        (letrec {E#1} in (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#5} in S#7);E#6} in A#8[(var X#4)])
    -SR,llet-e1->                 (letrec {X#4=S#7;E#5;E#6} in A#8[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#6} in S#8)
       ;E#7
       ;EE#10[X#5,(var X#4)]
     in
        A#12[(letrec {E#1} in (var X#5))]
     )
    ,
     (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#12[(var X#5)])
  )

where

   Delta1 = {A#9,T#11,T#3,A#12}
   Delta2 = {E#1,E#6}
   Delta3 = {((var X#5),(letrec {E#1} in [.])),
             ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),
             (A#12[(var X#5)],(letrec {E#6} in [.])),
             [{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#12[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#12[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#12[[.]]),
           A#9   |->  A#12,
           T#11  |->  A#12[[.]],
           T#13  |->  [.],
           S#2   |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#12[(var X#5)])
    -gc1->                        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#12[(letrec {E#1} in (var X#5))])
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#12[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#12[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#6} in S#8)
       ;E#7
       ;EE#10[X#5,(var X#4)]
     in
        A#12[(letrec {E#1} in A#13[(var X#5)])]
     )
    ,
     (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#12[A#13[(var X#5)]])
  )

where

   Delta1 = {A#9,T#11,T#3,A#12}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#13[(var X#5)],(letrec {E#1} in [.])),
             ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),
             (A#12[A#13[(var X#5)]],(letrec {E#6} in [.])),
             [{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#12[A#13[[.]]]),
             ((var X#4),[.]),
             ((var X#5),A#12[A#13[[.]]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#12),
           A#9   |->  A#12[A#13],
           T#11  |->  A#12,
           S#2   |->  A#13[(var X#5)]}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#12[A#13[(var X#5)]])
    -gc1->                        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#12[(letrec {E#1} in A#13[(var X#5)])])
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#12[A#13[(var X#5)]])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#12[A#13[(var X#5)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#6} in S#8)
       ;E#7
       ;EE#10[X#5,(var X#4)]
     in
        A#12[(app A#13[(var X#5)] T#14[(letrec {E#1} in S#2)])]
     )
    ,
     (letrec
        X#4= S#8
       ;E#6
       ;E#7
       ;EE#10[X#5,(var X#4)]
     in
        A#12[(app A#13[(var X#5)] T#14[S#2])]
     )
  )

where

   Delta1 = {A#9,T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),
             (A#12[(app A#13[(var X#5)] T#14[S#2])],(letrec {E#6} in [.])),
             [{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#12[(app A#13[[.]] T#14[S#2])]),
             ((var X#4),[.]),
             ((var X#5),A#12[(app A#13[[.]] T#14[S#2])])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#12[(app A#13[(var X#5)] T#14)]),
           T#11  |->  A#12[(app A#13[(var X#5)] T#14)],
           A#9   |->  A#12[(app A#13 T#14[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#12[(app A#13[(var X#5)] T#14[S#2])])
    -gc1->                        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#12[(app A#13[(var X#5)] T#14[(letrec {E#1} in S#2)])])
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#12[(app A#13[(var X#5)] T#14[S#2])])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#12[(app A#13[(var X#5)] T#14[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#6} in S#8)
       ;E#7
       ;EE#10[X#5,(var X#4)]
     in
        (letrec {E#1} in A#9[(var X#5)])
     )
    ,
     (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#9[(var X#5)],(letrec {E#1} in [.])),
             ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in [.]),
           T#11  |->  [.],
           S#2   |->  A#9[(var X#5)]}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in (letrec {E#1} in A#9[(var X#5)]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#6} in T#14[(letrec {E#1} in S#2)])
       ;E#7
       ;EE#10[X#5,(var X#4)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#4=T#14[S#2];E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
  )

where

   Delta1 = {T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(letrec {E#6} in T#14);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)]),
           X#12  |->  X#4,
           E#13  |->  {E#7;EE#10[X#5,(var X#4)]},
           T#11  |->  (letrec {E#6} in T#14),
           S#8   |->  T#14[S#2]}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#6} in T#14[S#2]);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#4=(letrec {E#6} in T#14[(letrec {E#1} in S#2)]);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in T#14[S#2]);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=T#14[S#2];E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {X#15=T#14[(letrec {E#1} in S#2)];E#17} in S#8)
       ;E#7
       ;EE#10[X#5,(var X#4)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#15= T#14[S#2]
       ;X#4= S#8
       ;E#17
       ;E#7
       ;EE#10[X#5,(var X#4)]
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#15=T#14[S#2];E#17;E#7;EE#10[X#5,(var X#4)]} in [.])),
             (A#9[(var X#5)],(letrec {X#15=T#14[S#2];E#17} in [.])),
             [{E#7;EE#10[X#5,(var X#4)]},(letrec {X#15=T#14[S#2];E#17} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=(letrec {X#15=T#14;E#17} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)]),
           X#12  |->  X#4,
           E#13  |->  {E#7;EE#10[X#5,(var X#4)]},
           T#11  |->  (letrec {X#15=T#14;E#17} in S#8),
           E#6   |->  {X#15=T#14[S#2];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {X#4=(letrec {X#15=T#14[S#2];E#17} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#4=(letrec {X#15=T#14[(letrec {E#1} in S#2)];E#17} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#4=(letrec {X#15=T#14[S#2];E#17} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#15=T#14[S#2];X#4=S#8;E#17;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#1} in (letrec {E#6} in S#8))
       ;E#7
       ;EE#10[X#5,(var X#4)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {((letrec {E#6} in S#8),(letrec {E#1} in [.])),
             ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#4=[.];E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)]),
           X#12  |->  X#4,
           E#13  |->  {E#7;EE#10[X#5,(var X#4)]},
           T#11  |->  [.],
           S#2   |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#4=(letrec {E#1} in (letrec {E#6} in S#8));E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#12= T#11[(letrec {E#1} in S#2)]
       ;X#4= (letrec {E#6} in S#8)
       ;E#14
       ;EE#10[X#5,(var X#4)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#12= T#11[S#2]
       ;X#4= S#8
       ;E#14
       ;E#6
       ;EE#10[X#5,(var X#4)]
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#12=T#11[S#2];E#14;E#6;EE#10[X#5,(var X#4)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#12=T#11[S#2];E#14;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#12=T#11;X#4=(letrec {E#6} in S#8);E#14;EE#10[X#5,(var X#4)]} in A#9[(var X#5)]),
           E#7   |->  {X#12=T#11[S#2];E#14},
           E#13  |->  {X#4=(letrec {E#6} in S#8);E#14;EE#10[X#5,(var X#4)]}}

and instantiated rules:

                                  (letrec {X#12=T#11[S#2];X#4=(letrec {E#6} in S#8);E#14;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#12=T#11[(letrec {E#1} in S#2)];X#4=(letrec {E#6} in S#8);E#14;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#12=T#11[S#2];X#4=(letrec {E#6} in S#8);E#14;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#12=T#11[S#2];X#4=S#8;E#14;E#6;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#6} in S#8)
       ;X#5= A#15[(letrec {E#1} in (var X#4))]
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#4=S#8;X#5=A#15[(var X#4)];E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {A#14,T#11,T#3,A#15}
   Delta2 = {E#1,E#6}
   Delta3 = {((var X#4),(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#5=A#15[(var X#4)];E#6;E#7} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#5=A#15[(var X#4)];E#7},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#15[[.]];E#7} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#12         |->  X#5,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7},
           A#14         |->  A#15,
           T#11         |->  A#15[[.]],
           T#16         |->  [.],
           S#2          |->  (var X#4)}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#15[(var X#4)];E#7} in A#9[(var X#5)])
    -gc1->                        (letrec {X#4=(letrec {E#6} in S#8);X#5=A#15[(letrec {E#1} in (var X#4))];E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#15[(var X#4)];E#7} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;X#5=A#15[(var X#4)];E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#6} in S#8)
       ;X#5= A#15[(letrec {E#1} in A#16[(var X#4)])]
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#4=S#8;X#5=A#15[A#16[(var X#4)]];E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {A#14,T#11,T#3,A#15}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#16[(var X#4)],(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#5=A#15[A#16[(var X#4)]];E#6;E#7} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#5=A#15[A#16[(var X#4)]];E#7},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#15;E#7} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {[.1]=A#15[A#16[[.2]]]},
           X#12         |->  X#5,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7},
           A#14         |->  A#15[A#16],
           T#11         |->  A#15,
           S#2          |->  A#16[(var X#4)]}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#15[A#16[(var X#4)]];E#7} in A#9[(var X#5)])
    -gc1->                        (letrec {X#4=(letrec {E#6} in S#8);X#5=A#15[(letrec {E#1} in A#16[(var X#4)])];E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#15[A#16[(var X#4)]];E#7} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;X#5=A#15[A#16[(var X#4)]];E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#6} in S#8)
       ;X#5= A#15[(app A#16[(var X#4)] T#17[(letrec {E#1} in S#2)])]
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#4= S#8
       ;X#5= A#15[(app A#16[(var X#4)] T#17[S#2])]
       ;E#6
       ;E#7
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#5=A#15[(app A#16[(var X#4)] T#17[S#2])];E#6;E#7} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#5=A#15[(app A#16[(var X#4)] T#17[S#2])];E#7},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#15[(app A#16[(var X#4)] T#17)];E#7} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {[.1]=A#15[(app A#16[[.2]] T#17[S#2])]},
           X#12         |->  X#5,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7},
           T#11         |->  A#15[(app A#16[(var X#4)] T#17)],
           A#14         |->  A#15[(app A#16 T#17[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#15[(app A#16[(var X#4)] T#17[S#2])];E#7} in A#9[(var X#5)])
    -gc1->                        (letrec {X#4=(letrec {E#6} in S#8);X#5=A#15[(app A#16[(var X#4)] T#17[(letrec {E#1} in S#2)])];E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#15[(app A#16[(var X#4)] T#17[S#2])];E#7} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;X#5=A#15[(app A#16[(var X#4)] T#17[S#2])];E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#6} in S#8)
       ;X#5= (letrec {E#1} in A#14[(var X#4)])
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#4=S#8;X#5=A#14[(var X#4)];E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#14[(var X#4)],(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#5=A#14[(var X#4)];E#6;E#7} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#5=A#14[(var X#4)];E#7},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(letrec {E#6} in S#8);X#5=[.];E#7} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {[.1]=A#14[[.2]]},
           X#12         |->  X#5,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7},
           T#11         |->  [.],
           S#2          |->  A#14[(var X#4)]}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#14[(var X#4)];E#7} in A#9[(var X#5)])
    -gc1->                        (letrec {X#4=(letrec {E#6} in S#8);X#5=(letrec {E#1} in A#14[(var X#4)]);E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#14[(var X#4)];E#7} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;X#5=A#14[(var X#4)];E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#6} in S#8)
       ;X#5= A#17[(letrec {E#1} in (var X#15))]
       ;E#7
       ;EE#16[X#15,(var X#4)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#4= S#8
       ;X#5= A#17[(var X#15)]
       ;E#6
       ;E#7
       ;EE#16[X#15,(var X#4)]
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#17}
   Delta2 = {E#1,E#6}
   Delta3 = {((var X#15),(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#5=A#17[(var X#15)];E#6;E#7;EE#16[X#15,(var X#4)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#5=A#17[(var X#15)];E#7;EE#16[X#15,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#17[[.]];E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {[.1]=A#17[(var X#15)];EE#16[X#15,[.2]]},
           X#12         |->  X#5,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7;EE#16[X#15,(var X#4)]},
           A#14         |->  A#17,
           T#11         |->  A#17[[.]],
           T#18         |->  [.],
           S#2          |->  (var X#15)}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#17[(var X#15)];E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#4=(letrec {E#6} in S#8);X#5=A#17[(letrec {E#1} in (var X#15))];E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#17[(var X#15)];E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;X#5=A#17[(var X#15)];E#6;E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#6} in S#8)
       ;X#5= A#17[(letrec {E#1} in A#18[(var X#15)])]
       ;E#7
       ;EE#16[X#15,(var X#4)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#4= S#8
       ;X#5= A#17[A#18[(var X#15)]]
       ;E#6
       ;E#7
       ;EE#16[X#15,(var X#4)]
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#17}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#18[(var X#15)],(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#5=A#17[A#18[(var X#15)]];E#6;E#7;EE#16[X#15,(var X#4)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#5=A#17[A#18[(var X#15)]];E#7;EE#16[X#15,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#17;E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {[.1]=A#17[A#18[(var X#15)]];EE#16[X#15,[.2]]},
           X#12         |->  X#5,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7;EE#16[X#15,(var X#4)]},
           A#14         |->  A#17[A#18],
           T#11         |->  A#17,
           S#2          |->  A#18[(var X#15)]}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#17[A#18[(var X#15)]];E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#4=(letrec {E#6} in S#8);X#5=A#17[(letrec {E#1} in A#18[(var X#15)])];E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#17[A#18[(var X#15)]];E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;X#5=A#17[A#18[(var X#15)]];E#6;E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#6} in S#8)
       ;X#5= A#17[(app A#18[(var X#15)] T#19[(letrec {E#1} in S#2)])]
       ;E#7
       ;EE#16[X#15,(var X#4)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#4= S#8
       ;X#5= A#17[(app A#18[(var X#15)] T#19[S#2])]
       ;E#6
       ;E#7
       ;EE#16[X#15,(var X#4)]
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#5=A#17[(app A#18[(var X#15)] T#19[S#2])];E#6;E#7;EE#16[X#15,(var X#4)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#5=A#17[(app A#18[(var X#15)] T#19[S#2])];E#7;EE#16[X#15,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#17[(app A#18[(var X#15)] T#19)];E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {[.1]=A#17[(app A#18[(var X#15)] T#19[S#2])];EE#16[X#15,[.2]]},
           X#12         |->  X#5,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7;EE#16[X#15,(var X#4)]},
           T#11         |->  A#17[(app A#18[(var X#15)] T#19)],
           A#14         |->  A#17[(app A#18 T#19[S#2])]}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#17[(app A#18[(var X#15)] T#19[S#2])];E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#4=(letrec {E#6} in S#8);X#5=A#17[(app A#18[(var X#15)] T#19[(letrec {E#1} in S#2)])];E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#17[(app A#18[(var X#15)] T#19[S#2])];E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;X#5=A#17[(app A#18[(var X#15)] T#19[S#2])];E#6;E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#6} in S#8)
       ;X#5= (letrec {E#1} in A#14[(var X#15)])
       ;E#7
       ;EE#16[X#15,(var X#4)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#4= S#8
       ;X#5= A#14[(var X#15)]
       ;E#6
       ;E#7
       ;EE#16[X#15,(var X#4)]
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#14[(var X#15)],(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#5=A#14[(var X#15)];E#6;E#7;EE#16[X#15,(var X#4)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#5=A#14[(var X#15)];E#7;EE#16[X#15,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(letrec {E#6} in S#8);X#5=[.];E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {[.1]=A#14[(var X#15)];EE#16[X#15,[.2]]},
           X#12         |->  X#5,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7;EE#16[X#15,(var X#4)]},
           T#11         |->  [.],
           S#2          |->  A#14[(var X#15)]}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#14[(var X#15)];E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#4=(letrec {E#6} in S#8);X#5=(letrec {E#1} in A#14[(var X#15)]);E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);X#5=A#14[(var X#15)];E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;X#5=A#14[(var X#15)];E#6;E#7;EE#16[X#15,(var X#4)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#19[(letrec {E#1} in (var X#16))]
       ;X#4= (letrec {E#6} in S#8)
       ;E#7
       ;EE#17[X#5,(var X#15)]
       ;EE#18[X#16,(var X#4)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#15= A#19[(var X#16)]
       ;X#4= S#8
       ;E#6
       ;E#7
       ;EE#17[X#5,(var X#15)]
       ;EE#18[X#16,(var X#4)]
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#19}
   Delta2 = {E#1,E#6}
   Delta3 = {((var X#16),(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#15=A#19[(var X#16)];E#6;E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#15=A#19[(var X#16)];E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#19[[.]];X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {X#15=A#19[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#12         |->  X#15,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]},
           A#14         |->  A#19,
           T#11         |->  A#19[[.]],
           T#20         |->  [.],
           S#2          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#15=A#19[(var X#16)];X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#15=A#19[(letrec {E#1} in (var X#16))];X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#15=A#19[(var X#16)];X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#15=A#19[(var X#16)];X#4=S#8;E#6;E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#19[(letrec {E#1} in A#20[(var X#16)])]
       ;X#4= (letrec {E#6} in S#8)
       ;E#7
       ;EE#17[X#5,(var X#15)]
       ;EE#18[X#16,(var X#4)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#15= A#19[A#20[(var X#16)]]
       ;X#4= S#8
       ;E#6
       ;E#7
       ;EE#17[X#5,(var X#15)]
       ;EE#18[X#16,(var X#4)]
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#19}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#20[(var X#16)],(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#15=A#19[A#20[(var X#16)]];E#6;E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#15=A#19[A#20[(var X#16)]];E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#19;X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {X#15=A#19[A#20[(var X#16)]];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#12         |->  X#15,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]},
           A#14         |->  A#19[A#20],
           T#11         |->  A#19,
           S#2          |->  A#20[(var X#16)]}

and instantiated rules:

                                  (letrec {X#15=A#19[A#20[(var X#16)]];X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#15=A#19[(letrec {E#1} in A#20[(var X#16)])];X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#15=A#19[A#20[(var X#16)]];X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#15=A#19[A#20[(var X#16)]];X#4=S#8;E#6;E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#19[(app A#20[(var X#16)] T#21[(letrec {E#1} in S#2)])]
       ;X#4= (letrec {E#6} in S#8)
       ;E#7
       ;EE#17[X#5,(var X#15)]
       ;EE#18[X#16,(var X#4)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#15= A#19[(app A#20[(var X#16)] T#21[S#2])]
       ;X#4= S#8
       ;E#6
       ;E#7
       ;EE#17[X#5,(var X#15)]
       ;EE#18[X#16,(var X#4)]
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#15=A#19[(app A#20[(var X#16)] T#21[S#2])];E#6;E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#15=A#19[(app A#20[(var X#16)] T#21[S#2])];E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#19[(app A#20[(var X#16)] T#21)];X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {X#15=A#19[(app A#20[(var X#16)] T#21[S#2])];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#12         |->  X#15,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]},
           T#11         |->  A#19[(app A#20[(var X#16)] T#21)],
           A#14         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#15=A#19[(app A#20[(var X#16)] T#21[S#2])];X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#15=A#19[(app A#20[(var X#16)] T#21[(letrec {E#1} in S#2)])];X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#15=A#19[(app A#20[(var X#16)] T#21[S#2])];X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#15=A#19[(app A#20[(var X#16)] T#21[S#2])];X#4=S#8;E#6;E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#1} in A#14[(var X#16)])
       ;X#4= (letrec {E#6} in S#8)
       ;E#7
       ;EE#17[X#5,(var X#15)]
       ;EE#18[X#16,(var X#4)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;X#4= S#8
       ;E#6
       ;E#7
       ;EE#17[X#5,(var X#15)]
       ;EE#18[X#16,(var X#4)]
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#14[(var X#16)],(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#15=A#14[(var X#16)];E#6;E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#15=A#14[(var X#16)];E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=[.];X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {X#15=A#14[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#12         |->  X#15,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]},
           T#11         |->  [.],
           S#2          |->  A#14[(var X#16)]}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#15=(letrec {E#1} in A#14[(var X#16)]);X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];X#4=(letrec {E#6} in S#8);E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#15=A#14[(var X#16)];X#4=S#8;E#6;E#7;EE#17[X#5,(var X#15)];EE#18[X#16,(var X#4)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#17[(letrec {E#1} in (var X#4))]
       ;X#4= (letrec {E#6} in S#8)
       ;E#7
       ;EE#16[X#5,(var X#15)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#15= A#17[(var X#4)]
       ;X#4= S#8
       ;E#6
       ;E#7
       ;EE#16[X#5,(var X#15)]
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#17}
   Delta2 = {E#1,E#6}
   Delta3 = {((var X#4),(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#15=A#17[(var X#4)];E#6;E#7;EE#16[X#5,(var X#15)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#15=A#17[(var X#4)];E#7;EE#16[X#5,(var X#15)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#17[[.]];X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {X#15=A#17[[.2]];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]},
           A#14         |->  A#17,
           T#11         |->  A#17[[.]],
           T#18         |->  [.],
           S#2          |->  (var X#4)}

and instantiated rules:

                                  (letrec {X#15=A#17[(var X#4)];X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#15=A#17[(letrec {E#1} in (var X#4))];X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#15=A#17[(var X#4)];X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#15=A#17[(var X#4)];X#4=S#8;E#6;E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#17[(letrec {E#1} in A#18[(var X#4)])]
       ;X#4= (letrec {E#6} in S#8)
       ;E#7
       ;EE#16[X#5,(var X#15)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#15= A#17[A#18[(var X#4)]]
       ;X#4= S#8
       ;E#6
       ;E#7
       ;EE#16[X#5,(var X#15)]
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#17}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#18[(var X#4)],(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#15=A#17[A#18[(var X#4)]];E#6;E#7;EE#16[X#5,(var X#15)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#15=A#17[A#18[(var X#4)]];E#7;EE#16[X#5,(var X#15)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#17;X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {X#15=A#17[A#18[[.2]]];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]},
           A#14         |->  A#17[A#18],
           T#11         |->  A#17,
           S#2          |->  A#18[(var X#4)]}

and instantiated rules:

                                  (letrec {X#15=A#17[A#18[(var X#4)]];X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#15=A#17[(letrec {E#1} in A#18[(var X#4)])];X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#15=A#17[A#18[(var X#4)]];X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#15=A#17[A#18[(var X#4)]];X#4=S#8;E#6;E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#17[(app A#18[(var X#4)] T#19[(letrec {E#1} in S#2)])]
       ;X#4= (letrec {E#6} in S#8)
       ;E#7
       ;EE#16[X#5,(var X#15)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#15= A#17[(app A#18[(var X#4)] T#19[S#2])]
       ;X#4= S#8
       ;E#6
       ;E#7
       ;EE#16[X#5,(var X#15)]
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#15=A#17[(app A#18[(var X#4)] T#19[S#2])];E#6;E#7;EE#16[X#5,(var X#15)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#15=A#17[(app A#18[(var X#4)] T#19[S#2])];E#7;EE#16[X#5,(var X#15)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#17[(app A#18[(var X#4)] T#19)];X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {X#15=A#17[(app A#18[[.2]] T#19[S#2])];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]},
           T#11         |->  A#17[(app A#18[(var X#4)] T#19)],
           A#14         |->  A#17[(app A#18 T#19[S#2])]}

and instantiated rules:

                                  (letrec {X#15=A#17[(app A#18[(var X#4)] T#19[S#2])];X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#15=A#17[(app A#18[(var X#4)] T#19[(letrec {E#1} in S#2)])];X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#15=A#17[(app A#18[(var X#4)] T#19[S#2])];X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#15=A#17[(app A#18[(var X#4)] T#19[S#2])];X#4=S#8;E#6;E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#1} in A#14[(var X#4)])
       ;X#4= (letrec {E#6} in S#8)
       ;E#7
       ;EE#16[X#5,(var X#15)]
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#15= A#14[(var X#4)]
       ;X#4= S#8
       ;E#6
       ;E#7
       ;EE#16[X#5,(var X#15)]
     in
        A#9[(var X#5)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#14[(var X#4)],(letrec {E#1} in [.])),
             ((var X#4),(letrec {X#15=A#14[(var X#4)];E#6;E#7;EE#16[X#5,(var X#15)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#15=A#14[(var X#4)];E#7;EE#16[X#5,(var X#15)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=[.];X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)]),
           EE#10[.1,.2] |-> {X#15=A#14[[.2]];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]},
           T#11         |->  [.],
           S#2          |->  A#14[(var X#4)]}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#4)];X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    -gc1->                        (letrec {X#15=(letrec {E#1} in A#14[(var X#4)]);X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#4)];X#4=(letrec {E#6} in S#8);E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#15=A#14[(var X#4)];X#4=S#8;E#6;E#7;EE#16[X#5,(var X#15)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#1
     in
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
     )
    ,
     (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#6}
   Delta3 = {((letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)]),(letrec {E#1} in [.])),
             ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],
             ((var X#4),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#4),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,llet-e2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    and constraints: E#6/= {}, ((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])), (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),((var X#4),(letrec {E#6;E#7;EE#10[X#5,(var X#4)]} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7;EE#10[X#5,(var X#4)]},(letrec {E#6} in [.])],((var X#4),[.]),((var X#5),A#9[[.]]),((var X#4),[.]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           S#2  |->  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])}

and instantiated rules:

                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -gc1->                        (letrec {E#1} in (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)]))
    ................................................................................
                                  (letrec {X#4=(letrec {E#6} in S#8);E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    -SR,llet-e2->                 (letrec {X#4=S#8;E#6;E#7;EE#10[X#5,(var X#4)]} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     A#8[(app (letrec {E#4} in T#11[(letrec {E#1} in S#2)]) S#5)]
    ,
     A#8[(letrec {E#4} in (app T#11[S#2] S#5))]
  )

where

   Delta1 = {T#10,T#9,A#7,T#3,A#8}
   Delta2 = {E#1,E#4}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#5,(letrec {E#4} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (letrec {E#4} in S#6) S#5)]
    -SR,lapp1->                   A#7[(letrec {E#4} in (app S#6 S#5))]
    and constraints: E#4/= {}, (S#5,(letrec {E#4} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (letrec {E#4} in S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1,E#4}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(letrec {E#4} in [.]))}


and found solution:

    Sol = {A#7   |->  A#8,
           T#3   |->  A#8[(app (letrec {E#4} in T#11) S#5)],
           T#9   |->  (app (letrec {E#4} in T#11) S#5),
           T#10  |->  (letrec {E#4} in T#11),
           S#6   |->  T#11[S#2]}

and instantiated rules:

                                  A#8[(app (letrec {E#4} in T#11[S#2]) S#5)]
    -gc1->                        A#8[(app (letrec {E#4} in T#11[(letrec {E#1} in S#2)]) S#5)]
    ................................................................................
                                  A#8[(app (letrec {E#4} in T#11[S#2]) S#5)]
    -SR,lapp1->                   A#8[(letrec {E#4} in (app T#11[S#2] S#5))]
    

================================================================================
Critical Pair:

  (
     A#8[(app (letrec {X#12=T#11[(letrec {E#1} in S#2)];E#14} in S#6) S#5)]
    ,
     A#8[(letrec {X#12=T#11[S#2];E#14} in (app S#6 S#5))]
  )

where

   Delta1 = {T#10,T#9,A#7,T#3,A#8}
   Delta2 = {E#1,E#4}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#5,(letrec {X#12=T#11[S#2];E#14} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (letrec {E#4} in S#6) S#5)]
    -SR,lapp1->                   A#7[(letrec {E#4} in (app S#6 S#5))]
    and constraints: E#4/= {}, (S#5,(letrec {E#4} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (letrec {E#4} in S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1,E#4}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(letrec {E#4} in [.]))}


and found solution:

    Sol = {A#7   |->  A#8,
           T#3   |->  A#8[(app (letrec {X#12=T#11;E#14} in S#6) S#5)],
           T#9   |->  (app (letrec {X#12=T#11;E#14} in S#6) S#5),
           T#10  |->  (letrec {X#12=T#11;E#14} in S#6),
           E#4   |->  {X#12=T#11[S#2];E#14},
           E#13  |->  {E#14}}

and instantiated rules:

                                  A#8[(app (letrec {X#12=T#11[S#2];E#14} in S#6) S#5)]
    -gc1->                        A#8[(app (letrec {X#12=T#11[(letrec {E#1} in S#2)];E#14} in S#6) S#5)]
    ................................................................................
                                  A#8[(app (letrec {X#12=T#11[S#2];E#14} in S#6) S#5)]
    -SR,lapp1->                   A#8[(letrec {X#12=T#11[S#2];E#14} in (app S#6 S#5))]
    

================================================================================
Critical Pair:

  (
     A#8[(app (letrec {E#1} in (letrec {E#4} in S#6)) S#5)]
    ,
     A#8[(letrec {E#4} in (app S#6 S#5))]
  )

where

   Delta1 = {T#9,A#7,T#3,A#8}
   Delta2 = {E#1,E#4}
   Delta3 = {((letrec {E#4} in S#6),(letrec {E#1} in [.])),
             (S#5,(letrec {E#4} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (letrec {E#4} in S#6) S#5)]
    -SR,lapp1->                   A#7[(letrec {E#4} in (app S#6 S#5))]
    and constraints: E#4/= {}, (S#5,(letrec {E#4} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (letrec {E#4} in S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1,E#4}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(letrec {E#4} in [.]))}


and found solution:

    Sol = {A#7   |->  A#8,
           T#3   |->  A#8[(app [.] S#5)],
           T#9   |->  (app [.] S#5),
           T#10  |->  [.],
           S#2   |->  (letrec {E#4} in S#6)}

and instantiated rules:

                                  A#8[(app (letrec {E#4} in S#6) S#5)]
    -gc1->                        A#8[(app (letrec {E#1} in (letrec {E#4} in S#6)) S#5)]
    ................................................................................
                                  A#8[(app (letrec {E#4} in S#6) S#5)]
    -SR,lapp1->                   A#8[(letrec {E#4} in (app S#6 S#5))]
    

================================================================================
Critical Pair:

  (
     A#8[(app (letrec {E#4} in S#6) T#10[(letrec {E#1} in S#2)])]
    ,
     A#8[(letrec {E#4} in (app S#6 T#10[S#2]))]
  )

where

   Delta1 = {T#9,A#7,T#3,A#8}
   Delta2 = {E#1,E#4}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#10[S#2],(letrec {E#4} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (letrec {E#4} in S#6) S#5)]
    -SR,lapp1->                   A#7[(letrec {E#4} in (app S#6 S#5))]
    and constraints: E#4/= {}, (S#5,(letrec {E#4} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (letrec {E#4} in S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1,E#4}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(letrec {E#4} in [.]))}


and found solution:

    Sol = {A#7  |->  A#8,
           T#3  |->  A#8[(app (letrec {E#4} in S#6) T#10)],
           T#9  |->  (app (letrec {E#4} in S#6) T#10),
           S#5  |->  T#10[S#2]}

and instantiated rules:

                                  A#8[(app (letrec {E#4} in S#6) T#10[S#2])]
    -gc1->                        A#8[(app (letrec {E#4} in S#6) T#10[(letrec {E#1} in S#2)])]
    ................................................................................
                                  A#8[(app (letrec {E#4} in S#6) T#10[S#2])]
    -SR,lapp1->                   A#8[(letrec {E#4} in (app S#6 T#10[S#2]))]
    

================================================================================
Critical Pair:

  (
     A#8[(letrec {E#1} in (app (letrec {E#4} in S#6) S#5))]
    ,
     A#8[(letrec {E#4} in (app S#6 S#5))]
  )

where

   Delta1 = {A#7,T#3,A#8}
   Delta2 = {E#1,E#4}
   Delta3 = {((app (letrec {E#4} in S#6) S#5),(letrec {E#1} in [.])),
             (S#5,(letrec {E#4} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (letrec {E#4} in S#6) S#5)]
    -SR,lapp1->                   A#7[(letrec {E#4} in (app S#6 S#5))]
    and constraints: E#4/= {}, (S#5,(letrec {E#4} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (letrec {E#4} in S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1,E#4}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(letrec {E#4} in [.]))}


and found solution:

    Sol = {A#7  |->  A#8,
           T#3  |->  A#8[[.]],
           T#9  |->  [.],
           S#2  |->  (app (letrec {E#4} in S#6) S#5)}

and instantiated rules:

                                  A#8[(app (letrec {E#4} in S#6) S#5)]
    -gc1->                        A#8[(letrec {E#1} in (app (letrec {E#4} in S#6) S#5))]
    ................................................................................
                                  A#8[(app (letrec {E#4} in S#6) S#5)]
    -SR,lapp1->                   A#8[(letrec {E#4} in (app S#6 S#5))]
    

================================================================================
Critical Pair:

  (
     A#8[(letrec {E#1} in A#9[(app (letrec {E#4} in S#6) S#5)])]
    ,
     A#8[A#9[(letrec {E#4} in (app S#6 S#5))]]
  )

where

   Delta1 = {A#7,T#3,A#8}
   Delta2 = {E#1,E#4}
   Delta3 = {(A#9[(app (letrec {E#4} in S#6) S#5)],(letrec {E#1} in [.])),
             (S#5,(letrec {E#4} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (letrec {E#4} in S#6) S#5)]
    -SR,lapp1->                   A#7[(letrec {E#4} in (app S#6 S#5))]
    and constraints: E#4/= {}, (S#5,(letrec {E#4} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (letrec {E#4} in S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1,E#4}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(letrec {E#4} in [.]))}


and found solution:

    Sol = {A#7  |->  A#8[A#9],
           T#3  |->  A#8,
           S#2  |->  A#9[(app (letrec {E#4} in S#6) S#5)]}

and instantiated rules:

                                  A#8[A#9[(app (letrec {E#4} in S#6) S#5)]]
    -gc1->                        A#8[(letrec {E#1} in A#9[(app (letrec {E#4} in S#6) S#5)])]
    ................................................................................
                                  A#8[A#9[(app (letrec {E#4} in S#6) S#5)]]
    -SR,lapp1->                   A#8[A#9[(letrec {E#4} in (app S#6 S#5))]]
    

================================================================================
Critical Pair:

  (
     A#8[(app A#9[(app (letrec {E#4} in S#6) S#5)] T#10[(letrec {E#1} in S#2)])]
    ,
     A#8[(app A#9[(letrec {E#4} in (app S#6 S#5))] T#10[S#2])]
  )

where

   Delta1 = {A#7,T#3}
   Delta2 = {E#1,E#4}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#5,(letrec {E#4} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (letrec {E#4} in S#6) S#5)]
    -SR,lapp1->                   A#7[(letrec {E#4} in (app S#6 S#5))]
    and constraints: E#4/= {}, (S#5,(letrec {E#4} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (letrec {E#4} in S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1,E#4}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(letrec {E#4} in [.]))}


and found solution:

    Sol = {T#3  |->  A#8[(app A#9[(app (letrec {E#4} in S#6) S#5)] T#10)],
           A#7  |->  A#8[(app A#9 T#10[S#2])]}

and instantiated rules:

                                  A#8[(app A#9[(app (letrec {E#4} in S#6) S#5)] T#10[S#2])]
    -gc1->                        A#8[(app A#9[(app (letrec {E#4} in S#6) S#5)] T#10[(letrec {E#1} in S#2)])]
    ................................................................................
                                  A#8[(app A#9[(app (letrec {E#4} in S#6) S#5)] T#10[S#2])]
    -SR,lapp1->                   A#8[(app A#9[(letrec {E#4} in (app S#6 S#5))] T#10[S#2])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#4} in T#9[(letrec {E#1} in S#2)]) S#5)
    ,
     (letrec {E#4} in (app T#9[S#2] S#5))
  )

where

   Delta1 = {T#8,T#3}
   Delta2 = {E#1,E#4}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#5,(letrec {E#4} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (letrec {E#4} in S#6) S#5)]
    -SR,lapp1->                   A#7[(letrec {E#4} in (app S#6 S#5))]
    and constraints: E#4/= {}, (S#5,(letrec {E#4} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (letrec {E#4} in S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1,E#4}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(letrec {E#4} in [.]))}


and found solution:

    Sol = {A#7  |->  [.],
           T#3  |->  (app (letrec {E#4} in T#9) S#5),
           T#8  |->  (letrec {E#4} in T#9),
           S#6  |->  T#9[S#2]}

and instantiated rules:

                                  (app (letrec {E#4} in T#9[S#2]) S#5)
    -gc1->                        (app (letrec {E#4} in T#9[(letrec {E#1} in S#2)]) S#5)
    ................................................................................
                                  (app (letrec {E#4} in T#9[S#2]) S#5)
    -SR,lapp1->                   (letrec {E#4} in (app T#9[S#2] S#5))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#10=T#9[(letrec {E#1} in S#2)];E#12} in S#6) S#5)
    ,
     (letrec {X#10=T#9[S#2];E#12} in (app S#6 S#5))
  )

where

   Delta1 = {T#8,T#3}
   Delta2 = {E#1,E#4}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#5,(letrec {X#10=T#9[S#2];E#12} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (letrec {E#4} in S#6) S#5)]
    -SR,lapp1->                   A#7[(letrec {E#4} in (app S#6 S#5))]
    and constraints: E#4/= {}, (S#5,(letrec {E#4} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (letrec {E#4} in S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1,E#4}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(letrec {E#4} in [.]))}


and found solution:

    Sol = {A#7   |->  [.],
           T#3   |->  (app (letrec {X#10=T#9;E#12} in S#6) S#5),
           T#8   |->  (letrec {X#10=T#9;E#12} in S#6),
           E#4   |->  {X#10=T#9[S#2];E#12},
           E#11  |->  {E#12}}

and instantiated rules:

                                  (app (letrec {X#10=T#9[S#2];E#12} in S#6) S#5)
    -gc1->                        (app (letrec {X#10=T#9[(letrec {E#1} in S#2)];E#12} in S#6) S#5)
    ................................................................................
                                  (app (letrec {X#10=T#9[S#2];E#12} in S#6) S#5)
    -SR,lapp1->                   (letrec {X#10=T#9[S#2];E#12} in (app S#6 S#5))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#1} in (letrec {E#4} in S#6)) S#5)
    ,
     (letrec {E#4} in (app S#6 S#5))
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#4}
   Delta3 = {((letrec {E#4} in S#6),(letrec {E#1} in [.])),
             (S#5,(letrec {E#4} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (letrec {E#4} in S#6) S#5)]
    -SR,lapp1->                   A#7[(letrec {E#4} in (app S#6 S#5))]
    and constraints: E#4/= {}, (S#5,(letrec {E#4} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (letrec {E#4} in S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1,E#4}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(letrec {E#4} in [.]))}


and found solution:

    Sol = {A#7  |->  [.],
           T#3  |->  (app [.] S#5),
           T#8  |->  [.],
           S#2  |->  (letrec {E#4} in S#6)}

and instantiated rules:

                                  (app (letrec {E#4} in S#6) S#5)
    -gc1->                        (app (letrec {E#1} in (letrec {E#4} in S#6)) S#5)
    ................................................................................
                                  (app (letrec {E#4} in S#6) S#5)
    -SR,lapp1->                   (letrec {E#4} in (app S#6 S#5))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#4} in S#6) T#8[(letrec {E#1} in S#2)])
    ,
     (letrec {E#4} in (app S#6 T#8[S#2]))
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#4}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#8[S#2],(letrec {E#4} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (letrec {E#4} in S#6) S#5)]
    -SR,lapp1->                   A#7[(letrec {E#4} in (app S#6 S#5))]
    and constraints: E#4/= {}, (S#5,(letrec {E#4} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (letrec {E#4} in S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1,E#4}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(letrec {E#4} in [.]))}


and found solution:

    Sol = {A#7  |->  [.],
           T#3  |->  (app (letrec {E#4} in S#6) T#8),
           S#5  |->  T#8[S#2]}

and instantiated rules:

                                  (app (letrec {E#4} in S#6) T#8[S#2])
    -gc1->                        (app (letrec {E#4} in S#6) T#8[(letrec {E#1} in S#2)])
    ................................................................................
                                  (app (letrec {E#4} in S#6) T#8[S#2])
    -SR,lapp1->                   (letrec {E#4} in (app S#6 T#8[S#2]))
    

================================================================================
Critical Pair:

  (
     (letrec {E#1} in A#7[(app (letrec {E#4} in S#6) S#5)])
    ,
     A#7[(letrec {E#4} in (app S#6 S#5))]
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#4}
   Delta3 = {(A#7[(app (letrec {E#4} in S#6) S#5)],(letrec {E#1} in [.])),
             (S#5,(letrec {E#4} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp1-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  A#7[(app (letrec {E#4} in S#6) S#5)]
    -SR,lapp1->                   A#7[(letrec {E#4} in (app S#6 S#5))]
    and constraints: E#4/= {}, (S#5,(letrec {E#4} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= A#7[(app (letrec {E#4} in S#6) S#5)]}
      Delta1=  {}
      Delta2=  {E#1,E#4}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#5,(letrec {E#4} in [.]))}


and found solution:

    Sol = {T#3  |->  [.],
           S#2  |->  A#7[(app (letrec {E#4} in S#6) S#5)]}

and instantiated rules:

                                  A#7[(app (letrec {E#4} in S#6) S#5)]
    -gc1->                        (letrec {E#1} in A#7[(app (letrec {E#4} in S#6) S#5)])
    ................................................................................
                                  A#7[(app (letrec {E#4} in S#6) S#5)]
    -SR,lapp1->                   A#7[(letrec {E#4} in (app S#6 S#5))]
    

================================================================================
Critical Pair:

  (
     (letrec {E#4} in A#10[(app (letrec {E#5} in T#13[(letrec {E#1} in S#2)]) S#6)])
    ,
     (letrec {E#4} in A#10[(letrec {E#5} in (app T#13[S#2] S#6))])
  )

where

   Delta1 = {T#12,T#11,A#8,T#9,T#3,A#10}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    and constraints: E#4/= {}, E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#3   |->  (letrec {E#4} in A#10[(app (letrec {E#5} in T#13) S#6)]),
           A#8   |->  A#10,
           T#9   |->  A#10[(app (letrec {E#5} in T#13) S#6)],
           T#11  |->  (app (letrec {E#5} in T#13) S#6),
           T#12  |->  (letrec {E#5} in T#13),
           S#7   |->  T#13[S#2]}

and instantiated rules:

                                  (letrec {E#4} in A#10[(app (letrec {E#5} in T#13[S#2]) S#6)])
    -gc1->                        (letrec {E#4} in A#10[(app (letrec {E#5} in T#13[(letrec {E#1} in S#2)]) S#6)])
    ................................................................................
                                  (letrec {E#4} in A#10[(app (letrec {E#5} in T#13[S#2]) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#10[(letrec {E#5} in (app T#13[S#2] S#6))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#4
     in
        A#10[(app (letrec {X#14=T#13[(letrec {E#1} in S#2)];E#16} in S#7) S#6)]
     )
    ,
     (letrec {E#4} in A#10[(letrec {X#14=T#13[S#2];E#16} in (app S#7 S#6))])
  )

where

   Delta1 = {T#12,T#11,A#8,T#9,T#3,A#10}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(letrec {X#14=T#13[S#2];E#16} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    and constraints: E#4/= {}, E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#3   |->  (letrec {E#4} in A#10[(app (letrec {X#14=T#13;E#16} in S#7) S#6)]),
           A#8   |->  A#10,
           T#9   |->  A#10[(app (letrec {X#14=T#13;E#16} in S#7) S#6)],
           T#11  |->  (app (letrec {X#14=T#13;E#16} in S#7) S#6),
           T#12  |->  (letrec {X#14=T#13;E#16} in S#7),
           E#5   |->  {X#14=T#13[S#2];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {E#4} in A#10[(app (letrec {X#14=T#13[S#2];E#16} in S#7) S#6)])
    -gc1->                        (letrec {E#4} in A#10[(app (letrec {X#14=T#13[(letrec {E#1} in S#2)];E#16} in S#7) S#6)])
    ................................................................................
                                  (letrec {E#4} in A#10[(app (letrec {X#14=T#13[S#2];E#16} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#10[(letrec {X#14=T#13[S#2];E#16} in (app S#7 S#6))])
    

================================================================================
Critical Pair:

  (
     (letrec {E#4} in A#10[(app (letrec {E#1} in (letrec {E#5} in S#7)) S#6)])
    ,
     (letrec {E#4} in A#10[(letrec {E#5} in (app S#7 S#6))])
  )

where

   Delta1 = {T#11,A#8,T#9,T#3,A#10}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {((letrec {E#5} in S#7),(letrec {E#1} in [.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    and constraints: E#4/= {}, E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#3   |->  (letrec {E#4} in A#10[(app [.] S#6)]),
           A#8   |->  A#10,
           T#9   |->  A#10[(app [.] S#6)],
           T#11  |->  (app [.] S#6),
           T#12  |->  [.],
           S#2   |->  (letrec {E#5} in S#7)}

and instantiated rules:

                                  (letrec {E#4} in A#10[(app (letrec {E#5} in S#7) S#6)])
    -gc1->                        (letrec {E#4} in A#10[(app (letrec {E#1} in (letrec {E#5} in S#7)) S#6)])
    ................................................................................
                                  (letrec {E#4} in A#10[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#10[(letrec {E#5} in (app S#7 S#6))])
    

================================================================================
Critical Pair:

  (
     (letrec {E#4} in A#10[(app (letrec {E#5} in S#7) T#12[(letrec {E#1} in S#2)])])
    ,
     (letrec {E#4} in A#10[(letrec {E#5} in (app S#7 T#12[S#2]))])
  )

where

   Delta1 = {T#11,A#8,T#9,T#3,A#10}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#12[S#2],(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    and constraints: E#4/= {}, E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#3   |->  (letrec {E#4} in A#10[(app (letrec {E#5} in S#7) T#12)]),
           A#8   |->  A#10,
           T#9   |->  A#10[(app (letrec {E#5} in S#7) T#12)],
           T#11  |->  (app (letrec {E#5} in S#7) T#12),
           S#6   |->  T#12[S#2]}

and instantiated rules:

                                  (letrec {E#4} in A#10[(app (letrec {E#5} in S#7) T#12[S#2])])
    -gc1->                        (letrec {E#4} in A#10[(app (letrec {E#5} in S#7) T#12[(letrec {E#1} in S#2)])])
    ................................................................................
                                  (letrec {E#4} in A#10[(app (letrec {E#5} in S#7) T#12[S#2])])
    -SR,lapp2->                   (letrec {E#4} in A#10[(letrec {E#5} in (app S#7 T#12[S#2]))])
    

================================================================================
Critical Pair:

  (
     (letrec {E#4} in A#10[(letrec {E#1} in (app (letrec {E#5} in S#7) S#6))])
    ,
     (letrec {E#4} in A#10[(letrec {E#5} in (app S#7 S#6))])
  )

where

   Delta1 = {A#8,T#9,T#3,A#10}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {((app (letrec {E#5} in S#7) S#6),(letrec {E#1} in [.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    and constraints: E#4/= {}, E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#3   |->  (letrec {E#4} in A#10[[.]]),
           A#8   |->  A#10,
           T#9   |->  A#10[[.]],
           T#11  |->  [.],
           S#2   |->  (app (letrec {E#5} in S#7) S#6)}

and instantiated rules:

                                  (letrec {E#4} in A#10[(app (letrec {E#5} in S#7) S#6)])
    -gc1->                        (letrec {E#4} in A#10[(letrec {E#1} in (app (letrec {E#5} in S#7) S#6))])
    ................................................................................
                                  (letrec {E#4} in A#10[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#10[(letrec {E#5} in (app S#7 S#6))])
    

================================================================================
Critical Pair:

  (
     (letrec {E#4} in A#10[(letrec {E#1} in A#11[(app (letrec {E#5} in S#7) S#6)])])
    ,
     (letrec {E#4} in A#10[A#11[(letrec {E#5} in (app S#7 S#6))]])
  )

where

   Delta1 = {A#8,T#9,T#3,A#10}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {(A#11[(app (letrec {E#5} in S#7) S#6)],(letrec {E#1} in [.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    and constraints: E#4/= {}, E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#3  |->  (letrec {E#4} in A#10),
           A#8  |->  A#10[A#11],
           T#9  |->  A#10,
           S#2  |->  A#11[(app (letrec {E#5} in S#7) S#6)]}

and instantiated rules:

                                  (letrec {E#4} in A#10[A#11[(app (letrec {E#5} in S#7) S#6)]])
    -gc1->                        (letrec {E#4} in A#10[(letrec {E#1} in A#11[(app (letrec {E#5} in S#7) S#6)])])
    ................................................................................
                                  (letrec {E#4} in A#10[A#11[(app (letrec {E#5} in S#7) S#6)]])
    -SR,lapp2->                   (letrec {E#4} in A#10[A#11[(letrec {E#5} in (app S#7 S#6))]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#4
     in
        A#10[(app A#11[(app (letrec {E#5} in S#7) S#6)] T#12[(letrec {E#1} in S#2)])]
     )
    ,
     (letrec {E#4} in A#10[(app A#11[(letrec {E#5} in (app S#7 S#6))] T#12[S#2])])
  )

where

   Delta1 = {A#8,T#9,T#3}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    and constraints: E#4/= {}, E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#3  |->  (letrec {E#4} in A#10[(app A#11[(app (letrec {E#5} in S#7) S#6)] T#12)]),
           T#9  |->  A#10[(app A#11[(app (letrec {E#5} in S#7) S#6)] T#12)],
           A#8  |->  A#10[(app A#11 T#12[S#2])]}

and instantiated rules:

                                  (letrec {E#4} in A#10[(app A#11[(app (letrec {E#5} in S#7) S#6)] T#12[S#2])])
    -gc1->                        (letrec {E#4} in A#10[(app A#11[(app (letrec {E#5} in S#7) S#6)] T#12[(letrec {E#1} in S#2)])])
    ................................................................................
                                  (letrec {E#4} in A#10[(app A#11[(app (letrec {E#5} in S#7) S#6)] T#12[S#2])])
    -SR,lapp2->                   (letrec {E#4} in A#10[(app A#11[(letrec {E#5} in (app S#7 S#6))] T#12[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec {E#4} in (app (letrec {E#5} in T#11[(letrec {E#1} in S#2)]) S#6))
    ,
     (letrec {E#4} in (letrec {E#5} in (app T#11[S#2] S#6)))
  )

where

   Delta1 = {T#10,T#9,T#3}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    and constraints: E#4/= {}, E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#3   |->  (letrec {E#4} in (app (letrec {E#5} in T#11) S#6)),
           A#8   |->  [.],
           T#9   |->  (app (letrec {E#5} in T#11) S#6),
           T#10  |->  (letrec {E#5} in T#11),
           S#7   |->  T#11[S#2]}

and instantiated rules:

                                  (letrec {E#4} in (app (letrec {E#5} in T#11[S#2]) S#6))
    -gc1->                        (letrec {E#4} in (app (letrec {E#5} in T#11[(letrec {E#1} in S#2)]) S#6))
    ................................................................................
                                  (letrec {E#4} in (app (letrec {E#5} in T#11[S#2]) S#6))
    -SR,lapp2->                   (letrec {E#4} in (letrec {E#5} in (app T#11[S#2] S#6)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#4
     in
        (app (letrec {X#12=T#11[(letrec {E#1} in S#2)];E#14} in S#7) S#6)
     )
    ,
     (letrec {E#4} in (letrec {X#12=T#11[S#2];E#14} in (app S#7 S#6)))
  )

where

   Delta1 = {T#10,T#9,T#3}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(letrec {X#12=T#11[S#2];E#14} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    and constraints: E#4/= {}, E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#3   |->  (letrec {E#4} in (app (letrec {X#12=T#11;E#14} in S#7) S#6)),
           A#8   |->  [.],
           T#9   |->  (app (letrec {X#12=T#11;E#14} in S#7) S#6),
           T#10  |->  (letrec {X#12=T#11;E#14} in S#7),
           E#5   |->  {X#12=T#11[S#2];E#14},
           E#13  |->  {E#14}}

and instantiated rules:

                                  (letrec {E#4} in (app (letrec {X#12=T#11[S#2];E#14} in S#7) S#6))
    -gc1->                        (letrec {E#4} in (app (letrec {X#12=T#11[(letrec {E#1} in S#2)];E#14} in S#7) S#6))
    ................................................................................
                                  (letrec {E#4} in (app (letrec {X#12=T#11[S#2];E#14} in S#7) S#6))
    -SR,lapp2->                   (letrec {E#4} in (letrec {X#12=T#11[S#2];E#14} in (app S#7 S#6)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#4} in (app (letrec {E#1} in (letrec {E#5} in S#7)) S#6))
    ,
     (letrec {E#4} in (letrec {E#5} in (app S#7 S#6)))
  )

where

   Delta1 = {T#9,T#3}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {((letrec {E#5} in S#7),(letrec {E#1} in [.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    and constraints: E#4/= {}, E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#3   |->  (letrec {E#4} in (app [.] S#6)),
           A#8   |->  [.],
           T#9   |->  (app [.] S#6),
           T#10  |->  [.],
           S#2   |->  (letrec {E#5} in S#7)}

and instantiated rules:

                                  (letrec {E#4} in (app (letrec {E#5} in S#7) S#6))
    -gc1->                        (letrec {E#4} in (app (letrec {E#1} in (letrec {E#5} in S#7)) S#6))
    ................................................................................
                                  (letrec {E#4} in (app (letrec {E#5} in S#7) S#6))
    -SR,lapp2->                   (letrec {E#4} in (letrec {E#5} in (app S#7 S#6)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#4} in (app (letrec {E#5} in S#7) T#10[(letrec {E#1} in S#2)]))
    ,
     (letrec {E#4} in (letrec {E#5} in (app S#7 T#10[S#2])))
  )

where

   Delta1 = {T#9,T#3}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#10[S#2],(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    and constraints: E#4/= {}, E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#3  |->  (letrec {E#4} in (app (letrec {E#5} in S#7) T#10)),
           A#8  |->  [.],
           T#9  |->  (app (letrec {E#5} in S#7) T#10),
           S#6  |->  T#10[S#2]}

and instantiated rules:

                                  (letrec {E#4} in (app (letrec {E#5} in S#7) T#10[S#2]))
    -gc1->                        (letrec {E#4} in (app (letrec {E#5} in S#7) T#10[(letrec {E#1} in S#2)]))
    ................................................................................
                                  (letrec {E#4} in (app (letrec {E#5} in S#7) T#10[S#2]))
    -SR,lapp2->                   (letrec {E#4} in (letrec {E#5} in (app S#7 T#10[S#2])))
    

================================================================================
Critical Pair:

  (
     (letrec {E#4} in (letrec {E#1} in A#8[(app (letrec {E#5} in S#7) S#6)]))
    ,
     (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {(A#8[(app (letrec {E#5} in S#7) S#6)],(letrec {E#1} in [.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    and constraints: E#4/= {}, E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#3  |->  (letrec {E#4} in [.]),
           T#9  |->  [.],
           S#2  |->  A#8[(app (letrec {E#5} in S#7) S#6)]}

and instantiated rules:

                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -gc1->                        (letrec {E#4} in (letrec {E#1} in A#8[(app (letrec {E#5} in S#7) S#6)]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= T#9[(letrec {E#1} in S#2)]
       ;E#12
     in
        A#8[(app (letrec {E#5} in S#7) S#6)]
     )
    ,
     (letrec {X#10=T#9[S#2];E#12} in A#8[(letrec {E#5} in (app S#7 S#6))])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    and constraints: E#4/= {}, E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#3   |->  (letrec {X#10=T#9;E#12} in A#8[(app (letrec {E#5} in S#7) S#6)]),
           E#4   |->  {X#10=T#9[S#2];E#12},
           E#11  |->  {E#12}}

and instantiated rules:

                                  (letrec {X#10=T#9[S#2];E#12} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -gc1->                        (letrec {X#10=T#9[(letrec {E#1} in S#2)];E#12} in A#8[(app (letrec {E#5} in S#7) S#6)])
    ................................................................................
                                  (letrec {X#10=T#9[S#2];E#12} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {X#10=T#9[S#2];E#12} in A#8[(letrec {E#5} in (app S#7 S#6))])
    

================================================================================
Critical Pair:

  (
     (letrec {E#1} in (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)]))
    ,
     (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#4,E#5}
   Delta3 = {((letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)]),(letrec {E#1} in [.])),
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp2-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    and constraints: E#4/= {}, E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2] =?= (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#4,E#5}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#3  |->  [.],
           S#2  |->  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])}

and instantiated rules:

                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -gc1->                        (letrec {E#1} in (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)]))
    ................................................................................
                                  (letrec {E#4} in A#8[(app (letrec {E#5} in S#7) S#6)])
    -SR,lapp2->                   (letrec {E#4} in A#8[(letrec {E#5} in (app S#7 S#6))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
       ;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]
     in
        A#12[(letrec {E#1} in (var X#4))]
     )
    ,
     (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#12[(var X#4)])
  )

where

   Delta1 = {A#9,T#11,T#3,A#12}
   Delta2 = {E#1,E#6}
   Delta3 = {((var X#4),(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#12[[.]]),
             ((var X#4),A#12[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#12[[.]]),
           A#9   |->  A#12,
           T#11  |->  A#12[[.]],
           T#13  |->  [.],
           S#2   |->  (var X#4)}

and instantiated rules:

                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#12[(var X#4)])
    -gc1->                        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#12[(letrec {E#1} in (var X#4))])
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#12[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#12[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
       ;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]
     in
        A#12[(letrec {E#1} in A#13[(var X#4)])]
     )
    ,
     (letrec
        E#5
       ;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]
     in
        A#12[A#13[(var X#4)]]
     )
  )

where

   Delta1 = {A#9,T#11,T#3,A#12}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#13[(var X#4)],(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#12[A#13[[.]]]),
             ((var X#4),A#12[A#13[[.]]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#12),
           A#9   |->  A#12[A#13],
           T#11  |->  A#12,
           S#2   |->  A#13[(var X#4)]}

and instantiated rules:

                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#12[A#13[(var X#4)]])
    -gc1->                        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#12[(letrec {E#1} in A#13[(var X#4)])])
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#12[A#13[(var X#4)]])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#12[A#13[(var X#4)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
       ;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]
     in
        A#12[(app A#13[(var X#4)] T#14[(letrec {E#1} in S#2)])]
     )
    ,
     (letrec
        E#5
       ;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]
     in
        A#12[(app A#13[(var X#4)] T#14[S#2])]
     )
  )

where

   Delta1 = {A#9,T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#12[(app A#13[[.]] T#14[S#2])]),
             ((var X#4),A#12[(app A#13[[.]] T#14[S#2])])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#12[(app A#13[(var X#4)] T#14)]),
           T#11  |->  A#12[(app A#13[(var X#4)] T#14)],
           A#9   |->  A#12[(app A#13 T#14[S#2])]}

and instantiated rules:

                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#12[(app A#13[(var X#4)] T#14[S#2])])
    -gc1->                        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#12[(app A#13[(var X#4)] T#14[(letrec {E#1} in S#2)])])
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#12[(app A#13[(var X#4)] T#14[S#2])])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#12[(app A#13[(var X#4)] T#14[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
       ;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]
     in
        (letrec {E#1} in A#9[(var X#4)])
     )
    ,
     (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#9[(var X#4)],(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in [.]),
           T#11  |->  [.],
           S#2   |->  A#9[(var X#4)]}

and instantiated rules:

                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in (letrec {E#1} in A#9[(var X#4)]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#12= T#11[(letrec {E#1} in S#2)]
       ;E#14
       ;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#12= T#11[S#2]
       ;E#14
       ;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#12=T#11;E#14;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)]),
           E#5   |->  {X#12=T#11[S#2];E#14},
           E#13  |->  {E#14;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]}}

and instantiated rules:

                                  (letrec {X#12=T#11[S#2];E#14;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#12=T#11[(letrec {E#1} in S#2)];E#14;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#12=T#11[S#2];E#14;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#12=T#11[S#2];E#14;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#15[(app (letrec {E#6} in T#18[(letrec {E#1} in S#2)]) S#7)]
       ;E#5
     in
        A#9[(var X#4)]
     )
    ,
     (letrec {X#4=A#15[(letrec {E#6} in (app T#18[S#2] S#7))];E#5} in A#9[(var X#4)])
  )

where

   Delta1 = {T#17,T#16,A#14,T#11,T#3,A#15}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#15[(app (letrec {E#6} in T#18) S#7)];E#5} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#5},
           A#14         |->  A#15,
           T#11         |->  A#15[(app (letrec {E#6} in T#18) S#7)],
           T#16         |->  (app (letrec {E#6} in T#18) S#7),
           T#17         |->  (letrec {E#6} in T#18),
           S#8          |->  T#18[S#2]}

and instantiated rules:

                                  (letrec {X#4=A#15[(app (letrec {E#6} in T#18[S#2]) S#7)];E#5} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#15[(app (letrec {E#6} in T#18[(letrec {E#1} in S#2)]) S#7)];E#5} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#15[(app (letrec {E#6} in T#18[S#2]) S#7)];E#5} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=A#15[(letrec {E#6} in (app T#18[S#2] S#7))];E#5} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#15[(app (letrec {X#19=T#18[(letrec {E#1} in S#2)];E#21} in S#8) S#7)]
       ;E#5
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#4= A#15[(letrec {X#19=T#18[S#2];E#21} in (app S#8 S#7))]
       ;E#5
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#17,T#16,A#14,T#11,T#3,A#15}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {X#19=T#18[S#2];E#21} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#15[(app (letrec {X#19=T#18;E#21} in S#8) S#7)];E#5} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#5},
           A#14         |->  A#15,
           T#11         |->  A#15[(app (letrec {X#19=T#18;E#21} in S#8) S#7)],
           T#16         |->  (app (letrec {X#19=T#18;E#21} in S#8) S#7),
           T#17         |->  (letrec {X#19=T#18;E#21} in S#8),
           E#6          |->  {X#19=T#18[S#2];E#21},
           E#20         |->  {E#21}}

and instantiated rules:

                                  (letrec {X#4=A#15[(app (letrec {X#19=T#18[S#2];E#21} in S#8) S#7)];E#5} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#15[(app (letrec {X#19=T#18[(letrec {E#1} in S#2)];E#21} in S#8) S#7)];E#5} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#15[(app (letrec {X#19=T#18[S#2];E#21} in S#8) S#7)];E#5} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=A#15[(letrec {X#19=T#18[S#2];E#21} in (app S#8 S#7))];E#5} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#15[(app (letrec {E#1} in (letrec {E#6} in S#8)) S#7)]
       ;E#5
     in
        A#9[(var X#4)]
     )
    ,
     (letrec {X#4=A#15[(letrec {E#6} in (app S#8 S#7))];E#5} in A#9[(var X#4)])
  )

where

   Delta1 = {T#16,A#14,T#11,T#3,A#15}
   Delta2 = {E#1,E#6}
   Delta3 = {((letrec {E#6} in S#8),(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#15[(app [.] S#7)];E#5} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#5},
           A#14         |->  A#15,
           T#11         |->  A#15[(app [.] S#7)],
           T#16         |->  (app [.] S#7),
           T#17         |->  [.],
           S#2          |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {X#4=A#15[(app (letrec {E#6} in S#8) S#7)];E#5} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#15[(app (letrec {E#1} in (letrec {E#6} in S#8)) S#7)];E#5} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#15[(app (letrec {E#6} in S#8) S#7)];E#5} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=A#15[(letrec {E#6} in (app S#8 S#7))];E#5} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#15[(app (letrec {E#6} in S#8) T#17[(letrec {E#1} in S#2)])]
       ;E#5
     in
        A#9[(var X#4)]
     )
    ,
     (letrec {X#4=A#15[(letrec {E#6} in (app S#8 T#17[S#2]))];E#5} in A#9[(var X#4)])
  )

where

   Delta1 = {T#16,A#14,T#11,T#3,A#15}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#17[S#2],(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#15[(app (letrec {E#6} in S#8) T#17)];E#5} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#5},
           A#14         |->  A#15,
           T#11         |->  A#15[(app (letrec {E#6} in S#8) T#17)],
           T#16         |->  (app (letrec {E#6} in S#8) T#17),
           S#7          |->  T#17[S#2]}

and instantiated rules:

                                  (letrec {X#4=A#15[(app (letrec {E#6} in S#8) T#17[S#2])];E#5} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#15[(app (letrec {E#6} in S#8) T#17[(letrec {E#1} in S#2)])];E#5} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#15[(app (letrec {E#6} in S#8) T#17[S#2])];E#5} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=A#15[(letrec {E#6} in (app S#8 T#17[S#2]))];E#5} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#15[(letrec {E#1} in (app (letrec {E#6} in S#8) S#7))]
       ;E#5
     in
        A#9[(var X#4)]
     )
    ,
     (letrec {X#4=A#15[(letrec {E#6} in (app S#8 S#7))];E#5} in A#9[(var X#4)])
  )

where

   Delta1 = {A#14,T#11,T#3,A#15}
   Delta2 = {E#1,E#6}
   Delta3 = {((app (letrec {E#6} in S#8) S#7),(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#15[[.]];E#5} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#5},
           A#14         |->  A#15,
           T#11         |->  A#15[[.]],
           T#16         |->  [.],
           S#2          |->  (app (letrec {E#6} in S#8) S#7)}

and instantiated rules:

                                  (letrec {X#4=A#15[(app (letrec {E#6} in S#8) S#7)];E#5} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#15[(letrec {E#1} in (app (letrec {E#6} in S#8) S#7))];E#5} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#15[(app (letrec {E#6} in S#8) S#7)];E#5} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=A#15[(letrec {E#6} in (app S#8 S#7))];E#5} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#15[(letrec {E#1} in A#16[(app (letrec {E#6} in S#8) S#7)])]
       ;E#5
     in
        A#9[(var X#4)]
     )
    ,
     (letrec {X#4=A#15[A#16[(letrec {E#6} in (app S#8 S#7))]];E#5} in A#9[(var X#4)])
  )

where

   Delta1 = {A#14,T#11,T#3,A#15}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#16[(app (letrec {E#6} in S#8) S#7)],(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#15;E#5} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#15[A#16[[.2]]]},
           X#12         |->  X#4,
           E#13         |->  {E#5},
           A#14         |->  A#15[A#16],
           T#11         |->  A#15,
           S#2          |->  A#16[(app (letrec {E#6} in S#8) S#7)]}

and instantiated rules:

                                  (letrec {X#4=A#15[A#16[(app (letrec {E#6} in S#8) S#7)]];E#5} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#15[(letrec {E#1} in A#16[(app (letrec {E#6} in S#8) S#7)])];E#5} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#15[A#16[(app (letrec {E#6} in S#8) S#7)]];E#5} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=A#15[A#16[(letrec {E#6} in (app S#8 S#7))]];E#5} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#15[(app A#16[(app (letrec {E#6} in S#8) S#7)] T#17[(letrec {E#1} in S#2)])]
       ;E#5
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#4= A#15[(app A#16[(letrec {E#6} in (app S#8 S#7))] T#17[S#2])]
       ;E#5
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#15[(app A#16[(app (letrec {E#6} in S#8) S#7)] T#17)];E#5} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#15[(app A#16[[.2]] T#17[S#2])]},
           X#12         |->  X#4,
           E#13         |->  {E#5},
           T#11         |->  A#15[(app A#16[(app (letrec {E#6} in S#8) S#7)] T#17)],
           A#14         |->  A#15[(app A#16 T#17[S#2])]}

and instantiated rules:

                                  (letrec {X#4=A#15[(app A#16[(app (letrec {E#6} in S#8) S#7)] T#17[S#2])];E#5} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#15[(app A#16[(app (letrec {E#6} in S#8) S#7)] T#17[(letrec {E#1} in S#2)])];E#5} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#15[(app A#16[(app (letrec {E#6} in S#8) S#7)] T#17[S#2])];E#5} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=A#15[(app A#16[(letrec {E#6} in (app S#8 S#7))] T#17[S#2])];E#5} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (app (letrec {E#6} in T#16[(letrec {E#1} in S#2)]) S#7)
       ;E#5
     in
        A#9[(var X#4)]
     )
    ,
     (letrec {X#4=(letrec {E#6} in (app T#16[S#2] S#7));E#5} in A#9[(var X#4)])
  )

where

   Delta1 = {T#15,T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(app (letrec {E#6} in T#16) S#7);E#5} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=[.2]},
           X#12         |->  X#4,
           E#13         |->  {E#5},
           A#14         |->  [.],
           T#11         |->  (app (letrec {E#6} in T#16) S#7),
           T#15         |->  (letrec {E#6} in T#16),
           S#8          |->  T#16[S#2]}

and instantiated rules:

                                  (letrec {X#4=(app (letrec {E#6} in T#16[S#2]) S#7);E#5} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=(app (letrec {E#6} in T#16[(letrec {E#1} in S#2)]) S#7);E#5} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=(app (letrec {E#6} in T#16[S#2]) S#7);E#5} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=(letrec {E#6} in (app T#16[S#2] S#7));E#5} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (app (letrec {X#17=T#16[(letrec {E#1} in S#2)];E#19} in S#8) S#7)
       ;E#5
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#4= (letrec {X#17=T#16[S#2];E#19} in (app S#8 S#7))
       ;E#5
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#15,T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {X#17=T#16[S#2];E#19} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(app (letrec {X#17=T#16;E#19} in S#8) S#7);E#5} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=[.2]},
           X#12         |->  X#4,
           E#13         |->  {E#5},
           A#14         |->  [.],
           T#11         |->  (app (letrec {X#17=T#16;E#19} in S#8) S#7),
           T#15         |->  (letrec {X#17=T#16;E#19} in S#8),
           E#6          |->  {X#17=T#16[S#2];E#19},
           E#18         |->  {E#19}}

and instantiated rules:

                                  (letrec {X#4=(app (letrec {X#17=T#16[S#2];E#19} in S#8) S#7);E#5} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=(app (letrec {X#17=T#16[(letrec {E#1} in S#2)];E#19} in S#8) S#7);E#5} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=(app (letrec {X#17=T#16[S#2];E#19} in S#8) S#7);E#5} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=(letrec {X#17=T#16[S#2];E#19} in (app S#8 S#7));E#5} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (app (letrec {E#1} in (letrec {E#6} in S#8)) S#7)
       ;E#5
     in
        A#9[(var X#4)]
     )
    ,
     (letrec {X#4=(letrec {E#6} in (app S#8 S#7));E#5} in A#9[(var X#4)])
  )

where

   Delta1 = {T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {((letrec {E#6} in S#8),(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(app [.] S#7);E#5} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=[.2]},
           X#12         |->  X#4,
           E#13         |->  {E#5},
           A#14         |->  [.],
           T#11         |->  (app [.] S#7),
           T#15         |->  [.],
           S#2          |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {X#4=(app (letrec {E#6} in S#8) S#7);E#5} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=(app (letrec {E#1} in (letrec {E#6} in S#8)) S#7);E#5} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=(app (letrec {E#6} in S#8) S#7);E#5} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=(letrec {E#6} in (app S#8 S#7));E#5} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (app (letrec {E#6} in S#8) T#15[(letrec {E#1} in S#2)])
       ;E#5
     in
        A#9[(var X#4)]
     )
    ,
     (letrec {X#4=(letrec {E#6} in (app S#8 T#15[S#2]));E#5} in A#9[(var X#4)])
  )

where

   Delta1 = {T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#15[S#2],(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=(app (letrec {E#6} in S#8) T#15);E#5} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=[.2]},
           X#12         |->  X#4,
           E#13         |->  {E#5},
           A#14         |->  [.],
           T#11         |->  (app (letrec {E#6} in S#8) T#15),
           S#7          |->  T#15[S#2]}

and instantiated rules:

                                  (letrec {X#4=(app (letrec {E#6} in S#8) T#15[S#2]);E#5} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=(app (letrec {E#6} in S#8) T#15[(letrec {E#1} in S#2)]);E#5} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=(app (letrec {E#6} in S#8) T#15[S#2]);E#5} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=(letrec {E#6} in (app S#8 T#15[S#2]));E#5} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#1} in A#14[(app (letrec {E#6} in S#8) S#7)])
       ;E#5
     in
        A#9[(var X#4)]
     )
    ,
     (letrec {X#4=A#14[(letrec {E#6} in (app S#8 S#7))];E#5} in A#9[(var X#4)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#14[(app (letrec {E#6} in S#8) S#7)],(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=[.];E#5} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#14[[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#5},
           T#11         |->  [.],
           S#2          |->  A#14[(app (letrec {E#6} in S#8) S#7)]}

and instantiated rules:

                                  (letrec {X#4=A#14[(app (letrec {E#6} in S#8) S#7)];E#5} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=(letrec {E#1} in A#14[(app (letrec {E#6} in S#8) S#7)]);E#5} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#14[(app (letrec {E#6} in S#8) S#7)];E#5} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=A#14[(letrec {E#6} in (app S#8 S#7))];E#5} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#17[(letrec {E#1} in (var X#15))]
       ;E#5
       ;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#4= A#17[(var X#15)]
       ;E#5
       ;EE#16[X#15,(letrec {E#6} in (app S#8 S#7))]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#17}
   Delta2 = {E#1,E#6}
   Delta3 = {((var X#15),(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#17[[.]];E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#17[(var X#15)];EE#16[X#15,[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]},
           A#14         |->  A#17,
           T#11         |->  A#17[[.]],
           T#18         |->  [.],
           S#2          |->  (var X#15)}

and instantiated rules:

                                  (letrec {X#4=A#17[(var X#15)];E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#17[(letrec {E#1} in (var X#15))];E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#17[(var X#15)];E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=A#17[(var X#15)];E#5;EE#16[X#15,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#17[(letrec {E#1} in A#18[(var X#15)])]
       ;E#5
       ;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#4= A#17[A#18[(var X#15)]]
       ;E#5
       ;EE#16[X#15,(letrec {E#6} in (app S#8 S#7))]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#17}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#18[(var X#15)],(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#17;E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#17[A#18[(var X#15)]];EE#16[X#15,[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]},
           A#14         |->  A#17[A#18],
           T#11         |->  A#17,
           S#2          |->  A#18[(var X#15)]}

and instantiated rules:

                                  (letrec {X#4=A#17[A#18[(var X#15)]];E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#17[(letrec {E#1} in A#18[(var X#15)])];E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#17[A#18[(var X#15)]];E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=A#17[A#18[(var X#15)]];E#5;EE#16[X#15,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= A#17[(app A#18[(var X#15)] T#19[(letrec {E#1} in S#2)])]
       ;E#5
       ;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#4= A#17[(app A#18[(var X#15)] T#19[S#2])]
       ;E#5
       ;EE#16[X#15,(letrec {E#6} in (app S#8 S#7))]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=A#17[(app A#18[(var X#15)] T#19)];E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#17[(app A#18[(var X#15)] T#19[S#2])];EE#16[X#15,[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]},
           T#11         |->  A#17[(app A#18[(var X#15)] T#19)],
           A#14         |->  A#17[(app A#18 T#19[S#2])]}

and instantiated rules:

                                  (letrec {X#4=A#17[(app A#18[(var X#15)] T#19[S#2])];E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=A#17[(app A#18[(var X#15)] T#19[(letrec {E#1} in S#2)])];E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#17[(app A#18[(var X#15)] T#19[S#2])];E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=A#17[(app A#18[(var X#15)] T#19[S#2])];E#5;EE#16[X#15,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#4= (letrec {E#1} in A#14[(var X#15)])
       ;E#5
       ;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#4= A#14[(var X#15)]
       ;E#5
       ;EE#16[X#15,(letrec {E#6} in (app S#8 S#7))]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#14[(var X#15)],(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#4=[.];E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {[.1]=A#14[(var X#15)];EE#16[X#15,[.2]]},
           X#12         |->  X#4,
           E#13         |->  {E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]},
           T#11         |->  [.],
           S#2          |->  A#14[(var X#15)]}

and instantiated rules:

                                  (letrec {X#4=A#14[(var X#15)];E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#4=(letrec {E#1} in A#14[(var X#15)]);E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#4=A#14[(var X#15)];E#5;EE#16[X#15,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#4=A#14[(var X#15)];E#5;EE#16[X#15,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#19[(letrec {E#1} in (var X#16))]
       ;E#5
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#19[(var X#16)]
       ;E#5
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(letrec {E#6} in (app S#8 S#7))]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#19}
   Delta2 = {E#1,E#6}
   Delta3 = {((var X#16),(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#19[[.]];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#19[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]},
           A#14         |->  A#19,
           T#11         |->  A#19[[.]],
           T#20         |->  [.],
           S#2          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#15=A#19[(var X#16)];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#19[(letrec {E#1} in (var X#16))];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#19[(var X#16)];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=A#19[(var X#16)];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#19[(letrec {E#1} in A#20[(var X#16)])]
       ;E#5
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#19[A#20[(var X#16)]]
       ;E#5
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(letrec {E#6} in (app S#8 S#7))]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#19}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#20[(var X#16)],(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#19;E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#19[A#20[(var X#16)]];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]},
           A#14         |->  A#19[A#20],
           T#11         |->  A#19,
           S#2          |->  A#20[(var X#16)]}

and instantiated rules:

                                  (letrec {X#15=A#19[A#20[(var X#16)]];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#19[(letrec {E#1} in A#20[(var X#16)])];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#19[A#20[(var X#16)]];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=A#19[A#20[(var X#16)]];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#19[(app A#20[(var X#16)] T#21[(letrec {E#1} in S#2)])]
       ;E#5
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#19[(app A#20[(var X#16)] T#21[S#2])]
       ;E#5
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(letrec {E#6} in (app S#8 S#7))]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#19[(app A#20[(var X#16)] T#21)];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#19[(app A#20[(var X#16)] T#21[S#2])];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]},
           T#11         |->  A#19[(app A#20[(var X#16)] T#21)],
           A#14         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#15=A#19[(app A#20[(var X#16)] T#21[S#2])];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#19[(app A#20[(var X#16)] T#21[(letrec {E#1} in S#2)])];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#19[(app A#20[(var X#16)] T#21[S#2])];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=A#19[(app A#20[(var X#16)] T#21[S#2])];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#1} in A#14[(var X#16)])
       ;E#5
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#14[(var X#16)]
       ;E#5
       ;EE#17[X#4,(var X#15)]
       ;EE#18[X#16,(letrec {E#6} in (app S#8 S#7))]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#14[(var X#16)],(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=[.];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#14[(var X#16)];EE#17[[.1],(var X#15)];EE#18[X#16,[.2]]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]},
           T#11         |->  [.],
           S#2          |->  A#14[(var X#16)]}

and instantiated rules:

                                  (letrec {X#15=A#14[(var X#16)];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=(letrec {E#1} in A#14[(var X#16)]);E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#14[(var X#16)];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=A#14[(var X#16)];E#5;EE#17[X#4,(var X#15)];EE#18[X#16,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#17[(app (letrec {E#6} in T#20[(letrec {E#1} in S#2)]) S#7)]
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#17[(letrec {E#6} in (app T#20[S#2] S#7))]
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#19,T#18,A#14,T#11,T#3,A#17}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#17[(app (letrec {E#6} in T#20) S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#17[[.2]];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#16[X#4,(var X#15)]},
           A#14         |->  A#17,
           T#11         |->  A#17[(app (letrec {E#6} in T#20) S#7)],
           T#18         |->  (app (letrec {E#6} in T#20) S#7),
           T#19         |->  (letrec {E#6} in T#20),
           S#8          |->  T#20[S#2]}

and instantiated rules:

                                  (letrec {X#15=A#17[(app (letrec {E#6} in T#20[S#2]) S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#17[(app (letrec {E#6} in T#20[(letrec {E#1} in S#2)]) S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#17[(app (letrec {E#6} in T#20[S#2]) S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=A#17[(letrec {E#6} in (app T#20[S#2] S#7))];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#17[(app (letrec {X#21=T#20[(letrec {E#1} in S#2)];E#23} in S#8) S#7)]
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#17[(letrec {X#21=T#20[S#2];E#23} in (app S#8 S#7))]
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#19,T#18,A#14,T#11,T#3,A#17}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {X#21=T#20[S#2];E#23} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#17[(app (letrec {X#21=T#20;E#23} in S#8) S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#17[[.2]];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#16[X#4,(var X#15)]},
           A#14         |->  A#17,
           T#11         |->  A#17[(app (letrec {X#21=T#20;E#23} in S#8) S#7)],
           T#18         |->  (app (letrec {X#21=T#20;E#23} in S#8) S#7),
           T#19         |->  (letrec {X#21=T#20;E#23} in S#8),
           E#6          |->  {X#21=T#20[S#2];E#23},
           E#22         |->  {E#23}}

and instantiated rules:

                                  (letrec {X#15=A#17[(app (letrec {X#21=T#20[S#2];E#23} in S#8) S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#17[(app (letrec {X#21=T#20[(letrec {E#1} in S#2)];E#23} in S#8) S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#17[(app (letrec {X#21=T#20[S#2];E#23} in S#8) S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=A#17[(letrec {X#21=T#20[S#2];E#23} in (app S#8 S#7))];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#17[(app (letrec {E#1} in (letrec {E#6} in S#8)) S#7)]
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#17[(letrec {E#6} in (app S#8 S#7))]
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#18,A#14,T#11,T#3,A#17}
   Delta2 = {E#1,E#6}
   Delta3 = {((letrec {E#6} in S#8),(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#17[(app [.] S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#17[[.2]];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#16[X#4,(var X#15)]},
           A#14         |->  A#17,
           T#11         |->  A#17[(app [.] S#7)],
           T#18         |->  (app [.] S#7),
           T#19         |->  [.],
           S#2          |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {X#15=A#17[(app (letrec {E#6} in S#8) S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#17[(app (letrec {E#1} in (letrec {E#6} in S#8)) S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#17[(app (letrec {E#6} in S#8) S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=A#17[(letrec {E#6} in (app S#8 S#7))];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#17[(app (letrec {E#6} in S#8) T#19[(letrec {E#1} in S#2)])]
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#17[(letrec {E#6} in (app S#8 T#19[S#2]))]
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#18,A#14,T#11,T#3,A#17}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#19[S#2],(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#17[(app (letrec {E#6} in S#8) T#19)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#17[[.2]];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#16[X#4,(var X#15)]},
           A#14         |->  A#17,
           T#11         |->  A#17[(app (letrec {E#6} in S#8) T#19)],
           T#18         |->  (app (letrec {E#6} in S#8) T#19),
           S#7          |->  T#19[S#2]}

and instantiated rules:

                                  (letrec {X#15=A#17[(app (letrec {E#6} in S#8) T#19[S#2])];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#17[(app (letrec {E#6} in S#8) T#19[(letrec {E#1} in S#2)])];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#17[(app (letrec {E#6} in S#8) T#19[S#2])];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=A#17[(letrec {E#6} in (app S#8 T#19[S#2]))];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#17[(letrec {E#1} in (app (letrec {E#6} in S#8) S#7))]
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#17[(letrec {E#6} in (app S#8 S#7))]
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#17}
   Delta2 = {E#1,E#6}
   Delta3 = {((app (letrec {E#6} in S#8) S#7),(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#17[[.]];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#17[[.2]];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#16[X#4,(var X#15)]},
           A#14         |->  A#17,
           T#11         |->  A#17[[.]],
           T#18         |->  [.],
           S#2          |->  (app (letrec {E#6} in S#8) S#7)}

and instantiated rules:

                                  (letrec {X#15=A#17[(app (letrec {E#6} in S#8) S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#17[(letrec {E#1} in (app (letrec {E#6} in S#8) S#7))];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#17[(app (letrec {E#6} in S#8) S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=A#17[(letrec {E#6} in (app S#8 S#7))];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#17[(letrec {E#1} in A#18[(app (letrec {E#6} in S#8) S#7)])]
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#17[A#18[(letrec {E#6} in (app S#8 S#7))]]
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3,A#17}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#18[(app (letrec {E#6} in S#8) S#7)],(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#17;E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#17[A#18[[.2]]];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#16[X#4,(var X#15)]},
           A#14         |->  A#17[A#18],
           T#11         |->  A#17,
           S#2          |->  A#18[(app (letrec {E#6} in S#8) S#7)]}

and instantiated rules:

                                  (letrec {X#15=A#17[A#18[(app (letrec {E#6} in S#8) S#7)]];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#17[(letrec {E#1} in A#18[(app (letrec {E#6} in S#8) S#7)])];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#17[A#18[(app (letrec {E#6} in S#8) S#7)]];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=A#17[A#18[(letrec {E#6} in (app S#8 S#7))]];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= A#17[(app A#18[(app (letrec {E#6} in S#8) S#7)] T#19[(letrec {E#1} in S#2)])]
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#17[(app A#18[(letrec {E#6} in (app S#8 S#7))] T#19[S#2])]
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {A#14,T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=A#17[(app A#18[(app (letrec {E#6} in S#8) S#7)] T#19)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#17[(app A#18[[.2]] T#19[S#2])];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#16[X#4,(var X#15)]},
           T#11         |->  A#17[(app A#18[(app (letrec {E#6} in S#8) S#7)] T#19)],
           A#14         |->  A#17[(app A#18 T#19[S#2])]}

and instantiated rules:

                                  (letrec {X#15=A#17[(app A#18[(app (letrec {E#6} in S#8) S#7)] T#19[S#2])];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=A#17[(app A#18[(app (letrec {E#6} in S#8) S#7)] T#19[(letrec {E#1} in S#2)])];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#17[(app A#18[(app (letrec {E#6} in S#8) S#7)] T#19[S#2])];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=A#17[(app A#18[(letrec {E#6} in (app S#8 S#7))] T#19[S#2])];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (app (letrec {E#6} in T#18[(letrec {E#1} in S#2)]) S#7)
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= (letrec {E#6} in (app T#18[S#2] S#7))
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#17,T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=(app (letrec {E#6} in T#18) S#7);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=[.2];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#16[X#4,(var X#15)]},
           A#14         |->  [.],
           T#11         |->  (app (letrec {E#6} in T#18) S#7),
           T#17         |->  (letrec {E#6} in T#18),
           S#8          |->  T#18[S#2]}

and instantiated rules:

                                  (letrec {X#15=(app (letrec {E#6} in T#18[S#2]) S#7);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=(app (letrec {E#6} in T#18[(letrec {E#1} in S#2)]) S#7);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=(app (letrec {E#6} in T#18[S#2]) S#7);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=(letrec {E#6} in (app T#18[S#2] S#7));E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (app (letrec {X#19=T#18[(letrec {E#1} in S#2)];E#21} in S#8) S#7)
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= (letrec {X#19=T#18[S#2];E#21} in (app S#8 S#7))
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#17,T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (S#7,(letrec {X#19=T#18[S#2];E#21} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=(app (letrec {X#19=T#18;E#21} in S#8) S#7);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=[.2];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#16[X#4,(var X#15)]},
           A#14         |->  [.],
           T#11         |->  (app (letrec {X#19=T#18;E#21} in S#8) S#7),
           T#17         |->  (letrec {X#19=T#18;E#21} in S#8),
           E#6          |->  {X#19=T#18[S#2];E#21},
           E#20         |->  {E#21}}

and instantiated rules:

                                  (letrec {X#15=(app (letrec {X#19=T#18[S#2];E#21} in S#8) S#7);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=(app (letrec {X#19=T#18[(letrec {E#1} in S#2)];E#21} in S#8) S#7);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=(app (letrec {X#19=T#18[S#2];E#21} in S#8) S#7);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=(letrec {X#19=T#18[S#2];E#21} in (app S#8 S#7));E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (app (letrec {E#1} in (letrec {E#6} in S#8)) S#7)
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= (letrec {E#6} in (app S#8 S#7))
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {((letrec {E#6} in S#8),(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=(app [.] S#7);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=[.2];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#16[X#4,(var X#15)]},
           A#14         |->  [.],
           T#11         |->  (app [.] S#7),
           T#17         |->  [.],
           S#2          |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {X#15=(app (letrec {E#6} in S#8) S#7);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=(app (letrec {E#1} in (letrec {E#6} in S#8)) S#7);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=(app (letrec {E#6} in S#8) S#7);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=(letrec {E#6} in (app S#8 S#7));E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (app (letrec {E#6} in S#8) T#17[(letrec {E#1} in S#2)])
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= (letrec {E#6} in (app S#8 T#17[S#2]))
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#11,T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(S#2,(letrec {E#1} in [.])),
             (T#17[S#2],(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=(app (letrec {E#6} in S#8) T#17);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=[.2];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#16[X#4,(var X#15)]},
           A#14         |->  [.],
           T#11         |->  (app (letrec {E#6} in S#8) T#17),
           S#7          |->  T#17[S#2]}

and instantiated rules:

                                  (letrec {X#15=(app (letrec {E#6} in S#8) T#17[S#2]);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=(app (letrec {E#6} in S#8) T#17[(letrec {E#1} in S#2)]);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=(app (letrec {E#6} in S#8) T#17[S#2]);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=(letrec {E#6} in (app S#8 T#17[S#2]));E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= (letrec {E#1} in A#14[(app (letrec {E#6} in S#8) S#7)])
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
    ,
     (letrec
        X#15= A#14[(letrec {E#6} in (app S#8 S#7))]
       ;E#5
       ;EE#16[X#4,(var X#15)]
     in
        A#9[(var X#4)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#1,E#6}
   Delta3 = {(A#14[(app (letrec {E#6} in S#8) S#7)],(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#15=[.];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)]),
           EE#10[.1,.2] |-> {X#15=A#14[[.2]];EE#16[[.1],(var X#15)]},
           X#12         |->  X#15,
           E#13         |->  {E#5;EE#16[X#4,(var X#15)]},
           T#11         |->  [.],
           S#2          |->  A#14[(app (letrec {E#6} in S#8) S#7)]}

and instantiated rules:

                                  (letrec {X#15=A#14[(app (letrec {E#6} in S#8) S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -gc1->                        (letrec {X#15=(letrec {E#1} in A#14[(app (letrec {E#6} in S#8) S#7)]);E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    ................................................................................
                                  (letrec {X#15=A#14[(app (letrec {E#6} in S#8) S#7)];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {X#15=A#14[(letrec {E#6} in (app S#8 S#7))];E#5;EE#16[X#4,(var X#15)]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#1
     in
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
     )
    ,
     (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#6}
   Delta3 = {((letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)]),(letrec {E#1} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#4),A#9[[.]]),
             ((var X#4),A#9[[.]])}
   Delta4=  {}

from overlapping -gc1-> . -SR,lapp3-> with input rules:

                                  T#3[S#2]
    -gc1->                        T#3[(letrec {E#1} in S#2)]
    and constraints: E#1/= {}, (S#2,(letrec {E#1} in [.]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[S#2]
        =?=
        (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}
      Delta1=  {}
      Delta2=  {E#1,E#6}
      Delta3=  {(S#2,(letrec {E#1} in [.])),(S#7,(letrec {E#6} in [.])),((var X#4),A#9[[.]]),((var X#4),A#9[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           S#2  |->  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])}

and instantiated rules:

                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -gc1->                        (letrec {E#1} in (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)]))
    ................................................................................
                                  (letrec {E#5;EE#10[X#4,(app (letrec {E#6} in S#8) S#7)]} in A#9[(var X#4)])
    -SR,lapp3->                   (letrec {E#5;EE#10[X#4,(letrec {E#6} in (app S#8 S#7))]} in A#9[(var X#4)])
    

================================================================================
Critical Pair:

  (
     A#9[(app (\ X#5.S#7) T#11[(letrec {E#1;E#2} in S#3)])]
    ,
     A#9[(letrec {X#5=T#11[(letrec {E#1} in S#3)]} in S#7)]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#11[(letrec {E#1} in S#3)],(\ X#5.[.])),
             (T#11[(letrec {E#1} in S#3)],(letrec {X#5=[.]} in S#7))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (\ X#5.S#7) T#11)],
           T#10  |->  (app (\ X#5.S#7) T#11),
           S#6   |->  T#11[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  A#9[(app (\ X#5.S#7) T#11[(letrec {E#1} in S#3)])]
    -gc2->                        A#9[(app (\ X#5.S#7) T#11[(letrec {E#1;E#2} in S#3)])]
    ................................................................................
                                  A#9[(app (\ X#5.S#7) T#11[(letrec {E#1} in S#3)])]
    -SR,lbeta1->                  A#9[(letrec {X#5=T#11[(letrec {E#1} in S#3)]} in S#7)]
    

================================================================================
Critical Pair:

  (
     A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(letrec {E#1;E#2} in S#3)])]
    ,
     A#9[(app A#10[(letrec {X#5=S#6} in S#7)] T#11[(letrec {E#1} in S#3)])]
  )

where

   Delta1 = {A#8,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7))}


and found solution:

    Sol = {T#4  |->  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11)],
           A#8  |->  A#9[(app A#10 T#11[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(letrec {E#1} in S#3)])]
    -gc2->                        A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(letrec {E#1;E#2} in S#3)])]
    ................................................................................
                                  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(letrec {E#1} in S#3)])]
    -SR,lbeta1->                  A#9[(app A#10[(letrec {X#5=S#6} in S#7)] T#11[(letrec {E#1} in S#3)])]
    

================================================================================
Critical Pair:

  (
     (app (\ X#5.S#7) T#9[(letrec {E#1;E#2} in S#3)])
    ,
     (letrec {X#5=T#9[(letrec {E#1} in S#3)]} in S#7)
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#9[(letrec {E#1} in S#3)],(\ X#5.[.])),
             (T#9[(letrec {E#1} in S#3)],(letrec {X#5=[.]} in S#7))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7))}


and found solution:

    Sol = {A#8  |->  [.],
           T#4  |->  (app (\ X#5.S#7) T#9),
           S#6  |->  T#9[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (app (\ X#5.S#7) T#9[(letrec {E#1} in S#3)])
    -gc2->                        (app (\ X#5.S#7) T#9[(letrec {E#1;E#2} in S#3)])
    ................................................................................
                                  (app (\ X#5.S#7) T#9[(letrec {E#1} in S#3)])
    -SR,lbeta1->                  (letrec {X#5=T#9[(letrec {E#1} in S#3)]} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(letrec {E#1;E#2} in S#3)])])
    ,
     (letrec {E#6} in A#11[(letrec {X#5=T#13[(letrec {E#1} in S#3)]} in S#8)])
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#13[(letrec {E#1} in S#3)],(\ X#5.[.])),
             (T#13[(letrec {E#1} in S#3)],(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (\ X#5.S#8) T#13)],
           T#12  |->  (app (\ X#5.S#8) T#13),
           S#7   |->  T#13[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(letrec {E#1} in S#3)])])
    -gc2->                        (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(letrec {E#1;E#2} in S#3)])])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(letrec {E#1} in S#3)])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=T#13[(letrec {E#1} in S#3)]} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(letrec {E#1;E#2} in S#3)])]
     )
    ,
     (letrec
        E#6
     in
        A#11[(app A#12[(letrec {X#5=S#7} in S#8)] T#13[(letrec {E#1} in S#3)])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)]),
           T#10  |->  A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(letrec {E#1} in S#3)])])
    -gc2->                        (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(letrec {E#1;E#2} in S#3)])])
    ................................................................................
                                  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(letrec {E#1} in S#3)])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(app A#12[(letrec {X#5=S#7} in S#8)] T#13[(letrec {E#1} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (app (\ X#5.S#8) T#11[(letrec {E#1;E#2} in S#3)]))
    ,
     (letrec {E#6} in (letrec {X#5=T#11[(letrec {E#1} in S#3)]} in S#8))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#11[(letrec {E#1} in S#3)],(\ X#5.[.])),
             (T#11[(letrec {E#1} in S#3)],(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in (app (\ X#5.S#8) T#11)),
           A#9   |->  [.],
           T#10  |->  (app (\ X#5.S#8) T#11),
           S#7   |->  T#11[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {E#6} in (app (\ X#5.S#8) T#11[(letrec {E#1} in S#3)]))
    -gc2->                        (letrec {E#6} in (app (\ X#5.S#8) T#11[(letrec {E#1;E#2} in S#3)]))
    ................................................................................
                                  (letrec {E#6} in (app (\ X#5.S#8) T#11[(letrec {E#1} in S#3)]))
    -SR,lbeta2->                  (letrec {E#6} in (letrec {X#5=T#11[(letrec {E#1} in S#3)]} in S#8))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(letrec {E#1;E#2} in S#3)]
       ;E#13
     in
        A#9[(app (\ X#5.S#8) S#7)]
     )
    ,
     (letrec
        X#11= T#10[(letrec {E#1} in S#3)]
       ;E#13
     in
        A#9[(letrec {X#5=S#7} in S#8)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;E#13} in A#9[(app (\ X#5.S#8) S#7)]),
           E#6   |->  {X#11=T#10[(letrec {E#1} in S#3)];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {E#1} in S#3)];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    -gc2->                        (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {E#1} in S#3)];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {X#11=T#10[(letrec {E#1} in S#3)];E#13} in A#9[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#2;E#6} in A#9[(app (\ X#5.S#8) S#7)])
    ,
     (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {(A#9[(app (\ X#5.S#8) S#7)],(letrec {E#2} in [.])),
             [{E#6},(letrec {E#2} in [.])],
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8))}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#9[(app (\ X#5.S#8) S#7)],
           E#1  |->  {E#6}}

and instantiated rules:

                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -gc2->                        (letrec {E#2;E#6} in A#9[(app (\ X#5.S#8) S#7)])
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        A#13[(app A#14[(var X#5)] T#15[(letrec {E#1;E#2} in S#3)])]
     )
    ,
     (letrec
        E#7
       ;EE#11[X#5,(letrec {X#6=S#8} in S#9)]
     in
        A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in S#3)])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {E#1} in S#3)])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {E#1} in S#3)])])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#5)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in S#3)])])
    -gc2->                        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1;E#2} in S#3)])])
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in S#3)])])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {E#1;E#2} in S#3)]
       ;E#15
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {E#1} in S#3)]
       ;E#15
       ;EE#11[X#5,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           E#7   |->  {X#13=T#12[(letrec {E#1} in S#3)];E#15},
           E#14  |->  {E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (\ X#6.S#9) T#18[(letrec {E#1;E#2} in S#3)])]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {X#6=T#18[(letrec {E#1} in S#3)]} in S#9)]
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#18[(letrec {E#1} in S#3)],(\ X#6.[.])),
             (T#18[(letrec {E#1} in S#3)],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18)];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (\ X#6.S#9) T#18)],
           T#17         |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(letrec {E#1} in S#3)])];E#7} in A#10[(var X#5)])
    -gc2->                        (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(letrec {E#1;E#2} in S#3)])];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(letrec {E#1} in S#3)])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=T#18[(letrec {E#1} in S#3)]} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(letrec {E#1;E#2} in S#3)])]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(app A#17[(letrec {X#6=S#8} in S#9)] T#18[(letrec {E#1} in S#3)])]
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[(letrec {E#1} in S#3)])]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           T#12         |->  A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(letrec {E#1} in S#3)])];E#7} in A#10[(var X#5)])
    -gc2->                        (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(letrec {E#1;E#2} in S#3)])];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(letrec {E#1} in S#3)])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(app A#17[(letrec {X#6=S#8} in S#9)] T#18[(letrec {E#1} in S#3)])];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (\ X#6.S#9) T#16[(letrec {E#1;E#2} in S#3)])
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {X#6=T#16[(letrec {E#1} in S#3)]} in S#9)
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#16[(letrec {E#1} in S#3)],(\ X#6.[.])),
             (T#16[(letrec {E#1} in S#3)],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (\ X#6.S#9) T#16);E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  [.],
           T#12         |->  (app (\ X#6.S#9) T#16),
           S#8          |->  T#16[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=(app (\ X#6.S#9) T#16[(letrec {E#1} in S#3)]);E#7} in A#10[(var X#5)])
    -gc2->                        (letrec {X#5=(app (\ X#6.S#9) T#16[(letrec {E#1;E#2} in S#3)]);E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (\ X#6.S#9) T#16[(letrec {E#1} in S#3)]);E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=(letrec {X#6=T#16[(letrec {E#1} in S#3)]} in S#9);E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])]
       ;E#7
       ;EE#17[X#16,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])]
       ;E#7
       ;EE#17[X#16,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])];E#7;EE#17[X#16,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (\ X#6.S#9) T#20[(letrec {E#1;E#2} in S#3)])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=T#20[(letrec {E#1} in S#3)]} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#20[(letrec {E#1} in S#3)],(\ X#6.[.])),
             (T#20[(letrec {E#1} in S#3)],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (\ X#6.S#9) T#20)],
           T#19         |->  (app (\ X#6.S#9) T#20),
           S#8          |->  T#20[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[(letrec {E#1} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[(letrec {E#1;E#2} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[(letrec {E#1} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=T#20[(letrec {E#1} in S#3)]} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(letrec {E#1;E#2} in S#3)])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[(letrec {E#1} in S#3)])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[(letrec {E#1} in S#3)])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           T#12         |->  A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(letrec {E#1} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(letrec {E#1;E#2} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(letrec {E#1} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[(letrec {E#1} in S#3)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (\ X#6.S#9) T#18[(letrec {E#1;E#2} in S#3)])
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#6=T#18[(letrec {E#1} in S#3)]} in S#9)
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#18[(letrec {E#1} in S#3)],(\ X#6.[.])),
             (T#18[(letrec {E#1} in S#3)],(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (\ X#6.S#9) T#18);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=(app (\ X#6.S#9) T#18[(letrec {E#1} in S#3)]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#16=(app (\ X#6.S#9) T#18[(letrec {E#1;E#2} in S#3)]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (\ X#6.S#9) T#18[(letrec {E#1} in S#3)]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=(letrec {X#6=T#18[(letrec {E#1} in S#3)]} in S#9);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#2;E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ,
     (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2}
   Delta3 = {(A#10[(var X#5)],(letrec {E#2} in [.])),
             [{E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]},(letrec {E#2} in [.])],
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#10[(var X#5)],
           E#1  |->  {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]}}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -gc2->                        (letrec {E#2;E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#8)
       ;E#7
     in
        A#11[(app A#12[(var X#5)] T#13[(letrec {E#1;E#2} in S#3)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#8)
       ;E#7
     in
        A#11[(app A#12[(\ X#6.S#8)] T#13[(letrec {E#1} in S#3)])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#11[(app A#12[[.]] T#13[(letrec {E#1} in S#3)])])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)]),
           T#10  |->  A#11[(app A#12[(var X#5)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in S#3)])])
    -gc2->                        (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1;E#2} in S#3)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in S#3)])])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(\ X#6.S#8)] T#13[(letrec {E#1} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(letrec {E#1;E#2} in S#3)]
       ;X#5= (\ X#6.S#8)
       ;E#13
     in
        A#9[(var X#5)]
     )
    ,
     (letrec
        X#11= T#10[(letrec {E#1} in S#3)]
       ;X#5= (\ X#6.S#8)
       ;E#13
     in
        A#9[(\ X#6.S#8)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)]),
           E#7   |->  {X#11=T#10[(letrec {E#1} in S#3)];E#13},
           E#12  |->  {X#5=(\ X#6.S#8);E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {E#1} in S#3)];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    -gc2->                        (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {E#1} in S#3)];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#11=T#10[(letrec {E#1} in S#3)];X#5=(\ X#6.S#8);E#13} in A#9[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(\ X#6.S#8);E#2;E#7} in A#9[(var X#5)])
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2}
   Delta3 = {(A#9[(var X#5)],(letrec {E#2} in [.])),
             [{X#5=(\ X#6.S#8);E#7},(letrec {E#2} in [.])],
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#9[(var X#5)],
           E#1  |->  {X#5=(\ X#6.S#8);E#7}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -gc2->                        (letrec {X#5=(\ X#6.S#8);E#2;E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(app A#14[(var X#7)] T#15[(letrec {E#1;E#2} in S#3)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(app A#14[(\ X#6.S#9)] T#15[(letrec {E#1} in S#3)])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#13[(app A#14[[.]] T#15[(letrec {E#1} in S#3)])]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#7)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[(letrec {E#1} in S#3)])])
    -gc2->                        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[(letrec {E#1;E#2} in S#3)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[(letrec {E#1} in S#3)])])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(\ X#6.S#9)] T#15[(letrec {E#1} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {E#1;E#2} in S#3)]
       ;X#5= (\ X#6.S#9)
       ;E#15
       ;VV#11|X#7,(var X#5)|
     in
        A#10[(var X#7)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {E#1} in S#3)]
       ;X#5= (\ X#6.S#9)
       ;E#15
       ;VV#11|X#7,(var X#5)|
     in
        A#10[(\ X#6.S#9)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)]),
           E#8   |->  {X#13=T#12[(letrec {E#1} in S#3)];E#15},
           E#14  |->  {X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {E#1} in S#3)];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -gc2->                        (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {E#1} in S#3)];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#13=T#12[(letrec {E#1} in S#3)];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(\ X#6.S#9);E#2;E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2}
   Delta3 = {(A#10[(var X#7)],(letrec {E#2} in [.])),
             [{X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#10[(var X#7)],
           E#1  |->  {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -gc2->                        (letrec {X#5=(\ X#6.S#9);E#2;E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#14[(app A#15[(var X#7)] T#16[(letrec {E#1;E#2} in S#3)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#14[(app A#15[(var X#7)] T#16[(letrec {E#1} in S#3)])]
     )
  )

where

   Delta1 = {A#11,T#13,T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#14[(app A#15[[.]] T#16[(letrec {E#1} in S#3)])]),
             ((var X#7),A#14[(app A#15[[.]] T#16[(letrec {E#1} in S#3)])])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#7)] T#16)],
           A#11  |->  A#14[(app A#15 T#16[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[(letrec {E#1} in S#3)])])
    -gc2->                        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[(letrec {E#1;E#2} in S#3)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[(letrec {E#1} in S#3)])])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[(app A#15[(var X#7)] T#16[(letrec {E#1} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {E#1;E#2} in S#3)]
       ;X#5= (\ X#6.S#9)
       ;E#16
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {E#1} in S#3)]
       ;X#5= (\ X#6.S#9)
       ;E#16
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#14=T#13;X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)]),
           E#8   |->  {X#14=T#13[(letrec {E#1} in S#3)];E#16},
           E#15  |->  {X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {E#1} in S#3)];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -gc2->                        (letrec {X#14=T#13[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {E#1} in S#3)];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#14=T#13[(letrec {E#1} in S#3)];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[(var X#5)] T#21[(letrec {E#1;E#2} in S#3)])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {E#1} in S#3)])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#18,A#16,T#13,T#4,A#10,A#17}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#19[(app A#20[[.]] T#21[(letrec {E#1} in S#3)])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21)]];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[A#19[(app A#20[(var X#5)] T#21)]],
           T#18         |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[(letrec {E#1} in S#3)])]];E#8} in A#11[(var X#7)])
    -gc2->                        (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[(letrec {E#1;E#2} in S#3)])]];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[(letrec {E#1} in S#3)])]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {E#1} in S#3)])]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[A#10[(var X#5)]] T#19[(letrec {E#1;E#2} in S#3)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[A#10[(\ X#6.S#9)]] T#19[(letrec {E#1} in S#3)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19)];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] T#19[(letrec {E#1} in S#3)])]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  A#17[(app A#18[A#10[(var X#5)]] T#19)],
           A#16         |->  A#17[(app A#18 T#19[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[(letrec {E#1} in S#3)])];E#8} in A#11[(var X#7)])
    -gc2->                        (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[(letrec {E#1;E#2} in S#3)])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[(letrec {E#1} in S#3)])];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(\ X#6.S#9)]] T#19[(letrec {E#1} in S#3)])];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[(var X#5)] T#19[(letrec {E#1;E#2} in S#3)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[(\ X#6.S#9)] T#19[(letrec {E#1} in S#3)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#17[(app A#18[[.]] T#19[(letrec {E#1} in S#3)])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19)];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  [.],
           T#13         |->  A#17[(app A#18[(var X#5)] T#19)],
           A#10         |->  A#17[(app A#18 T#19[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[(letrec {E#1} in S#3)])];E#8} in A#11[(var X#7)])
    -gc2->                        (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[(letrec {E#1;E#2} in S#3)])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[(letrec {E#1} in S#3)])];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(\ X#6.S#9)] T#19[(letrec {E#1} in S#3)])];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(app A#20[(var X#17)] T#21[(letrec {E#1;E#2} in S#3)])]
       ;E#8
       ;EE#18[X#17,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(app A#20[(var X#17)] T#21[(letrec {E#1} in S#3)])]
       ;E#8
       ;EE#18[X#17,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21)];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] T#21[(letrec {E#1} in S#3)])];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#17,A#10[(var X#5)]]},
           T#13         |->  A#19[(app A#20[(var X#17)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#1} in S#3)])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -gc2->                        (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#1;E#2} in S#3)])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#1} in S#3)])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#1} in S#3)])];E#8;EE#18[X#17,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {E#1;E#2} in S#3)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {E#1} in S#3)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#1} in S#3)])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]},
           T#13         |->  A#21[(app A#22[(var X#18)] T#23)],
           A#16         |->  A#21[(app A#22 T#23[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -gc2->                        (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[A#21[(app A#22[(var X#5)] T#23[(letrec {E#1;E#2} in S#3)])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[(letrec {E#1} in S#3)])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#16,T#13,T#4,A#10,A#19}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#21[(app A#22[[.]] T#23[(letrec {E#1} in S#3)])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[A#21[(app A#22[(var X#5)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#5)] T#23)],
           A#10         |->  A#21[(app A#22 T#23[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[(letrec {E#1} in S#3)])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -gc2->                        (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[(letrec {E#1;E#2} in S#3)])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[(letrec {E#1} in S#3)])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[(letrec {E#1} in S#3)])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[A#10[(var X#5)]] T#21[(letrec {E#1;E#2} in S#3)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[(letrec {E#1} in S#3)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] T#21[(letrec {E#1} in S#3)])];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  A#19[(app A#20[A#10[(var X#5)]] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -gc2->                        (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[(var X#5)] T#21[(letrec {E#1;E#2} in S#3)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {E#1} in S#3)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#4,A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),A#19[(app A#20[[.]] T#21[(letrec {E#1} in S#3)])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -gc2->                        (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[(\ X#6.S#9)] T#21[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(\ X#6.S#9);E#2;E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
  )

where

   Delta1 = {A#10}
   Delta2 = {E#1,E#2}
   Delta3 = {(A#11[(var X#7)],(letrec {E#2} in [.])),
             [{X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]},(letrec {E#2} in [.])],
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#11[(var X#7)],
           E#1  |->  {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -gc2->                        (letrec {X#5=(\ X#6.S#9);E#2;E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(app A#17[(var X#7)] T#18[(letrec {E#1;E#2} in S#3)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(app A#17[(var X#7)] T#18[(letrec {E#1} in S#3)])]
     )
  )

where

   Delta1 = {A#12,T#15,T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#16[(app A#17[[.]] T#18[(letrec {E#1} in S#3)])]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[(app A#17[[.]] T#18[(letrec {E#1} in S#3)])])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#7)] T#18)],
           A#12  |->  A#16[(app A#17 T#18[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(letrec {E#1} in S#3)])])
    -gc2->                        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(letrec {E#1;E#2} in S#3)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(letrec {E#1} in S#3)])])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(letrec {E#1} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(letrec {E#1;E#2} in S#3)]
       ;X#5= (\ X#6.S#10)
       ;E#18
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {E#1} in S#3)]
       ;X#5= (\ X#6.S#10)
       ;E#18
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#16=T#15;X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           E#9   |->  {X#16=T#15[(letrec {E#1} in S#3)];E#18},
           E#17  |->  {X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|}}

and instantiated rules:

                                  (letrec {X#16=T#15[(letrec {E#1} in S#3)];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -gc2->                        (letrec {X#16=T#15[(letrec {E#1;E#2} in S#3)];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#16=T#15[(letrec {E#1} in S#3)];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#16=T#15[(letrec {E#1} in S#3)];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[(var X#8)] T#23[(letrec {E#1;E#2} in S#3)])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {E#1} in S#3)])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#4,A#11,A#19}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[(letrec {E#1} in S#3)])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19,
           T#15         |->  A#19[A#21[(app A#22[(var X#8)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[(letrec {E#1} in S#3)])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -gc2->                        (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[(letrec {E#1;E#2} in S#3)])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[(letrec {E#1} in S#3)])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {E#1} in S#3)])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[A#11[(var X#8)]] T#21[(letrec {E#1;E#2} in S#3)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[A#11[(\ X#6.S#10)]] T#21[(letrec {E#1} in S#3)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[(letrec {E#1} in S#3)])]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  A#19[(app A#20[A#11[(var X#8)]] T#21)],
           A#18         |->  A#19[(app A#20 T#21[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[(letrec {E#1} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -gc2->                        (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[(letrec {E#1;E#2} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[(letrec {E#1} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(\ X#6.S#10)]] T#21[(letrec {E#1} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[(var X#8)] T#21[(letrec {E#1;E#2} in S#3)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[(\ X#6.S#10)] T#21[(letrec {E#1} in S#3)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#19[(app A#20[[.]] T#21[(letrec {E#1} in S#3)])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           T#15         |->  A#19[(app A#20[(var X#8)] T#21)],
           A#11         |->  A#19[(app A#20 T#21[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[(letrec {E#1} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -gc2->                        (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[(letrec {E#1;E#2} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[(letrec {E#1} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(\ X#6.S#10)] T#21[(letrec {E#1} in S#3)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(app A#22[(var X#19)] T#23[(letrec {E#1;E#2} in S#3)])]
       ;E#9
       ;EE#20[X#19,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(app A#22[(var X#19)] T#23[(letrec {E#1} in S#3)])]
       ;E#9
       ;EE#20[X#19,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23)];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[(letrec {E#1} in S#3)])];EE#20[X#19,[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(letrec {E#1} in S#3)])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -gc2->                        (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(letrec {E#1;E#2} in S#3)])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(letrec {E#1} in S#3)])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(letrec {E#1} in S#3)])];E#9;EE#20[X#19,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {E#1;E#2} in S#3)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {E#1} in S#3)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {E#1} in S#3)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -gc2->                        (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(app A#24[(var X#8)] T#25[(letrec {E#1;E#2} in S#3)])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[(letrec {E#1} in S#3)])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#4,A#11,A#21}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[(app A#24[[.]] T#25[(letrec {E#1} in S#3)])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[A#23[(app A#24[(var X#8)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#8)] T#25)],
           A#11         |->  A#23[(app A#24 T#25[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[(letrec {E#1} in S#3)])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -gc2->                        (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[(letrec {E#1;E#2} in S#3)])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[(letrec {E#1} in S#3)])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[(letrec {E#1} in S#3)])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[A#11[(var X#8)]] T#23[(letrec {E#1;E#2} in S#3)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[(letrec {E#1} in S#3)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[(letrec {E#1} in S#3)])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  A#21[(app A#22[A#11[(var X#8)]] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -gc2->                        (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(var X#8)] T#23[(letrec {E#1;E#2} in S#3)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {E#1} in S#3)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#4,A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[(letrec {E#1} in S#3)])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           T#15         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -gc2->                        (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {E#1;E#2} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[(\ X#6.S#10)] T#23[(letrec {E#1} in S#3)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#2
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#11}
   Delta2 = {E#1,E#2}
   Delta3 = {(A#12[(var X#7)],(letrec {E#2} in [.])),
             [{X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},(letrec {E#2} in [.])],
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {E#1,E#2}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#12[(var X#7)],
           E#1  |->  {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|}}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -gc2->                        (letrec {X#5=(\ X#6.S#10);E#2;E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (letrec {E#6} in T#9[(letrec {E#1;E#2} in S#3)]))
    ,
     (letrec {E#5;E#6} in T#9[(letrec {E#1} in S#3)])
  )

where

   Delta1 = {T#8,T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             [{E#5},(letrec {E#6} in [.])]}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4  |->  (letrec {E#5} in (letrec {E#6} in T#9)),
           T#8  |->  (letrec {E#6} in T#9),
           S#7  |->  T#9[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {E#5} in (letrec {E#6} in T#9[(letrec {E#1} in S#3)]))
    -gc2->                        (letrec {E#5} in (letrec {E#6} in T#9[(letrec {E#1;E#2} in S#3)]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in T#9[(letrec {E#1} in S#3)]))
    -SR,llet-in1->                (letrec {E#5;E#6} in T#9[(letrec {E#1} in S#3)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (letrec {X#10=T#9[(letrec {E#1;E#2} in S#3)];E#12} in S#7))
    ,
     (letrec {X#10=T#9[(letrec {E#1} in S#3)];E#12;E#5} in S#7)
  )

where

   Delta1 = {T#8,T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             [{E#5},(letrec {X#10=T#9[(letrec {E#1} in S#3)];E#12} in [.])]}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (letrec {X#10=T#9;E#12} in S#7)),
           T#8   |->  (letrec {X#10=T#9;E#12} in S#7),
           E#6   |->  {X#10=T#9[(letrec {E#1} in S#3)];E#12},
           E#11  |->  {E#12}}

and instantiated rules:

                                  (letrec {E#5} in (letrec {X#10=T#9[(letrec {E#1} in S#3)];E#12} in S#7))
    -gc2->                        (letrec {E#5} in (letrec {X#10=T#9[(letrec {E#1;E#2} in S#3)];E#12} in S#7))
    ................................................................................
                                  (letrec {E#5} in (letrec {X#10=T#9[(letrec {E#1} in S#3)];E#12} in S#7))
    -SR,llet-in1->                (letrec {X#10=T#9[(letrec {E#1} in S#3)];E#12;E#5} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (letrec {E#2;E#6} in S#7))
    ,
     (letrec {E#5;E#6} in S#7)
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {(S#7,(letrec {E#2} in [.])),
             [{E#6},(letrec {E#2} in [.])],
             [{E#5},(letrec {E#6} in [.])]}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4  |->  (letrec {E#5} in [.]),
           T#8  |->  [.],
           S#3  |->  S#7,
           E#1  |->  {E#6}}

and instantiated rules:

                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -gc2->                        (letrec {E#5} in (letrec {E#2;E#6} in S#7))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {X#9=T#8[(letrec {E#1;E#2} in S#3)];E#11} in (letrec {E#6} in S#7))
    ,
     (letrec {X#9=T#8[(letrec {E#1} in S#3)];E#11;E#6} in S#7)
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             [{X#9=T#8[(letrec {E#1} in S#3)];E#11},(letrec {E#6} in [.])]}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4   |->  (letrec {X#9=T#8;E#11} in (letrec {E#6} in S#7)),
           E#5   |->  {X#9=T#8[(letrec {E#1} in S#3)];E#11},
           E#10  |->  {E#11}}

and instantiated rules:

                                  (letrec {X#9=T#8[(letrec {E#1} in S#3)];E#11} in (letrec {E#6} in S#7))
    -gc2->                        (letrec {X#9=T#8[(letrec {E#1;E#2} in S#3)];E#11} in (letrec {E#6} in S#7))
    ................................................................................
                                  (letrec {X#9=T#8[(letrec {E#1} in S#3)];E#11} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {X#9=T#8[(letrec {E#1} in S#3)];E#11;E#6} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {E#2;E#5} in (letrec {E#6} in S#7))
    ,
     (letrec {E#5;E#6} in S#7)
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {((letrec {E#6} in S#7),(letrec {E#2} in [.])),
             [{E#5},(letrec {E#2} in [.])],
             [{E#5},(letrec {E#6} in [.])]}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],[{E#5},(letrec {E#6} in [.])]}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  (letrec {E#6} in S#7),
           E#1  |->  {E#5}}

and instantiated rules:

                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -gc2->                        (letrec {E#2;E#5} in (letrec {E#6} in S#7))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in S#8)
       ;E#7
     in
        A#11[(app A#12[(var X#5)] T#13[(letrec {E#1;E#2} in S#3)])]
     )
    ,
     (letrec
        X#5= S#8
       ;E#6
       ;E#7
     in
        A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in S#3)])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in S#3)])],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#5),A#11[(app A#12[[.]] T#13[(letrec {E#1} in S#3)])]),
             ((var X#5),A#11[(app A#12[[.]] T#13[(letrec {E#1} in S#3)])])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)]),
           T#10  |->  A#11[(app A#12[(var X#5)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in S#3)])])
    -gc2->                        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1;E#2} in S#3)])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in S#3)])])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {E#1} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in T#13[(letrec {E#1;E#2} in S#3)])
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#5=T#13[(letrec {E#1} in S#3)];E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#6} in T#13);E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  (letrec {E#6} in T#13),
           S#8   |->  T#13[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in T#13[(letrec {E#1} in S#3)]);E#7} in A#9[(var X#5)])
    -gc2->                        (letrec {X#5=(letrec {E#6} in T#13[(letrec {E#1;E#2} in S#3)]);E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in T#13[(letrec {E#1} in S#3)]);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=T#13[(letrec {E#1} in S#3)];E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#14=T#13[(letrec {E#1;E#2} in S#3)];E#16} in S#8)
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#14=T#13[(letrec {E#1} in S#3)];X#5=S#8;E#16;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (A#9[(var X#5)],(letrec {X#14=T#13[(letrec {E#1} in S#3)];E#16} in [.])),
             [{E#7},(letrec {X#14=T#13[(letrec {E#1} in S#3)];E#16} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {X#14=T#13;E#16} in S#8);E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  (letrec {X#14=T#13;E#16} in S#8),
           E#6   |->  {X#14=T#13[(letrec {E#1} in S#3)];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#14=T#13[(letrec {E#1} in S#3)];E#16} in S#8);E#7} in A#9[(var X#5)])
    -gc2->                        (letrec {X#5=(letrec {X#14=T#13[(letrec {E#1;E#2} in S#3)];E#16} in S#8);E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {X#14=T#13[(letrec {E#1} in S#3)];E#16} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#14=T#13[(letrec {E#1} in S#3)];X#5=S#8;E#16;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(letrec {E#2;E#6} in S#8);E#7} in A#9[(var X#5)])
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {(S#8,(letrec {E#2} in [.])),
             [{E#6},(letrec {E#2} in [.])],
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=[.];E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  [.],
           S#3   |->  S#8,
           E#1   |->  {E#6}}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -gc2->                        (letrec {X#5=(letrec {E#2;E#6} in S#8);E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(letrec {E#1;E#2} in S#3)]
       ;X#5= (letrec {E#6} in S#8)
       ;E#13
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#11=T#10[(letrec {E#1} in S#3)];X#5=S#8;E#13;E#6} in A#9[(var X#5)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#11=T#10[(letrec {E#1} in S#3)];E#13},(letrec {E#6} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)]),
           E#7   |->  {X#11=T#10[(letrec {E#1} in S#3)];E#13},
           E#12  |->  {X#5=(letrec {E#6} in S#8);E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {E#1} in S#3)];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    -gc2->                        (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {E#1} in S#3)];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#11=T#10[(letrec {E#1} in S#3)];X#5=S#8;E#13;E#6} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(letrec {E#6} in S#8);E#2;E#7} in A#9[(var X#5)])
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#6}
   Delta3 = {(A#9[(var X#5)],(letrec {E#2} in [.])),
             [{X#5=(letrec {E#6} in S#8);E#7},(letrec {E#2} in [.])],
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#9[(var X#5)],
           E#1  |->  {X#5=(letrec {E#6} in S#8);E#7}}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -gc2->                        (letrec {X#5=(letrec {E#6} in S#8);E#2;E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(app A#14[(var X#6)] T#15[(letrec {E#1;E#2} in S#3)])]
     )
    ,
     (letrec
        X#5= S#9
       ;E#7
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(app A#14[(var X#6)] T#15[(letrec {E#1} in S#3)])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#13[(app A#14[(var X#6)] T#15[(letrec {E#1} in S#3)])],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#13[(app A#14[[.]] T#15[(letrec {E#1} in S#3)])]),
             ((var X#5),[.]),
             ((var X#6),A#13[(app A#14[[.]] T#15[(letrec {E#1} in S#3)])])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#6)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(letrec {E#1} in S#3)])])
    -gc2->                        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(letrec {E#1;E#2} in S#3)])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(letrec {E#1} in S#3)])])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(letrec {E#1} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in T#15[(letrec {E#1;E#2} in S#3)])
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= T#15[(letrec {E#1} in S#3)]
       ;E#7
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {E#7} in T#15);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  (letrec {E#7} in T#15),
           S#9   |->  T#15[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in T#15[(letrec {E#1} in S#3)]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -gc2->                        (letrec {X#5=(letrec {E#7} in T#15[(letrec {E#1;E#2} in S#3)]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in T#15[(letrec {E#1} in S#3)]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=T#15[(letrec {E#1} in S#3)];E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#16=T#15[(letrec {E#1;E#2} in S#3)];E#18} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {E#1} in S#3)]
       ;X#5= S#9
       ;E#18
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {X#16=T#15[(letrec {E#1} in S#3)];E#18;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {X#16=T#15[(letrec {E#1} in S#3)];E#18} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {X#16=T#15[(letrec {E#1} in S#3)];E#18} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=(letrec {X#16=T#15;E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  (letrec {X#16=T#15;E#18} in S#9),
           E#7   |->  {X#16=T#15[(letrec {E#1} in S#3)];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#16=T#15[(letrec {E#1} in S#3)];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -gc2->                        (letrec {X#5=(letrec {X#16=T#15[(letrec {E#1;E#2} in S#3)];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {X#16=T#15[(letrec {E#1} in S#3)];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=T#15[(letrec {E#1} in S#3)];X#5=S#9;E#18;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#2;E#7} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#9,(letrec {E#2} in [.])),
             [{E#7},(letrec {E#2} in [.])],
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#5=[.];E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  [.],
           S#3   |->  S#9,
           E#1   |->  {E#7}}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -gc2->                        (letrec {X#5=(letrec {E#2;E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {E#1;E#2} in S#3)]
       ;X#5= (letrec {E#7} in S#9)
       ;E#15
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {E#1} in S#3)]
       ;X#5= S#9
       ;E#15
       ;E#7
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15;E#7;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#13=T#12[(letrec {E#1} in S#3)];E#15;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           E#8   |->  {X#13=T#12[(letrec {E#1} in S#3)];E#15},
           E#14  |->  {X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {E#1} in S#3)];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -gc2->                        (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {E#1} in S#3)];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#13=T#12[(letrec {E#1} in S#3)];X#5=S#9;E#15;E#7;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#16[(app A#17[(var X#5)] T#18[(letrec {E#1;E#2} in S#3)])]
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#16[(app A#17[(var X#5)] T#18[(letrec {E#1} in S#3)])]
       ;E#7
       ;E#8
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1} in S#3)])];E#7;E#8} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1} in S#3)])];E#8},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18)];E#8} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[(letrec {E#1} in S#3)])]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8},
           T#12         |->  A#16[(app A#17[(var X#5)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1} in S#3)])];E#8} in A#10[(var X#6)])
    -gc2->                        (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1;E#2} in S#3)])];E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1} in S#3)])];E#8} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {E#1} in S#3)])];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])]
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])]
       ;E#7
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])];E#7;E#8;EE#17[X#16,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])];E#8;EE#17[X#16,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20)];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#16,(var X#5)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -gc2->                        (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])];E#7;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])];E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])];E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -gc2->                        (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])];X#5=S#9;E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(var X#5)] T#20[(letrec {E#1;E#2} in S#3)])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(var X#5)] T#20[(letrec {E#1} in S#3)])]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             ((var X#5),(letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1} in S#3)])];E#7;E#8;EE#17[X#6,(var X#16)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1} in S#3)])];E#8;EE#17[X#6,(var X#16)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20)];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[(letrec {E#1} in S#3)])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]},
           T#12         |->  A#18[(app A#19[(var X#5)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1} in S#3)])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -gc2->                        (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1;E#2} in S#3)])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1} in S#3)])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {E#1} in S#3)])];X#5=S#9;E#7;E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#2
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(A#10[(var X#6)],(letrec {E#2} in [.])),
             [{X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]},(letrec {E#2} in [.])],
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#10[(var X#6)],
           E#1  |->  {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]}}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -gc2->                        (letrec {X#5=(letrec {E#7} in S#9);E#2;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {E#5} in T#12[(letrec {E#1;E#2} in S#3)]) S#6)]
    ,
     A#9[(letrec {E#5} in (app T#12[(letrec {E#1} in S#3)] S#6))]
  )

where

   Delta1 = {T#11,T#10,A#8,T#4,A#9}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (letrec {E#5} in T#12) S#6)],
           T#10  |->  (app (letrec {E#5} in T#12) S#6),
           T#11  |->  (letrec {E#5} in T#12),
           S#7   |->  T#12[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in T#12[(letrec {E#1} in S#3)]) S#6)]
    -gc2->                        A#9[(app (letrec {E#5} in T#12[(letrec {E#1;E#2} in S#3)]) S#6)]
    ................................................................................
                                  A#9[(app (letrec {E#5} in T#12[(letrec {E#1} in S#3)]) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app T#12[(letrec {E#1} in S#3)] S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15} in S#7) S#6)]
    ,
     A#9[(letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15} in (app S#7 S#6))]
  )

where

   Delta1 = {T#11,T#10,A#8,T#4,A#9}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#6,(letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (letrec {X#13=T#12;E#15} in S#7) S#6)],
           T#10  |->  (app (letrec {X#13=T#12;E#15} in S#7) S#6),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#7),
           E#5   |->  {X#13=T#12[(letrec {E#1} in S#3)];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  A#9[(app (letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15} in S#7) S#6)]
    -gc2->                        A#9[(app (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15} in S#7) S#6)]
    ................................................................................
                                  A#9[(app (letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {E#2;E#5} in S#7) S#6)]
    ,
     A#9[(letrec {E#5} in (app S#7 S#6))]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {(S#7,(letrec {E#2} in [.])),
             [{E#5},(letrec {E#2} in [.])],
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app [.] S#6)],
           T#10  |->  (app [.] S#6),
           T#11  |->  [.],
           S#3   |->  S#7,
           E#1   |->  {E#5}}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in S#7) S#6)]
    -gc2->                        A#9[(app (letrec {E#2;E#5} in S#7) S#6)]
    ................................................................................
                                  A#9[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {E#5} in S#7) T#11[(letrec {E#1;E#2} in S#3)])]
    ,
     A#9[(letrec {E#5} in (app S#7 T#11[(letrec {E#1} in S#3)]))]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#11[(letrec {E#1} in S#3)],(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  A#9,
           T#4   |->  A#9[(app (letrec {E#5} in S#7) T#11)],
           T#10  |->  (app (letrec {E#5} in S#7) T#11),
           S#6   |->  T#11[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in S#7) T#11[(letrec {E#1} in S#3)])]
    -gc2->                        A#9[(app (letrec {E#5} in S#7) T#11[(letrec {E#1;E#2} in S#3)])]
    ................................................................................
                                  A#9[(app (letrec {E#5} in S#7) T#11[(letrec {E#1} in S#3)])]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app S#7 T#11[(letrec {E#1} in S#3)]))]
    

================================================================================
Critical Pair:

  (
     A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(letrec {E#1;E#2} in S#3)])]
    ,
     A#9[(app A#10[(letrec {E#5} in (app S#7 S#6))] T#11[(letrec {E#1} in S#3)])]
  )

where

   Delta1 = {A#8,T#4}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {T#4  |->  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11)],
           A#8  |->  A#9[(app A#10 T#11[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(letrec {E#1} in S#3)])]
    -gc2->                        A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(letrec {E#1;E#2} in S#3)])]
    ................................................................................
                                  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(letrec {E#1} in S#3)])]
    -SR,lapp1->                   A#9[(app A#10[(letrec {E#5} in (app S#7 S#6))] T#11[(letrec {E#1} in S#3)])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#5} in T#10[(letrec {E#1;E#2} in S#3)]) S#6)
    ,
     (letrec {E#5} in (app T#10[(letrec {E#1} in S#3)] S#6))
  )

where

   Delta1 = {T#9,T#4}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8  |->  [.],
           T#4  |->  (app (letrec {E#5} in T#10) S#6),
           T#9  |->  (letrec {E#5} in T#10),
           S#7  |->  T#10[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (app (letrec {E#5} in T#10[(letrec {E#1} in S#3)]) S#6)
    -gc2->                        (app (letrec {E#5} in T#10[(letrec {E#1;E#2} in S#3)]) S#6)
    ................................................................................
                                  (app (letrec {E#5} in T#10[(letrec {E#1} in S#3)]) S#6)
    -SR,lapp1->                   (letrec {E#5} in (app T#10[(letrec {E#1} in S#3)] S#6))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13} in S#7) S#6)
    ,
     (letrec {X#11=T#10[(letrec {E#1} in S#3)];E#13} in (app S#7 S#6))
  )

where

   Delta1 = {T#9,T#4}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#6,(letrec {X#11=T#10[(letrec {E#1} in S#3)];E#13} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8   |->  [.],
           T#4   |->  (app (letrec {X#11=T#10;E#13} in S#7) S#6),
           T#9   |->  (letrec {X#11=T#10;E#13} in S#7),
           E#5   |->  {X#11=T#10[(letrec {E#1} in S#3)];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (app (letrec {X#11=T#10[(letrec {E#1} in S#3)];E#13} in S#7) S#6)
    -gc2->                        (app (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13} in S#7) S#6)
    ................................................................................
                                  (app (letrec {X#11=T#10[(letrec {E#1} in S#3)];E#13} in S#7) S#6)
    -SR,lapp1->                   (letrec {X#11=T#10[(letrec {E#1} in S#3)];E#13} in (app S#7 S#6))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#2;E#5} in S#7) S#6)
    ,
     (letrec {E#5} in (app S#7 S#6))
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {(S#7,(letrec {E#2} in [.])),
             [{E#5},(letrec {E#2} in [.])],
             (S#6,(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8  |->  [.],
           T#4  |->  (app [.] S#6),
           T#9  |->  [.],
           S#3  |->  S#7,
           E#1  |->  {E#5}}

and instantiated rules:

                                  (app (letrec {E#5} in S#7) S#6)
    -gc2->                        (app (letrec {E#2;E#5} in S#7) S#6)
    ................................................................................
                                  (app (letrec {E#5} in S#7) S#6)
    -SR,lapp1->                   (letrec {E#5} in (app S#7 S#6))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#5} in S#7) T#9[(letrec {E#1;E#2} in S#3)])
    ,
     (letrec {E#5} in (app S#7 T#9[(letrec {E#1} in S#3)]))
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#5}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#9[(letrec {E#1} in S#3)],(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#6,(letrec {E#5} in [.]))}


and found solution:

    Sol = {A#8  |->  [.],
           T#4  |->  (app (letrec {E#5} in S#7) T#9),
           S#6  |->  T#9[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (app (letrec {E#5} in S#7) T#9[(letrec {E#1} in S#3)])
    -gc2->                        (app (letrec {E#5} in S#7) T#9[(letrec {E#1;E#2} in S#3)])
    ................................................................................
                                  (app (letrec {E#5} in S#7) T#9[(letrec {E#1} in S#3)])
    -SR,lapp1->                   (letrec {E#5} in (app S#7 T#9[(letrec {E#1} in S#3)]))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {E#6} in T#14[(letrec {E#1;E#2} in S#3)]) S#7)]
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[(letrec {E#1} in S#3)] S#7))])
  )

where

   Delta1 = {T#13,T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14) S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {E#6} in T#14) S#7)],
           T#12  |->  (app (letrec {E#6} in T#14) S#7),
           T#13  |->  (letrec {E#6} in T#14),
           S#8   |->  T#14[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(letrec {E#1} in S#3)]) S#7)])
    -gc2->                        (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(letrec {E#1;E#2} in S#3)]) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(letrec {E#1} in S#3)]) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[(letrec {E#1} in S#3)] S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {X#15=T#14[(letrec {E#1;E#2} in S#3)];E#17} in S#8) S#7)]
     )
    ,
     (letrec
        E#5
     in
        A#11[(letrec {X#15=T#14[(letrec {E#1} in S#3)];E#17} in (app S#8 S#7))]
     )
  )

where

   Delta1 = {T#13,T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#7,(letrec {X#15=T#14[(letrec {E#1} in S#3)];E#17} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)],
           T#12  |->  (app (letrec {X#15=T#14;E#17} in S#8) S#7),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#8),
           E#6   |->  {X#15=T#14[(letrec {E#1} in S#3)];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[(letrec {E#1} in S#3)];E#17} in S#8) S#7)])
    -gc2->                        (letrec {E#5} in A#11[(app (letrec {X#15=T#14[(letrec {E#1;E#2} in S#3)];E#17} in S#8) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[(letrec {E#1} in S#3)];E#17} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {X#15=T#14[(letrec {E#1} in S#3)];E#17} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in A#11[(app (letrec {E#2;E#6} in S#8) S#7)])
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {(S#8,(letrec {E#2} in [.])),
             [{E#6},(letrec {E#2} in [.])],
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app [.] S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app [.] S#7)],
           T#12  |->  (app [.] S#7),
           T#13  |->  [.],
           S#3   |->  S#8,
           E#1   |->  {E#6}}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -gc2->                        (letrec {E#5} in A#11[(app (letrec {E#2;E#6} in S#8) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {E#6} in S#8) T#13[(letrec {E#1;E#2} in S#3)])]
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 T#13[(letrec {E#1} in S#3)]))])
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#13[(letrec {E#1} in S#3)],(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {E#6} in S#8) T#13)],
           T#12  |->  (app (letrec {E#6} in S#8) T#13),
           S#7   |->  T#13[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(letrec {E#1} in S#3)])])
    -gc2->                        (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(letrec {E#1;E#2} in S#3)])])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(letrec {E#1} in S#3)])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 T#13[(letrec {E#1} in S#3)]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(letrec {E#1;E#2} in S#3)])]
     )
    ,
     (letrec
        E#5
     in
        A#11[(app A#12[(letrec {E#6} in (app S#8 S#7))] T#13[(letrec {E#1} in S#3)])]
     )
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)]),
           T#10  |->  A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(letrec {E#1} in S#3)])])
    -gc2->                        (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(letrec {E#1;E#2} in S#3)])])
    ................................................................................
                                  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(letrec {E#1} in S#3)])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(app A#12[(letrec {E#6} in (app S#8 S#7))] T#13[(letrec {E#1} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (app (letrec {E#6} in T#12[(letrec {E#1;E#2} in S#3)]) S#7))
    ,
     (letrec {E#5} in (letrec {E#6} in (app T#12[(letrec {E#1} in S#3)] S#7)))
  )

where

   Delta1 = {T#11,T#10,T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app (letrec {E#6} in T#12) S#7)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {E#6} in T#12) S#7),
           T#11  |->  (letrec {E#6} in T#12),
           S#8   |->  T#12[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in T#12[(letrec {E#1} in S#3)]) S#7))
    -gc2->                        (letrec {E#5} in (app (letrec {E#6} in T#12[(letrec {E#1;E#2} in S#3)]) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in T#12[(letrec {E#1} in S#3)]) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app T#12[(letrec {E#1} in S#3)] S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (app (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15} in S#8) S#7)
     )
    ,
     (letrec
        E#5
     in
        (letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15} in (app S#8 S#7))
     )
  )

where

   Delta1 = {T#11,T#10,T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#7,(letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app (letrec {X#13=T#12;E#15} in S#8) S#7)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {X#13=T#12;E#15} in S#8) S#7),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#8),
           E#6   |->  {X#13=T#12[(letrec {E#1} in S#3)];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15} in S#8) S#7))
    -gc2->                        (letrec {E#5} in (app (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15} in S#8) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15} in S#8) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15} in (app S#8 S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (app (letrec {E#2;E#6} in S#8) S#7))
    ,
     (letrec {E#5} in (letrec {E#6} in (app S#8 S#7)))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {(S#8,(letrec {E#2} in [.])),
             [{E#6},(letrec {E#2} in [.])],
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app [.] S#7)),
           A#9   |->  [.],
           T#10  |->  (app [.] S#7),
           T#11  |->  [.],
           S#3   |->  S#8,
           E#1   |->  {E#6}}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in S#8) S#7))
    -gc2->                        (letrec {E#5} in (app (letrec {E#2;E#6} in S#8) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in S#8) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app S#8 S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(letrec {E#1;E#2} in S#3)]))
    ,
     (letrec {E#5} in (letrec {E#6} in (app S#8 T#11[(letrec {E#1} in S#3)])))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#11[(letrec {E#1} in S#3)],(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {E#6} in S#8) T#11),
           S#7   |->  T#11[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(letrec {E#1} in S#3)]))
    -gc2->                        (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(letrec {E#1;E#2} in S#3)]))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(letrec {E#1} in S#3)]))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app S#8 T#11[(letrec {E#1} in S#3)])))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(letrec {E#1;E#2} in S#3)]
       ;E#13
     in
        A#9[(app (letrec {E#6} in S#8) S#7)]
     )
    ,
     (letrec
        X#11= T#10[(letrec {E#1} in S#3)]
       ;E#13
     in
        A#9[(letrec {E#6} in (app S#8 S#7))]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4   |->  (letrec {X#11=T#10;E#13} in A#9[(app (letrec {E#6} in S#8) S#7)]),
           E#5   |->  {X#11=T#10[(letrec {E#1} in S#3)];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[(letrec {E#1} in S#3)];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -gc2->                        (letrec {X#11=T#10[(letrec {E#1;E#2} in S#3)];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    ................................................................................
                                  (letrec {X#11=T#10[(letrec {E#1} in S#3)];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {X#11=T#10[(letrec {E#1} in S#3)];E#13} in A#9[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec {E#2;E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    ,
     (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#5,E#6}
   Delta3 = {(A#9[(app (letrec {E#6} in S#8) S#7)],(letrec {E#2} in [.])),
             [{E#5},(letrec {E#2} in [.])],
             (S#7,(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#5,E#6}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#7,(letrec {E#6} in [.]))}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#9[(app (letrec {E#6} in S#8) S#7)],
           E#1  |->  {E#5}}

and instantiated rules:

                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -gc2->                        (letrec {E#2;E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        A#13[(app A#14[(var X#5)] T#15[(letrec {E#1;E#2} in S#3)])]
     )
    ,
     (letrec
        E#6
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in S#3)])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {E#1} in S#3)])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[(letrec {E#1} in S#3)])])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#5)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in S#3)])])
    -gc2->                        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1;E#2} in S#3)])])
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in S#3)])])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[(app A#14[(var X#5)] T#15[(letrec {E#1} in S#3)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {E#1;E#2} in S#3)]
       ;E#15
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#13= T#12[(letrec {E#1} in S#3)]
       ;E#15
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#13=T#12;E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           E#6   |->  {X#13=T#12[(letrec {E#1} in S#3)];E#15},
           E#14  |->  {E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#13=T#12[(letrec {E#1;E#2} in S#3)];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#13=T#12[(letrec {E#1} in S#3)];E#15;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {E#7} in T#19[(letrec {E#1;E#2} in S#3)]) S#8)]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app T#19[(letrec {E#1} in S#3)] S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (letrec {E#7} in T#19) S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {E#7} in T#19) S#8)],
           T#17         |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[(letrec {E#1} in S#3)]) S#8)];E#6} in A#10[(var X#5)])
    -gc2->                        (letrec {X#5=A#16[(app (letrec {E#7} in T#19[(letrec {E#1;E#2} in S#3)]) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[(letrec {E#1} in S#3)]) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app T#19[(letrec {E#1} in S#3)] S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22} in S#9) S#8)]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {X#20=T#19[(letrec {E#1} in S#3)];E#22} in (app S#9 S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {X#20=T#19[(letrec {E#1} in S#3)];E#22} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)],
           T#17         |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[(letrec {E#1} in S#3)];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[(letrec {E#1} in S#3)];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -gc2->                        (letrec {X#5=A#16[(app (letrec {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[(letrec {E#1} in S#3)];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {X#20=T#19[(letrec {E#1} in S#3)];E#22} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=A#16[(app (letrec {E#2;E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    ,
     (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#9,(letrec {E#2} in [.])),
             [{E#7},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app [.] S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app [.] S#8)],
           T#17         |->  (app [.] S#8),
           T#18         |->  [.],
           S#3          |->  S#9,
           E#1          |->  {E#7}}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -gc2->                        (letrec {X#5=A#16[(app (letrec {E#2;E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {E#7} in S#9) T#18[(letrec {E#1;E#2} in S#3)])]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app S#9 T#18[(letrec {E#1} in S#3)]))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#18[(letrec {E#1} in S#3)],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {E#7} in S#9) T#18)],
           T#17         |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[(letrec {E#1} in S#3)])];E#6} in A#10[(var X#5)])
    -gc2->                        (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[(letrec {E#1;E#2} in S#3)])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[(letrec {E#1} in S#3)])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 T#18[(letrec {E#1} in S#3)]))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(letrec {E#1;E#2} in S#3)])]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(app A#17[(letrec {E#7} in (app S#9 S#8))] T#18[(letrec {E#1} in S#3)])]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[(letrec {E#1} in S#3)])]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(letrec {E#1} in S#3)])];E#6} in A#10[(var X#5)])
    -gc2->                        (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(letrec {E#1;E#2} in S#3)])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(letrec {E#1} in S#3)])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(app A#17[(letrec {E#7} in (app S#9 S#8))] T#18[(letrec {E#1} in S#3)])];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {E#7} in T#17[(letrec {E#1;E#2} in S#3)]) S#8)
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {E#7} in (app T#17[(letrec {E#1} in S#3)] S#8))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#16,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (letrec {E#7} in T#17) S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in T#17) S#8),
           T#16         |->  (letrec {E#7} in T#17),
           S#9          |->  T#17[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in T#17[(letrec {E#1} in S#3)]) S#8);E#6} in A#10[(var X#5)])
    -gc2->                        (letrec {X#5=(app (letrec {E#7} in T#17[(letrec {E#1;E#2} in S#3)]) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in T#17[(letrec {E#1} in S#3)]) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app T#17[(letrec {E#1} in S#3)] S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {X#18=T#17[(letrec {E#1;E#2} in S#3)];E#20} in S#9) S#8)
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {X#18=T#17[(letrec {E#1} in S#3)];E#20} in (app S#9 S#8))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#16,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {X#18=T#17[(letrec {E#1} in S#3)];E#20} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (letrec {X#18=T#17;E#20} in S#9) S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {X#18=T#17;E#20} in S#9) S#8),
           T#16         |->  (letrec {X#18=T#17;E#20} in S#9),
           E#7          |->  {X#18=T#17[(letrec {E#1} in S#3)];E#20},
           E#19         |->  {E#20}}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {X#18=T#17[(letrec {E#1} in S#3)];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -gc2->                        (letrec {X#5=(app (letrec {X#18=T#17[(letrec {E#1;E#2} in S#3)];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {X#18=T#17[(letrec {E#1} in S#3)];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {X#18=T#17[(letrec {E#1} in S#3)];E#20} in (app S#9 S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(app (letrec {E#2;E#7} in S#9) S#8);E#6} in A#10[(var X#5)])
    ,
     (letrec {X#5=(letrec {E#7} in (app S#9 S#8));E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#9,(letrec {E#2} in [.])),
             [{E#7},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app [.] S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#16         |->  [.],
           S#3          |->  S#9,
           E#1          |->  {E#7}}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in S#9) S#8);E#6} in A#10[(var X#5)])
    -gc2->                        (letrec {X#5=(app (letrec {E#2;E#7} in S#9) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in S#9) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app S#9 S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {E#7} in S#9) T#16[(letrec {E#1;E#2} in S#3)])
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {E#7} in (app S#9 T#16[(letrec {E#1} in S#3)]))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#16[(letrec {E#1} in S#3)],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=(app (letrec {E#7} in S#9) T#16);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in S#9) T#16),
           S#8          |->  T#16[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in S#9) T#16[(letrec {E#1} in S#3)]);E#6} in A#10[(var X#5)])
    -gc2->                        (letrec {X#5=(app (letrec {E#7} in S#9) T#16[(letrec {E#1;E#2} in S#3)]);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in S#9) T#16[(letrec {E#1} in S#3)]);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app S#9 T#16[(letrec {E#1} in S#3)]));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])]
       ;E#6
       ;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])]
       ;E#6
       ;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1;E#2} in S#3)])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {E#1} in S#3)])];E#6;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1;E#2} in S#3)])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {E#1} in S#3)])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {E#7} in T#21[(letrec {E#1;E#2} in S#3)]) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app T#21[(letrec {E#1} in S#3)] S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (letrec {E#7} in T#21) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {E#7} in T#21) S#8)],
           T#19         |->  (app (letrec {E#7} in T#21) S#8),
           T#20         |->  (letrec {E#7} in T#21),
           S#9          |->  T#21[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[(letrec {E#1} in S#3)]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#16=A#18[(app (letrec {E#7} in T#21[(letrec {E#1;E#2} in S#3)]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[(letrec {E#1} in S#3)]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app T#21[(letrec {E#1} in S#3)] S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {X#22=T#21[(letrec {E#1;E#2} in S#3)];E#24} in S#9) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#22=T#21[(letrec {E#1} in S#3)];E#24} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {X#22=T#21[(letrec {E#1} in S#3)];E#24} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)],
           T#19         |->  (app (letrec {X#22=T#21;E#24} in S#9) S#8),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#9),
           E#7          |->  {X#22=T#21[(letrec {E#1} in S#3)];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[(letrec {E#1} in S#3)];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#16=A#18[(app (letrec {X#22=T#21[(letrec {E#1;E#2} in S#3)];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[(letrec {E#1} in S#3)];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {X#22=T#21[(letrec {E#1} in S#3)];E#24} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {E#2;E#7} in S#9) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#9,(letrec {E#2} in [.])),
             [{E#7},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app [.] S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app [.] S#8)],
           T#19         |->  (app [.] S#8),
           T#20         |->  [.],
           S#3          |->  S#9,
           E#1          |->  {E#7}}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#16=A#18[(app (letrec {E#2;E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {E#7} in S#9) T#20[(letrec {E#1;E#2} in S#3)])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 T#20[(letrec {E#1} in S#3)]))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#20[(letrec {E#1} in S#3)],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {E#7} in S#9) T#20)],
           T#19         |->  (app (letrec {E#7} in S#9) T#20),
           S#8          |->  T#20[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[(letrec {E#1} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[(letrec {E#1;E#2} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[(letrec {E#1} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 T#20[(letrec {E#1} in S#3)]))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(letrec {E#1;E#2} in S#3)])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[(letrec {E#1} in S#3)])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[(letrec {E#1} in S#3)])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[(letrec {E#1} in S#3)])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(letrec {E#1} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(letrec {E#1;E#2} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(letrec {E#1} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[(letrec {E#1} in S#3)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {E#7} in T#19[(letrec {E#1;E#2} in S#3)]) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app T#19[(letrec {E#1} in S#3)] S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (letrec {E#7} in T#19) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in T#19[(letrec {E#1} in S#3)]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#16=(app (letrec {E#7} in T#19[(letrec {E#1;E#2} in S#3)]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in T#19[(letrec {E#1} in S#3)]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app T#19[(letrec {E#1} in S#3)] S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22} in S#9) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#20=T#19[(letrec {E#1} in S#3)];E#22} in (app S#9 S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (S#8,(letrec {X#20=T#19[(letrec {E#1} in S#3)];E#22} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (letrec {X#20=T#19;E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[(letrec {E#1} in S#3)];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {X#20=T#19[(letrec {E#1} in S#3)];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#16=(app (letrec {X#20=T#19[(letrec {E#1;E#2} in S#3)];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {X#20=T#19[(letrec {E#1} in S#3)];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {X#20=T#19[(letrec {E#1} in S#3)];E#22} in (app S#9 S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {E#2;E#7} in S#9) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app S#9 S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#9,(letrec {E#2} in [.])),
             [{E#7},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app [.] S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#18         |->  [.],
           S#3          |->  S#9,
           E#1          |->  {E#7}}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#16=(app (letrec {E#2;E#7} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app S#9 S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {E#7} in S#9) T#18[(letrec {E#1;E#2} in S#3)])
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app S#9 T#18[(letrec {E#1} in S#3)]))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(S#3,(letrec {E#2} in [.])),
             [{E#1},(letrec {E#2} in [.])],
             (T#18[(letrec {E#1} in S#3)],(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#16=(app (letrec {E#7} in S#9) T#18);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[(letrec {E#1} in S#3)]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in S#9) T#18[(letrec {E#1} in S#3)]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -gc2->                        (letrec {X#16=(app (letrec {E#7} in S#9) T#18[(letrec {E#1;E#2} in S#3)]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in S#9) T#18[(letrec {E#1} in S#3)]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app S#9 T#18[(letrec {E#1} in S#3)]));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#2;E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ,
     (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
  )

where

   Delta1 = {}
   Delta2 = {E#1,E#2,E#7}
   Delta3 = {(A#10[(var X#5)],(letrec {E#2} in [.])),
             [{E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]},(letrec {E#2} in [.])],
             (S#8,(letrec {E#7} in [.])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -gc2-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#1} in S#3)]
    -gc2->                        T#4[(letrec {E#1;E#2} in S#3)]
    and constraints: E#1/= {}, E#2/= {}, (S#3,(letrec {E#2} in [.])), ({E#1},(letrec {E#2} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#1} in S#3)]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#1,E#2,E#7}
      Delta3=  {(S#3,(letrec {E#2} in [.])),[{E#1},(letrec {E#2} in [.])],(S#8,(letrec {E#7} in [.])),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           S#3  |->  A#10[(var X#5)],
           E#1  |->  {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]}}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -gc2->                        (letrec {E#2;E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     A#10[(app (\ X#6.S#8) T#12[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
    ,
     A#10[(letrec {X#6=T#12[(letrec {E#2} in T#5[S#3])]} in S#8)]
  )

where

   Delta1 = {T#11,A#9,T#4,A#10}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#12[(letrec {E#2} in T#5[S#3])],(\ X#6.[.])),
             (T#12[(letrec {E#2} in T#5[S#3])],(letrec {X#6=[.]} in S#8)),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#9[(app (\ X#6.S#8) S#7)]
    -SR,lbeta1->                  A#9[(letrec {X#6=S#7} in S#8)]
    and constraints: (S#7,(\ X#6.[.])), (S#7,(letrec {X#6=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= A#9[(app (\ X#6.S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#6.[.])),(S#7,(letrec {X#6=[.]} in S#8)),((var X#1),T#5[[.]])}


and found solution:

    Sol = {A#9   |->  A#10,
           T#4   |->  A#10[(app (\ X#6.S#8) T#12)],
           T#11  |->  (app (\ X#6.S#8) T#12),
           S#7   |->  T#12[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  A#10[(app (\ X#6.S#8) T#12[(letrec {E#2} in T#5[S#3])])]
    -ucp1->                       A#10[(app (\ X#6.S#8) T#12[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
    ................................................................................
                                  A#10[(app (\ X#6.S#8) T#12[(letrec {E#2} in T#5[S#3])])]
    -SR,lbeta1->                  A#10[(letrec {X#6=T#12[(letrec {E#2} in T#5[S#3])]} in S#8)]
    

================================================================================
Critical Pair:

  (
     A#10[(app A#11[(app (\ X#6.S#8) S#7)] T#12[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
    ,
     A#10[(app A#11[(letrec {X#6=S#7} in S#8)] T#12[(letrec {E#2} in T#5[S#3])])]
  )

where

   Delta1 = {A#9,T#4}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#6.[.])),
             (S#7,(letrec {X#6=[.]} in S#8)),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#9[(app (\ X#6.S#8) S#7)]
    -SR,lbeta1->                  A#9[(letrec {X#6=S#7} in S#8)]
    and constraints: (S#7,(\ X#6.[.])), (S#7,(letrec {X#6=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= A#9[(app (\ X#6.S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#6.[.])),(S#7,(letrec {X#6=[.]} in S#8)),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4  |->  A#10[(app A#11[(app (\ X#6.S#8) S#7)] T#12)],
           A#9  |->  A#10[(app A#11 T#12[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  A#10[(app A#11[(app (\ X#6.S#8) S#7)] T#12[(letrec {E#2} in T#5[S#3])])]
    -ucp1->                       A#10[(app A#11[(app (\ X#6.S#8) S#7)] T#12[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
    ................................................................................
                                  A#10[(app A#11[(app (\ X#6.S#8) S#7)] T#12[(letrec {E#2} in T#5[S#3])])]
    -SR,lbeta1->                  A#10[(app A#11[(letrec {X#6=S#7} in S#8)] T#12[(letrec {E#2} in T#5[S#3])])]
    

================================================================================
Critical Pair:

  (
     (app (\ X#6.S#8) T#10[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])
    ,
     (letrec {X#6=T#10[(letrec {E#2} in T#5[S#3])]} in S#8)
  )

where

   Delta1 = {T#4}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#10[(letrec {E#2} in T#5[S#3])],(\ X#6.[.])),
             (T#10[(letrec {E#2} in T#5[S#3])],(letrec {X#6=[.]} in S#8)),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#9[(app (\ X#6.S#8) S#7)]
    -SR,lbeta1->                  A#9[(letrec {X#6=S#7} in S#8)]
    and constraints: (S#7,(\ X#6.[.])), (S#7,(letrec {X#6=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= A#9[(app (\ X#6.S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#6.[.])),(S#7,(letrec {X#6=[.]} in S#8)),((var X#1),T#5[[.]])}


and found solution:

    Sol = {A#9  |->  [.],
           T#4  |->  (app (\ X#6.S#8) T#10),
           S#7  |->  T#10[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (app (\ X#6.S#8) T#10[(letrec {E#2} in T#5[S#3])])
    -ucp1->                       (app (\ X#6.S#8) T#10[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])
    ................................................................................
                                  (app (\ X#6.S#8) T#10[(letrec {E#2} in T#5[S#3])])
    -SR,lbeta1->                  (letrec {X#6=T#10[(letrec {E#2} in T#5[S#3])]} in S#8)
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#12[(app (\ X#6.S#9) T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
     )
    ,
     (letrec {E#7} in A#12[(letrec {X#6=T#14[(letrec {E#2} in T#5[S#3])]} in S#9)])
  )

where

   Delta1 = {T#13,A#10,T#11,T#4,A#12}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#14[(letrec {E#2} in T#5[S#3])],(\ X#6.[.])),
             (T#14[(letrec {E#2} in T#5[S#3])],(letrec {X#6=[.]} in S#9)),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#7} in A#12[(app (\ X#6.S#9) T#14)]),
           A#10  |->  A#12,
           T#11  |->  A#12[(app (\ X#6.S#9) T#14)],
           T#13  |->  (app (\ X#6.S#9) T#14),
           S#8   |->  T#14[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {E#7} in A#12[(app (\ X#6.S#9) T#14[(letrec {E#2} in T#5[S#3])])])
    -ucp1->                       (letrec {E#7} in A#12[(app (\ X#6.S#9) T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])])
    ................................................................................
                                  (letrec {E#7} in A#12[(app (\ X#6.S#9) T#14[(letrec {E#2} in T#5[S#3])])])
    -SR,lbeta2->                  (letrec {E#7} in A#12[(letrec {X#6=T#14[(letrec {E#2} in T#5[S#3])]} in S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        A#12[(app A#13[(app (\ X#6.S#9) S#8)] T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
     )
    ,
     (letrec
        E#7
     in
        A#12[(app A#13[(letrec {X#6=S#8} in S#9)] T#14[(letrec {E#2} in T#5[S#3])])]
     )
  )

where

   Delta1 = {A#10,T#11,T#4}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#7} in A#12[(app A#13[(app (\ X#6.S#9) S#8)] T#14)]),
           T#11  |->  A#12[(app A#13[(app (\ X#6.S#9) S#8)] T#14)],
           A#10  |->  A#12[(app A#13 T#14[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {E#7} in A#12[(app A#13[(app (\ X#6.S#9) S#8)] T#14[(letrec {E#2} in T#5[S#3])])])
    -ucp1->                       (letrec {E#7} in A#12[(app A#13[(app (\ X#6.S#9) S#8)] T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])])
    ................................................................................
                                  (letrec {E#7} in A#12[(app A#13[(app (\ X#6.S#9) S#8)] T#14[(letrec {E#2} in T#5[S#3])])])
    -SR,lbeta2->                  (letrec {E#7} in A#12[(app A#13[(letrec {X#6=S#8} in S#9)] T#14[(letrec {E#2} in T#5[S#3])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
     in
        (app (\ X#6.S#9) T#12[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])
     )
    ,
     (letrec {E#7} in (letrec {X#6=T#12[(letrec {E#2} in T#5[S#3])]} in S#9))
  )

where

   Delta1 = {T#11,T#4}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#12[(letrec {E#2} in T#5[S#3])],(\ X#6.[.])),
             (T#12[(letrec {E#2} in T#5[S#3])],(letrec {X#6=[.]} in S#9)),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#7} in (app (\ X#6.S#9) T#12)),
           A#10  |->  [.],
           T#11  |->  (app (\ X#6.S#9) T#12),
           S#8   |->  T#12[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {E#7} in (app (\ X#6.S#9) T#12[(letrec {E#2} in T#5[S#3])]))
    -ucp1->                       (letrec {E#7} in (app (\ X#6.S#9) T#12[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]))
    ................................................................................
                                  (letrec {E#7} in (app (\ X#6.S#9) T#12[(letrec {E#2} in T#5[S#3])]))
    -SR,lbeta2->                  (letrec {E#7} in (letrec {X#6=T#12[(letrec {E#2} in T#5[S#3])]} in S#9))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#12= T#11[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
       ;E#14
     in
        A#10[(app (\ X#6.S#9) S#8)]
     )
    ,
     (letrec
        X#12= T#11[(letrec {E#2} in T#5[S#3])]
       ;E#14
     in
        A#10[(letrec {X#6=S#8} in S#9)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#12=T#11;E#14} in A#10[(app (\ X#6.S#9) S#8)]),
           E#7   |->  {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14},
           E#13  |->  {E#14}}

and instantiated rules:

                                  (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14} in A#10[(app (\ X#6.S#9) S#8)])
    -ucp1->                       (letrec {X#12=T#11[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#14} in A#10[(app (\ X#6.S#9) S#8)])
    ................................................................................
                                  (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14} in A#10[(letrec {X#6=S#8} in S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#6.S#9);E#7} in A#11[(app (var X#1) S#8)])
    ,
     (letrec {E#7} in A#11[(letrec {X#6=S#8} in S#9)])
  )

where

   Delta1 = {T#12,A#10,T#5,A#11}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),A#11[(app [.] S#8)]),
             ((\ X#6.S#9),A#11[(app [.] S#8)]),
             ((letrec {E#7} in A#11[(app (dummy3 ) S#8)]),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#11[(app [.] S#8)])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#7},
           A#10  |->  A#11,
           T#5   |->  A#11[(app [.] S#8)],
           T#12  |->  (app [.] S#8),
           T#13  |->  [.],
           S#3   |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {E#7} in A#11[(app (\ X#6.S#9) S#8)])
    -ucp1->                       (letrec {X#1=(\ X#6.S#9);E#7} in A#11[(app (var X#1) S#8)])
    ................................................................................
                                  (letrec {E#7} in A#11[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#11[(letrec {X#6=S#8} in S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#3;E#7} in A#11[(app (\ X#6.S#9) T#13[(var X#1)])])
    ,
     (letrec {E#7} in A#11[(letrec {X#6=T#13[S#3]} in S#9)])
  )

where

   Delta1 = {T#12,A#10,T#5,A#11}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),A#11[(app (\ X#6.S#9) T#13)]),
             (S#3,A#11[(app (\ X#6.S#9) T#13)]),
             ((letrec {E#7} in A#11[(app (\ X#6.S#9) T#13[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#13[S#3],(\ X#6.[.])),
             (T#13[S#3],(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#11[(app (\ X#6.S#9) T#13[[.]])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#7},
           A#10  |->  A#11,
           T#5   |->  A#11[(app (\ X#6.S#9) T#13)],
           T#12  |->  (app (\ X#6.S#9) T#13),
           S#8   |->  T#13[S#3]}

and instantiated rules:

                                  (letrec {E#7} in A#11[(app (\ X#6.S#9) T#13[S#3])])
    -ucp1->                       (letrec {X#1=S#3;E#7} in A#11[(app (\ X#6.S#9) T#13[(var X#1)])])
    ................................................................................
                                  (letrec {E#7} in A#11[(app (\ X#6.S#9) T#13[S#3])])
    -SR,lbeta2->                  (letrec {E#7} in A#11[(letrec {X#6=T#13[S#3]} in S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(app (\ X#6.S#9) S#8);E#7} in A#11[(var X#1)])
    ,
     (letrec {E#7} in A#11[(letrec {X#6=S#8} in S#9)])
  )

where

   Delta1 = {A#10,T#5,A#11}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),A#11[[.]]),
             ((app (\ X#6.S#9) S#8),A#11[[.]]),
             ((letrec {E#7} in A#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#6.S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#7},
           A#10  |->  A#11,
           T#5   |->  A#11[[.]],
           T#12  |->  [.],
           S#3   |->  (app (\ X#6.S#9) S#8)}

and instantiated rules:

                                  (letrec {E#7} in A#11[(app (\ X#6.S#9) S#8)])
    -ucp1->                       (letrec {X#1=(app (\ X#6.S#9) S#8);E#7} in A#11[(var X#1)])
    ................................................................................
                                  (letrec {E#7} in A#11[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#11[(letrec {X#6=S#8} in S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=A#12[(app (\ X#6.S#9) S#8)];E#7} in A#11[(var X#1)])
    ,
     (letrec {E#7} in A#11[A#12[(letrec {X#6=S#8} in S#9)]])
  )

where

   Delta1 = {A#10,T#5,A#11}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),A#11),
             (A#12[(app (\ X#6.S#9) S#8)],A#11),
             ((letrec {E#7} in A#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(app (\ X#6.S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#7},
           A#10  |->  A#11[A#12],
           T#5   |->  A#11,
           S#3   |->  A#12[(app (\ X#6.S#9) S#8)]}

and instantiated rules:

                                  (letrec {E#7} in A#11[A#12[(app (\ X#6.S#9) S#8)]])
    -ucp1->                       (letrec {X#1=A#12[(app (\ X#6.S#9) S#8)];E#7} in A#11[(var X#1)])
    ................................................................................
                                  (letrec {E#7} in A#11[A#12[(app (\ X#6.S#9) S#8)]])
    -SR,lbeta2->                  (letrec {E#7} in A#11[A#12[(letrec {X#6=S#8} in S#9)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#3
       ;E#7
     in
        A#11[(app A#12[(app (\ X#6.S#9) S#8)] T#13[(var X#1)])]
     )
    ,
     (letrec {E#7} in A#11[(app A#12[(letrec {X#6=S#8} in S#9)] T#13[S#3])])
  )

where

   Delta1 = {A#10,T#5}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),A#11[(app A#12[(app (\ X#6.S#9) S#8)] T#13)]),
             (S#3,A#11[(app A#12[(app (\ X#6.S#9) S#8)] T#13)]),
             ((letrec {E#7} in A#11[(app A#12[(app (\ X#6.S#9) S#8)] T#13[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#11[(app A#12[(app (\ X#6.S#9) S#8)] T#13[[.]])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#7},
           T#5   |->  A#11[(app A#12[(app (\ X#6.S#9) S#8)] T#13)],
           A#10  |->  A#11[(app A#12 T#13[S#3])]}

and instantiated rules:

                                  (letrec {E#7} in A#11[(app A#12[(app (\ X#6.S#9) S#8)] T#13[S#3])])
    -ucp1->                       (letrec {X#1=S#3;E#7} in A#11[(app A#12[(app (\ X#6.S#9) S#8)] T#13[(var X#1)])])
    ................................................................................
                                  (letrec {E#7} in A#11[(app A#12[(app (\ X#6.S#9) S#8)] T#13[S#3])])
    -SR,lbeta2->                  (letrec {E#7} in A#11[(app A#12[(letrec {X#6=S#8} in S#9)] T#13[S#3])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#6.S#9);E#7} in (app (var X#1) S#8))
    ,
     (letrec {E#7} in (letrec {X#6=S#8} in S#9))
  )

where

   Delta1 = {T#5}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),(app [.] S#8)),
             ((\ X#6.S#9),(app [.] S#8)),
             ((letrec {E#7} in (app (dummy3 ) S#8)),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(app [.] S#8))}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#7},
           A#10  |->  [.],
           T#5   |->  (app [.] S#8),
           T#11  |->  [.],
           S#3   |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {E#7} in (app (\ X#6.S#9) S#8))
    -ucp1->                       (letrec {X#1=(\ X#6.S#9);E#7} in (app (var X#1) S#8))
    ................................................................................
                                  (letrec {E#7} in (app (\ X#6.S#9) S#8))
    -SR,lbeta2->                  (letrec {E#7} in (letrec {X#6=S#8} in S#9))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#3;E#7} in (app (\ X#6.S#9) T#11[(var X#1)]))
    ,
     (letrec {E#7} in (letrec {X#6=T#11[S#3]} in S#9))
  )

where

   Delta1 = {T#5}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),(app (\ X#6.S#9) T#11)),
             (S#3,(app (\ X#6.S#9) T#11)),
             ((letrec {E#7} in (app (\ X#6.S#9) T#11[(dummy3 )])),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[S#3],(\ X#6.[.])),
             (T#11[S#3],(letrec {X#6=[.]} in S#9)),
             ((var X#1),(app (\ X#6.S#9) T#11[[.]]))}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#7},
           A#10  |->  [.],
           T#5   |->  (app (\ X#6.S#9) T#11),
           S#8   |->  T#11[S#3]}

and instantiated rules:

                                  (letrec {E#7} in (app (\ X#6.S#9) T#11[S#3]))
    -ucp1->                       (letrec {X#1=S#3;E#7} in (app (\ X#6.S#9) T#11[(var X#1)]))
    ................................................................................
                                  (letrec {E#7} in (app (\ X#6.S#9) T#11[S#3]))
    -SR,lbeta2->                  (letrec {E#7} in (letrec {X#6=T#11[S#3]} in S#9))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=A#10[(app (\ X#6.S#9) S#8)];E#7} in (var X#1))
    ,
     (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),[.]),
             (A#10[(app (\ X#6.S#9) S#8)],[.]),
             ((letrec {E#7} in (dummy3 )),(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(app (\ X#6.S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    and constraints: E#7/= {}, (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           E#2  |->  {E#7},
           T#5  |->  [.],
           S#3  |->  A#10[(app (\ X#6.S#9) S#8)]}

and instantiated rules:

                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -ucp1->                       (letrec {X#1=A#10[(app (\ X#6.S#9) S#8)];E#7} in (var X#1))
    ................................................................................
                                  (letrec {E#7} in A#10[(app (\ X#6.S#9) S#8)])
    -SR,lbeta2->                  (letrec {E#7} in A#10[(letrec {X#6=S#8} in S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
       ;EE#12[X#6,(app (\ X#7.S#10) S#9)]
     in
        A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
     )
    ,
     (letrec
        E#8
       ;EE#12[X#6,(letrec {X#7=S#9} in S#10)]
     in
        A#14[(app A#15[(var X#6)] T#16[(letrec {E#2} in T#5[S#3])])]
     )
  )

where

   Delta1 = {A#11,T#13,T#4}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#14[(app A#15[[.]] T#16[(letrec {E#2} in T#5[S#3])])]),
             ((var X#6),A#14[(app A#15[[.]] T#16[(letrec {E#2} in T#5[S#3])])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#6)] T#16)],
           A#11  |->  A#14[(app A#15 T#16[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16[(letrec {E#2} in T#5[S#3])])])
    -ucp1->                       (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])])
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16[(letrec {E#2} in T#5[S#3])])])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#14[(app A#15[(var X#6)] T#16[(letrec {E#2} in T#5[S#3])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
       ;E#16
       ;EE#12[X#6,(app (\ X#7.S#10) S#9)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {E#2} in T#5[S#3])]
       ;E#16
       ;EE#12[X#6,(letrec {X#7=S#9} in S#10)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#14=T#13;E#16;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)]),
           E#8   |->  {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16},
           E#15  |->  {E#16;EE#12[X#6,(app (\ X#7.S#10) S#9)]}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#14=T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#16;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#17[(app (\ X#7.S#10) T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#8
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#17[(letrec {X#7=T#19[(letrec {E#2} in T#5[S#3])]} in S#10)]
       ;E#8
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#18,A#16,T#13,T#4,A#17}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#19[(letrec {E#2} in T#5[S#3])],(\ X#7.[.])),
             (T#19[(letrec {E#2} in T#5[S#3])],(letrec {X#7=[.]} in S#10)),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#17[(app (\ X#7.S#10) T#19)];E#8} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#6,
           E#15         |->  {E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[(app (\ X#7.S#10) T#19)],
           T#18         |->  (app (\ X#7.S#10) T#19),
           S#9          |->  T#19[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {X#6=A#17[(app (\ X#7.S#10) T#19[(letrec {E#2} in T#5[S#3])])];E#8} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#6=A#17[(app (\ X#7.S#10) T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#8} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#17[(app (\ X#7.S#10) T#19[(letrec {E#2} in T#5[S#3])])];E#8} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#6=A#17[(letrec {X#7=T#19[(letrec {E#2} in T#5[S#3])]} in S#10)];E#8} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#17[(app A#18[(app (\ X#7.S#10) S#9)] T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#8
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#17[(app A#18[(letrec {X#7=S#9} in S#10)] T#19[(letrec {E#2} in T#5[S#3])])]
       ;E#8
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#17[(app A#18[(app (\ X#7.S#10) S#9)] T#19)];E#8} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] T#19[(letrec {E#2} in T#5[S#3])])]},
           X#14         |->  X#6,
           E#15         |->  {E#8},
           T#13         |->  A#17[(app A#18[(app (\ X#7.S#10) S#9)] T#19)],
           A#16         |->  A#17[(app A#18 T#19[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=A#17[(app A#18[(app (\ X#7.S#10) S#9)] T#19[(letrec {E#2} in T#5[S#3])])];E#8} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#6=A#17[(app A#18[(app (\ X#7.S#10) S#9)] T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#8} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#17[(app A#18[(app (\ X#7.S#10) S#9)] T#19[(letrec {E#2} in T#5[S#3])])];E#8} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#6=A#17[(app A#18[(letrec {X#7=S#9} in S#10)] T#19[(letrec {E#2} in T#5[S#3])])];E#8} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (app (\ X#7.S#10) T#17[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])
       ;E#8
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= (letrec {X#7=T#17[(letrec {E#2} in T#5[S#3])]} in S#10)
       ;E#8
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#17[(letrec {E#2} in T#5[S#3])],(\ X#7.[.])),
             (T#17[(letrec {E#2} in T#5[S#3])],(letrec {X#7=[.]} in S#10)),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(app (\ X#7.S#10) T#17);E#8} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#6,
           E#15         |->  {E#8},
           A#16         |->  [.],
           T#13         |->  (app (\ X#7.S#10) T#17),
           S#9          |->  T#17[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {X#6=(app (\ X#7.S#10) T#17[(letrec {E#2} in T#5[S#3])]);E#8} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#6=(app (\ X#7.S#10) T#17[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]);E#8} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(app (\ X#7.S#10) T#17[(letrec {E#2} in T#5[S#3])]);E#8} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#6=(letrec {X#7=T#17[(letrec {E#2} in T#5[S#3])]} in S#10);E#8} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#8
       ;EE#18[X#17,(app (\ X#7.S#10) S#9)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])]
       ;E#8
       ;EE#18[X#17,(letrec {X#7=S#9} in S#10)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#19[(app A#20[(var X#17)] T#21)];E#8;EE#18[X#17,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])];EE#18[X#17,[.2]]},
           X#14         |->  X#6,
           E#15         |->  {E#8;EE#18[X#17,(app (\ X#7.S#10) S#9)]},
           T#13         |->  A#19[(app A#20[(var X#17)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])];E#8;EE#18[X#17,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#8;EE#18[X#17,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])];E#8;EE#18[X#17,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])];E#8;EE#18[X#17,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#8
       ;EE#19[X#6,(var X#17)]
       ;EE#20[X#18,(app (\ X#7.S#10) S#9)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])]
       ;E#8
       ;EE#19[X#6,(var X#17)]
       ;EE#20[X#18,(letrec {X#7=S#9} in S#10)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23)];E#8;EE#19[X#6,(var X#17)];EE#20[X#18,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {E#8;EE#19[X#6,(var X#17)];EE#20[X#18,(app (\ X#7.S#10) S#9)]},
           T#13         |->  A#21[(app A#22[(var X#18)] T#23)],
           A#16         |->  A#21[(app A#22 T#23[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])];E#8;EE#19[X#6,(var X#17)];EE#20[X#18,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#8;EE#19[X#6,(var X#17)];EE#20[X#18,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])];E#8;EE#19[X#6,(var X#17)];EE#20[X#18,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])];E#8;EE#19[X#6,(var X#17)];EE#20[X#18,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app (\ X#7.S#10) T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#8
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#19[(letrec {X#7=T#21[(letrec {E#2} in T#5[S#3])]} in S#10)]
       ;E#8
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#20,A#16,T#13,T#4,A#19}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#21[(letrec {E#2} in T#5[S#3])],(\ X#7.[.])),
             (T#21[(letrec {E#2} in T#5[S#3])],(letrec {X#7=[.]} in S#10)),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app (\ X#7.S#10) T#21)];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#8;EE#18[X#6,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[(app (\ X#7.S#10) T#21)],
           T#20         |->  (app (\ X#7.S#10) T#21),
           S#9          |->  T#21[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app (\ X#7.S#10) T#21[(letrec {E#2} in T#5[S#3])])];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#17=A#19[(app (\ X#7.S#10) T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#19[(app (\ X#7.S#10) T#21[(letrec {E#2} in T#5[S#3])])];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#17=A#19[(letrec {X#7=T#21[(letrec {E#2} in T#5[S#3])]} in S#10)];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[(app (\ X#7.S#10) S#9)] T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#8
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(letrec {X#7=S#9} in S#10)] T#21[(letrec {E#2} in T#5[S#3])])]
       ;E#8
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app A#20[(app (\ X#7.S#10) S#9)] T#21)];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] T#21[(letrec {E#2} in T#5[S#3])])];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#8;EE#18[X#6,(var X#17)]},
           T#13         |->  A#19[(app A#20[(app (\ X#7.S#10) S#9)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(app (\ X#7.S#10) S#9)] T#21[(letrec {E#2} in T#5[S#3])])];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#17=A#19[(app A#20[(app (\ X#7.S#10) S#9)] T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(app (\ X#7.S#10) S#9)] T#21[(letrec {E#2} in T#5[S#3])])];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#17=A#19[(app A#20[(letrec {X#7=S#9} in S#10)] T#21[(letrec {E#2} in T#5[S#3])])];E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (app (\ X#7.S#10) T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])
       ;E#8
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= (letrec {X#7=T#19[(letrec {E#2} in T#5[S#3])]} in S#10)
       ;E#8
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#19[(letrec {E#2} in T#5[S#3])],(\ X#7.[.])),
             (T#19[(letrec {E#2} in T#5[S#3])],(letrec {X#7=[.]} in S#10)),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=(app (\ X#7.S#10) T#19);E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#8;EE#18[X#6,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  (app (\ X#7.S#10) T#19),
           S#9          |->  T#19[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {X#17=(app (\ X#7.S#10) T#19[(letrec {E#2} in T#5[S#3])]);E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#17=(app (\ X#7.S#10) T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]);E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=(app (\ X#7.S#10) T#19[(letrec {E#2} in T#5[S#3])]);E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {X#17=(letrec {X#7=T#19[(letrec {E#2} in T#5[S#3])]} in S#10);E#8;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#6)
       ;E#8
       ;EE#12[X#6,(app (\ X#7.S#10) S#9)]
     in
        A#13[(var X#1)]
     )
    ,
     (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#13[(var X#6)])
  )

where

   Delta1 = {A#11,T#5,A#13}
   Delta2 = {E#2}
   Delta3 = {((var X#1),A#13[[.]]),
             ((var X#6),A#13[[.]]),
             ((letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#13[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),A#13[[.]]),
             ((var X#6),A#13[[.]]),
             ((var X#6),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]},
           A#11  |->  A#13,
           T#5   |->  A#13[[.]],
           T#14  |->  [.],
           S#3   |->  (var X#6)}

and instantiated rules:

                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#13[(var X#6)])
    -ucp1->                       (letrec {X#1=(var X#6);E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#13[(var X#1)])
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#13[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#13[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(var X#6)]
       ;E#8
       ;EE#12[X#6,(app (\ X#7.S#10) S#9)]
     in
        A#13[(var X#1)]
     )
    ,
     (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#13[A#14[(var X#6)]])
  )

where

   Delta1 = {A#11,T#5,A#13}
   Delta2 = {E#2}
   Delta3 = {((var X#1),A#13),
             (A#14[(var X#6)],A#13),
             ((letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#13[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(var X#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),A#13[[.]]),
             ((var X#6),A#13[A#14[[.]]]),
             ((var X#6),A#13[A#14[[.]]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]},
           A#11  |->  A#13[A#14],
           T#5   |->  A#13,
           S#3   |->  A#14[(var X#6)]}

and instantiated rules:

                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#13[A#14[(var X#6)]])
    -ucp1->                       (letrec {X#1=A#14[(var X#6)];E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#13[(var X#1)])
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#13[A#14[(var X#6)]])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#13[A#14[(var X#6)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#3
       ;E#8
       ;EE#12[X#6,(app (\ X#7.S#10) S#9)]
     in
        A#13[(app A#14[(var X#6)] T#15[(var X#1)])]
     )
    ,
     (letrec
        E#8
       ;EE#12[X#6,(letrec {X#7=S#9} in S#10)]
     in
        A#13[(app A#14[(var X#6)] T#15[S#3])]
     )
  )

where

   Delta1 = {A#11,T#5}
   Delta2 = {E#2}
   Delta3 = {((var X#1),A#13[(app A#14[(var X#6)] T#15)]),
             (S#3,A#13[(app A#14[(var X#6)] T#15)]),
             ((letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#13[(app A#14[(var X#6)] T#15[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),A#13[(app A#14[(var X#6)] T#15[[.]])]),
             ((var X#6),A#13[(app A#14[[.]] T#15[S#3])]),
             ((var X#6),A#13[(app A#14[[.]] T#15[S#3])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]},
           T#5   |->  A#13[(app A#14[(var X#6)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[S#3])]}

and instantiated rules:

                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#13[(app A#14[(var X#6)] T#15[S#3])])
    -ucp1->                       (letrec {X#1=S#3;E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#13[(app A#14[(var X#6)] T#15[(var X#1)])])
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#13[(app A#14[(var X#6)] T#15[S#3])])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#13[(app A#14[(var X#6)] T#15[S#3])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#11[(var X#6)]
       ;E#8
       ;EE#12[X#6,(app (\ X#7.S#10) S#9)]
     in
        (var X#1)
     )
    ,
     (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
  )

where

   Delta1 = {}
   Delta2 = {E#2}
   Delta3 = {((var X#1),[.]),
             (A#11[(var X#6)],[.]),
             ((letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in (dummy3 )),(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(var X#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(\ X#7.[.])),
             (S#9,(letrec {X#7=[.]} in S#10)),
             ((var X#1),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lbeta3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    and constraints: (S#9,(\ X#7.[.])), (S#9,(letrec {X#7=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(\ X#7.[.])),(S#9,(letrec {X#7=[.]} in S#10)),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           E#2  |->  {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]},
           T#5  |->  [.],
           S#3  |->  A#11[(var X#6)]}

and instantiated rules:

                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#1=A#11[(var X#6)];E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in (var X#1))
    ................................................................................
                                  (letrec {E#8;EE#12[X#6,(app (\ X#7.S#10) S#9)]} in A#11[(var X#6)])
    -SR,lbeta3->                  (letrec {E#8;EE#12[X#6,(letrec {X#7=S#9} in S#10)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#9)
       ;E#8
     in
        A#12[(app A#13[(var X#6)] T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#9)
       ;E#8
     in
        A#12[(app A#13[(\ X#7.S#9)] T#14[(letrec {E#2} in T#5[S#3])])]
     )
  )

where

   Delta1 = {A#10,T#11,T#4}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#12[(app A#13[[.]] T#14[(letrec {E#2} in T#5[S#3])])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(\ X#7.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(\ X#7.S#9);E#8} in A#12[(app A#13[(var X#6)] T#14)]),
           T#11  |->  A#12[(app A#13[(var X#6)] T#14)],
           A#10  |->  A#12[(app A#13 T#14[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#12[(app A#13[(var X#6)] T#14[(letrec {E#2} in T#5[S#3])])])
    -ucp1->                       (letrec {X#6=(\ X#7.S#9);E#8} in A#12[(app A#13[(var X#6)] T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#12[(app A#13[(var X#6)] T#14[(letrec {E#2} in T#5[S#3])])])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#12[(app A#13[(\ X#7.S#9)] T#14[(letrec {E#2} in T#5[S#3])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#12= T#11[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
       ;X#6= (\ X#7.S#9)
       ;E#14
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#12= T#11[(letrec {E#2} in T#5[S#3])]
       ;X#6= (\ X#7.S#9)
       ;E#14
     in
        A#10[(\ X#7.S#9)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(\ X#7.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#12=T#11;X#6=(\ X#7.S#9);E#14} in A#10[(var X#6)]),
           E#8   |->  {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14},
           E#13  |->  {X#6=(\ X#7.S#9);E#14}}

and instantiated rules:

                                  (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];X#6=(\ X#7.S#9);E#14} in A#10[(var X#6)])
    -ucp1->                       (letrec {X#12=T#11[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];X#6=(\ X#7.S#9);E#14} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];X#6=(\ X#7.S#9);E#14} in A#10[(var X#6)])
    -SR,cp-in1->                  (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];X#6=(\ X#7.S#9);E#14} in A#10[(\ X#7.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#6);X#6=(\ X#7.S#9);E#8} in A#11[(var X#1)])
    ,
     (letrec {X#6=(\ X#7.S#9);E#8} in A#11[(\ X#7.S#9)])
  )

where

   Delta1 = {A#10,T#5,A#11}
   Delta2 = {E#2}
   Delta3 = {((var X#1),A#11[[.]]),
             ((var X#6),A#11[[.]]),
             ((letrec {X#6=(\ X#7.S#9);E#8} in A#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(\ X#7.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(\ X#7.S#9);E#8},
           A#10  |->  A#11,
           T#5   |->  A#11[[.]],
           T#12  |->  [.],
           S#3   |->  (var X#6)}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#1=(var X#6);X#6=(\ X#7.S#9);E#8} in A#11[(var X#1)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#11[(var X#6)])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#11[(\ X#7.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=A#12[(var X#6)];X#6=(\ X#7.S#9);E#8} in A#11[(var X#1)])
    ,
     (letrec {X#6=(\ X#7.S#9);E#8} in A#11[A#12[(\ X#7.S#9)]])
  )

where

   Delta1 = {A#10,T#5,A#11}
   Delta2 = {E#2}
   Delta3 = {((var X#1),A#11),
             (A#12[(var X#6)],A#11),
             ((letrec {X#6=(\ X#7.S#9);E#8} in A#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(var X#6)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#11[[.]]),
             ((var X#6),A#11[A#12[[.]]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(\ X#7.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(\ X#7.S#9);E#8},
           A#10  |->  A#11[A#12],
           T#5   |->  A#11,
           S#3   |->  A#12[(var X#6)]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#11[A#12[(var X#6)]])
    -ucp1->                       (letrec {X#1=A#12[(var X#6)];X#6=(\ X#7.S#9);E#8} in A#11[(var X#1)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#11[A#12[(var X#6)]])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#11[A#12[(\ X#7.S#9)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#3
       ;X#6= (\ X#7.S#9)
       ;E#8
     in
        A#11[(app A#12[(var X#6)] T#13[(var X#1)])]
     )
    ,
     (letrec {X#6=(\ X#7.S#9);E#8} in A#11[(app A#12[(\ X#7.S#9)] T#13[S#3])])
  )

where

   Delta1 = {A#10,T#5}
   Delta2 = {E#2}
   Delta3 = {((var X#1),A#11[(app A#12[(var X#6)] T#13)]),
             (S#3,A#11[(app A#12[(var X#6)] T#13)]),
             ((letrec {X#6=(\ X#7.S#9);E#8} in A#11[(app A#12[(var X#6)] T#13[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#11[(app A#12[(var X#6)] T#13[[.]])]),
             ((var X#6),A#11[(app A#12[[.]] T#13[S#3])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(\ X#7.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(\ X#7.S#9);E#8},
           T#5   |->  A#11[(app A#12[(var X#6)] T#13)],
           A#10  |->  A#11[(app A#12 T#13[S#3])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#11[(app A#12[(var X#6)] T#13[S#3])])
    -ucp1->                       (letrec {X#1=S#3;X#6=(\ X#7.S#9);E#8} in A#11[(app A#12[(var X#6)] T#13[(var X#1)])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#11[(app A#12[(var X#6)] T#13[S#3])])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#11[(app A#12[(\ X#7.S#9)] T#13[S#3])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=A#10[(var X#6)];X#6=(\ X#7.S#9);E#8} in (var X#1))
    ,
     (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(\ X#7.S#9)])
  )

where

   Delta1 = {}
   Delta2 = {E#2}
   Delta3 = {((var X#1),[.]),
             (A#10[(var X#6)],[.]),
             ((letrec {X#6=(\ X#7.S#9);E#8} in (dummy3 )),(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#6)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-in1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(\ X#7.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           E#2  |->  {X#6=(\ X#7.S#9);E#8},
           T#5  |->  [.],
           S#3  |->  A#10[(var X#6)]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])
    -ucp1->                       (letrec {X#1=A#10[(var X#6)];X#6=(\ X#7.S#9);E#8} in (var X#1))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(var X#6)])
    -SR,cp-in1->                  (letrec {X#6=(\ X#7.S#9);E#8} in A#10[(\ X#7.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#10)
       ;E#9
       ;VV#12|X#8,(var X#6)|
     in
        A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;E#9
       ;VV#12|X#8,(var X#6)|
     in
        A#14[(app A#15[(\ X#7.S#10)] T#16[(letrec {E#2} in T#5[S#3])])]
     )
  )

where

   Delta1 = {A#11,T#13,T#4}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#14[(app A#15[[.]] T#16[(letrec {E#2} in T#5[S#3])])]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#14[(app A#15[(var X#8)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#8)] T#16)],
           A#11  |->  A#14[(app A#15 T#16[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#14[(app A#15[(var X#8)] T#16[(letrec {E#2} in T#5[S#3])])])
    -ucp1->                       (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#14[(app A#15[(var X#8)] T#16[(letrec {E#2} in T#5[S#3])])])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#14[(app A#15[(\ X#7.S#10)] T#16[(letrec {E#2} in T#5[S#3])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
       ;X#6= (\ X#7.S#10)
       ;E#16
       ;VV#12|X#8,(var X#6)|
     in
        A#11[(var X#8)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {E#2} in T#5[S#3])]
       ;X#6= (\ X#7.S#10)
       ;E#16
       ;VV#12|X#8,(var X#6)|
     in
        A#11[(\ X#7.S#10)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#11[[.]]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4   |->  (letrec {X#14=T#13;X#6=(\ X#7.S#10);E#16;VV#12|X#8,(var X#6)|} in A#11[(var X#8)]),
           E#9   |->  {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16},
           E#15  |->  {X#6=(\ X#7.S#10);E#16;VV#12|X#8,(var X#6)|}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];X#6=(\ X#7.S#10);E#16;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -ucp1->                       (letrec {X#14=T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];X#6=(\ X#7.S#10);E#16;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];X#6=(\ X#7.S#10);E#16;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];X#6=(\ X#7.S#10);E#16;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#8)
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;VV#12|X#8,(var X#6)|
     in
        A#13[(var X#1)]
     )
    ,
     (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[(\ X#7.S#10)])
  )

where

   Delta1 = {A#11,T#5,A#13}
   Delta2 = {E#2}
   Delta3 = {((var X#1),A#13[[.]]),
             ((var X#8),A#13[[.]]),
             ((letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#13[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|},
           A#11  |->  A#13,
           T#5   |->  A#13[[.]],
           T#14  |->  [.],
           S#3   |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[(var X#8)])
    -ucp1->                       (letrec {X#1=(var X#8);X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[(var X#1)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[(\ X#7.S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(var X#8)]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;VV#12|X#8,(var X#6)|
     in
        A#13[(var X#1)]
     )
    ,
     (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[A#14[(\ X#7.S#10)]])
  )

where

   Delta1 = {A#11,T#5,A#13}
   Delta2 = {E#2}
   Delta3 = {((var X#1),A#13),
             (A#14[(var X#8)],A#13),
             ((letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#13[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[A#14[[.]]]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|},
           A#11  |->  A#13[A#14],
           T#5   |->  A#13,
           S#3   |->  A#14[(var X#8)]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[A#14[(var X#8)]])
    -ucp1->                       (letrec {X#1=A#14[(var X#8)];X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[(var X#1)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[A#14[(var X#8)]])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[A#14[(\ X#7.S#10)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#3
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;VV#12|X#8,(var X#6)|
     in
        A#13[(app A#14[(var X#8)] T#15[(var X#1)])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;E#9
       ;VV#12|X#8,(var X#6)|
     in
        A#13[(app A#14[(\ X#7.S#10)] T#15[S#3])]
     )
  )

where

   Delta1 = {A#11,T#5}
   Delta2 = {E#2}
   Delta3 = {((var X#1),A#13[(app A#14[(var X#8)] T#15)]),
             (S#3,A#13[(app A#14[(var X#8)] T#15)]),
             ((letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[(app A#14[(var X#8)] T#15[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#13[(app A#14[(var X#8)] T#15[[.]])]),
             ((var X#6),[.]),
             ((var X#8),A#13[(app A#14[[.]] T#15[S#3])]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|},
           T#5   |->  A#13[(app A#14[(var X#8)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[S#3])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[(app A#14[(var X#8)] T#15[S#3])])
    -ucp1->                       (letrec {X#1=S#3;X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[(app A#14[(var X#8)] T#15[(var X#1)])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[(app A#14[(var X#8)] T#15[S#3])])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#13[(app A#14[(\ X#7.S#10)] T#15[S#3])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#11[(var X#8)]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;VV#12|X#8,(var X#6)|
     in
        (var X#1)
     )
    ,
     (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
  )

where

   Delta1 = {}
   Delta2 = {E#2}
   Delta3 = {((var X#1),[.]),
             (A#11[(var X#8)],[.]),
             ((letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in (dummy3 )),(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#6),[.]),
             ((var X#8),A#11[[.]]),
             ((var X#6),[.])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-in2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#11[[.]]),((var X#6),[.])}


and found solution:

    Sol = {T#4  |->  [.],
           E#2  |->  {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|},
           T#5  |->  [.],
           S#3  |->  A#11[(var X#8)]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -ucp1->                       (letrec {X#1=A#11[(var X#8)];X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in (var X#1))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(var X#8)])
    -SR,cp-in2->                  (letrec {X#6=(\ X#7.S#10);E#9;VV#12|X#8,(var X#6)|} in A#11[(\ X#7.S#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#10)
       ;E#9
       ;EE#13[X#8,A#11[(var X#6)]]
     in
        A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;E#9
       ;EE#13[X#8,A#11[(\ X#7.S#10)]]
     in
        A#15[(app A#16[(var X#8)] T#17[(letrec {E#2} in T#5[S#3])])]
     )
  )

where

   Delta1 = {A#12,T#14,T#4,A#11}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#15[(app A#16[[.]] T#17[(letrec {E#2} in T#5[S#3])])]),
             ((var X#8),A#15[(app A#16[[.]] T#17[(letrec {E#2} in T#5[S#3])])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#15[(app A#16[(var X#8)] T#17)]),
           T#14  |->  A#15[(app A#16[(var X#8)] T#17)],
           A#12  |->  A#15[(app A#16 T#17[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#15[(app A#16[(var X#8)] T#17[(letrec {E#2} in T#5[S#3])])])
    -ucp1->                       (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#15[(app A#16[(var X#8)] T#17[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#15[(app A#16[(var X#8)] T#17[(letrec {E#2} in T#5[S#3])])])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#15[(app A#16[(var X#8)] T#17[(letrec {E#2} in T#5[S#3])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#15= T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
       ;X#6= (\ X#7.S#10)
       ;E#17
       ;EE#13[X#8,A#11[(var X#6)]]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {E#2} in T#5[S#3])]
       ;X#6= (\ X#7.S#10)
       ;E#17
       ;EE#13[X#8,A#11[(\ X#7.S#10)]]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#4,A#11}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#15=T#14;X#6=(\ X#7.S#10);E#17;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)]),
           E#9   |->  {X#15=T#14[(letrec {E#2} in T#5[S#3])];E#17},
           E#16  |->  {X#6=(\ X#7.S#10);E#17;EE#13[X#8,A#11[(var X#6)]]}}

and instantiated rules:

                                  (letrec {X#15=T#14[(letrec {E#2} in T#5[S#3])];X#6=(\ X#7.S#10);E#17;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -ucp1->                       (letrec {X#15=T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];X#6=(\ X#7.S#10);E#17;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#15=T#14[(letrec {E#2} in T#5[S#3])];X#6=(\ X#7.S#10);E#17;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#15=T#14[(letrec {E#2} in T#5[S#3])];X#6=(\ X#7.S#10);E#17;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#18[A#20[(app A#21[(var X#6)] T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]]
       ;E#9
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#18[A#20[(app A#21[(\ X#7.S#10)] T#22[(letrec {E#2} in T#5[S#3])])]]
       ;E#9
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#19,A#17,T#14,T#4,A#11,A#18}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#20[(app A#21[[.]] T#22[(letrec {E#2} in T#5[S#3])])]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#10);X#8=A#18[A#20[(app A#21[(var X#6)] T#22)]];E#9} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#15         |->  X#8,
           E#16         |->  {X#6=(\ X#7.S#10);E#9},
           A#17         |->  A#18,
           T#14         |->  A#18[A#20[(app A#21[(var X#6)] T#22)]],
           T#19         |->  A#20[(app A#21[(var X#6)] T#22)],
           A#11         |->  A#20[(app A#21 T#22[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);X#8=A#18[A#20[(app A#21[(var X#6)] T#22[(letrec {E#2} in T#5[S#3])])]];E#9} in A#12[(var X#8)])
    -ucp1->                       (letrec {X#6=(\ X#7.S#10);X#8=A#18[A#20[(app A#21[(var X#6)] T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]];E#9} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);X#8=A#18[A#20[(app A#21[(var X#6)] T#22[(letrec {E#2} in T#5[S#3])])]];E#9} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);X#8=A#18[A#20[(app A#21[(\ X#7.S#10)] T#22[(letrec {E#2} in T#5[S#3])])]];E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#18[(app A#19[A#11[(var X#6)]] T#20[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#9
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#18[(app A#19[A#11[(\ X#7.S#10)]] T#20[(letrec {E#2} in T#5[S#3])])]
       ;E#9
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#4,A#11}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[A#11[(var X#6)]] T#20)];E#9} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {[.1]=A#18[(app A#19[[.2]] T#20[(letrec {E#2} in T#5[S#3])])]},
           X#15         |->  X#8,
           E#16         |->  {X#6=(\ X#7.S#10);E#9},
           T#14         |->  A#18[(app A#19[A#11[(var X#6)]] T#20)],
           A#17         |->  A#18[(app A#19 T#20[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[A#11[(var X#6)]] T#20[(letrec {E#2} in T#5[S#3])])];E#9} in A#12[(var X#8)])
    -ucp1->                       (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[A#11[(var X#6)]] T#20[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#9} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[A#11[(var X#6)]] T#20[(letrec {E#2} in T#5[S#3])])];E#9} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[A#11[(\ X#7.S#10)]] T#20[(letrec {E#2} in T#5[S#3])])];E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#18[(app A#19[(var X#6)] T#20[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#9
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#18[(app A#19[(\ X#7.S#10)] T#20[(letrec {E#2} in T#5[S#3])])]
       ;E#9
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#14,T#4,A#11}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#18[(app A#19[[.]] T#20[(letrec {E#2} in T#5[S#3])])]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[(var X#6)] T#20)];E#9} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#15         |->  X#8,
           E#16         |->  {X#6=(\ X#7.S#10);E#9},
           A#17         |->  [.],
           T#14         |->  A#18[(app A#19[(var X#6)] T#20)],
           A#11         |->  A#18[(app A#19 T#20[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[(var X#6)] T#20[(letrec {E#2} in T#5[S#3])])];E#9} in A#12[(var X#8)])
    -ucp1->                       (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[(var X#6)] T#20[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#9} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[(var X#6)] T#20[(letrec {E#2} in T#5[S#3])])];E#9} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);X#8=A#18[(app A#19[(\ X#7.S#10)] T#20[(letrec {E#2} in T#5[S#3])])];E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#9
       ;EE#19[X#18,A#11[(var X#6)]]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;X#8= A#20[(app A#21[(var X#18)] T#22[(letrec {E#2} in T#5[S#3])])]
       ;E#9
       ;EE#19[X#18,A#11[(\ X#7.S#10)]]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#4,A#11}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#10);X#8=A#20[(app A#21[(var X#18)] T#22)];E#9;EE#19[X#18,A#11[(var X#6)]]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {[.1]=A#20[(app A#21[(var X#18)] T#22[(letrec {E#2} in T#5[S#3])])];EE#19[X#18,[.2]]},
           X#15         |->  X#8,
           E#16         |->  {X#6=(\ X#7.S#10);E#9;EE#19[X#18,A#11[(var X#6)]]},
           T#14         |->  A#20[(app A#21[(var X#18)] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {E#2} in T#5[S#3])])];E#9;EE#19[X#18,A#11[(var X#6)]]} in A#12[(var X#8)])
    -ucp1->                       (letrec {X#6=(\ X#7.S#10);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#9;EE#19[X#18,A#11[(var X#6)]]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {E#2} in T#5[S#3])])];E#9;EE#19[X#18,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);X#8=A#20[(app A#21[(var X#18)] T#22[(letrec {E#2} in T#5[S#3])])];E#9;EE#19[X#18,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#20[X#8,(var X#18)]
       ;EE#21[X#19,A#11[(var X#6)]]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= A#22[(app A#23[(var X#19)] T#24[(letrec {E#2} in T#5[S#3])])]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#20[X#8,(var X#18)]
       ;EE#21[X#19,A#11[(\ X#7.S#10)]]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#4,A#11}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24)];X#6=(\ X#7.S#10);E#9;EE#20[X#8,(var X#18)];EE#21[X#19,A#11[(var X#6)]]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {E#2} in T#5[S#3])])];EE#20[[.1],(var X#18)];EE#21[X#19,[.2]]},
           X#15         |->  X#18,
           E#16         |->  {X#6=(\ X#7.S#10);E#9;EE#20[X#8,(var X#18)];EE#21[X#19,A#11[(var X#6)]]},
           T#14         |->  A#22[(app A#23[(var X#19)] T#24)],
           A#17         |->  A#22[(app A#23 T#24[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#10);E#9;EE#20[X#8,(var X#18)];EE#21[X#19,A#11[(var X#6)]]} in A#12[(var X#8)])
    -ucp1->                       (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];X#6=(\ X#7.S#10);E#9;EE#20[X#8,(var X#18)];EE#21[X#19,A#11[(var X#6)]]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#10);E#9;EE#20[X#8,(var X#18)];EE#21[X#19,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#18=A#22[(app A#23[(var X#19)] T#24[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#10);E#9;EE#20[X#8,(var X#18)];EE#21[X#19,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[A#22[(app A#23[(var X#6)] T#24[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= A#20[A#22[(app A#23[(\ X#7.S#10)] T#24[(letrec {E#2} in T#5[S#3])])]]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#21,A#17,T#14,T#4,A#11,A#20}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#22[(app A#23[[.]] T#24[(letrec {E#2} in T#5[S#3])])]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#18=A#20[A#22[(app A#23[(var X#6)] T#24)]];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {X#18=A#20[[.2]];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]},
           A#17         |->  A#20,
           T#14         |->  A#20[A#22[(app A#23[(var X#6)] T#24)]],
           T#21         |->  A#22[(app A#23[(var X#6)] T#24)],
           A#11         |->  A#22[(app A#23 T#24[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#18=A#20[A#22[(app A#23[(var X#6)] T#24[(letrec {E#2} in T#5[S#3])])]];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -ucp1->                       (letrec {X#18=A#20[A#22[(app A#23[(var X#6)] T#24[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#18=A#20[A#22[(app A#23[(var X#6)] T#24[(letrec {E#2} in T#5[S#3])])]];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#18=A#20[A#22[(app A#23[(\ X#7.S#10)] T#24[(letrec {E#2} in T#5[S#3])])]];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[A#11[(var X#6)]] T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[A#11[(\ X#7.S#10)]] T#22[(letrec {E#2} in T#5[S#3])])]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {A#17,T#14,T#4,A#11}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#18=A#20[(app A#21[A#11[(var X#6)]] T#22)];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {X#18=A#20[(app A#21[[.2]] T#22[(letrec {E#2} in T#5[S#3])])];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]},
           T#14         |->  A#20[(app A#21[A#11[(var X#6)]] T#22)],
           A#17         |->  A#20[(app A#21 T#22[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[A#11[(var X#6)]] T#22[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -ucp1->                       (letrec {X#18=A#20[(app A#21[A#11[(var X#6)]] T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[A#11[(var X#6)]] T#22[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#18=A#20[(app A#21[A#11[(\ X#7.S#10)]] T#22[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#18= A#20[(app A#21[(var X#6)] T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#18= A#20[(app A#21[(\ X#7.S#10)] T#22[(letrec {E#2} in T#5[S#3])])]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#19[X#8,(var X#18)]
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#14,T#4,A#11}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#20[(app A#21[[.]] T#22[(letrec {E#2} in T#5[S#3])])]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#18=A#20[(app A#21[(var X#6)] T#22)];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)]),
           EE#13[.1,.2] |-> {X#18=[.2];EE#19[[.1],(var X#18)]},
           X#15         |->  X#18,
           E#16         |->  {X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]},
           A#17         |->  [.],
           T#14         |->  A#20[(app A#21[(var X#6)] T#22)],
           A#11         |->  A#20[(app A#21 T#22[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#18=A#20[(app A#21[(var X#6)] T#22[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -ucp1->                       (letrec {X#18=A#20[(app A#21[(var X#6)] T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#18=A#20[(app A#21[(var X#6)] T#22[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#18=A#20[(app A#21[(\ X#7.S#10)] T#22[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#10);E#9;EE#19[X#8,(var X#18)]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#8)
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#13[X#8,A#11[(var X#6)]]
     in
        A#14[(var X#1)]
     )
    ,
     (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#14[(var X#8)])
  )

where

   Delta1 = {A#12,T#5,A#11,A#14}
   Delta2 = {E#2}
   Delta3 = {((var X#1),A#14[[.]]),
             ((var X#8),A#14[[.]]),
             ((letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#14[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#14[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#14[[.]]),
             ((var X#8),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]},
           A#12  |->  A#14,
           T#5   |->  A#14[[.]],
           T#15  |->  [.],
           S#3   |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#14[(var X#8)])
    -ucp1->                       (letrec {X#1=(var X#8);X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#14[(var X#1)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#14[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#14[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#15[(var X#8)]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#13[X#8,A#11[(var X#6)]]
     in
        A#14[(var X#1)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;E#9
       ;EE#13[X#8,A#11[(\ X#7.S#10)]]
     in
        A#14[A#15[(var X#8)]]
     )
  )

where

   Delta1 = {A#12,T#5,A#11,A#14}
   Delta2 = {E#2}
   Delta3 = {((var X#1),A#14),
             (A#15[(var X#8)],A#14),
             ((letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#14[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#14[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#14[A#15[[.]]]),
             ((var X#8),A#14[A#15[[.]]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]},
           A#12  |->  A#14[A#15],
           T#5   |->  A#14,
           S#3   |->  A#15[(var X#8)]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#14[A#15[(var X#8)]])
    -ucp1->                       (letrec {X#1=A#15[(var X#8)];X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#14[(var X#1)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#14[A#15[(var X#8)]])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#14[A#15[(var X#8)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#3
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#13[X#8,A#11[(var X#6)]]
     in
        A#14[(app A#15[(var X#8)] T#16[(var X#1)])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#10)
       ;E#9
       ;EE#13[X#8,A#11[(\ X#7.S#10)]]
     in
        A#14[(app A#15[(var X#8)] T#16[S#3])]
     )
  )

where

   Delta1 = {A#12,T#5,A#11}
   Delta2 = {E#2}
   Delta3 = {((var X#1),A#14[(app A#15[(var X#8)] T#16)]),
             (S#3,A#14[(app A#15[(var X#8)] T#16)]),
             ((letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#14[(app A#15[(var X#8)] T#16[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#14[(app A#15[(var X#8)] T#16[[.]])]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#14[(app A#15[[.]] T#16[S#3])]),
             ((var X#8),A#14[(app A#15[[.]] T#16[S#3])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]},
           T#5   |->  A#14[(app A#15[(var X#8)] T#16)],
           A#12  |->  A#14[(app A#15 T#16[S#3])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#14[(app A#15[(var X#8)] T#16[S#3])])
    -ucp1->                       (letrec {X#1=S#3;X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#14[(app A#15[(var X#8)] T#16[(var X#1)])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#14[(app A#15[(var X#8)] T#16[S#3])])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#14[(app A#15[(var X#8)] T#16[S#3])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#12[(var X#8)]
       ;X#6= (\ X#7.S#10)
       ;E#9
       ;EE#13[X#8,A#11[(var X#6)]]
     in
        (var X#1)
     )
    ,
     (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
  )

where

   Delta1 = {A#11}
   Delta2 = {E#2}
   Delta3 = {((var X#1),[.]),
             (A#12[(var X#8)],[.]),
             ((letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in (dummy3 )),(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])}
      Delta1=  {A#11}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           E#2  |->  {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]},
           T#5  |->  [.],
           S#3  |->  A#12[(var X#8)]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -ucp1->                       (letrec {X#1=A#12[(var X#8)];X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in (var X#1))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(var X#6)]]} in A#12[(var X#8)])
    -SR,cp-e1->                   (letrec {X#6=(\ X#7.S#10);E#9;EE#13[X#8,A#11[(\ X#7.S#10)]]} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#17[(app A#18[(var X#8)] T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#17[(app A#18[(var X#8)] T#19[(letrec {E#2} in T#5[S#3])])]
     )
  )

where

   Delta1 = {A#13,T#16,T#4,A#12}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#17[(app A#18[[.]] T#19[(letrec {E#2} in T#5[S#3])])]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#17[(app A#18[[.]] T#19[(letrec {E#2} in T#5[S#3])])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(app A#18[(var X#8)] T#19)]),
           T#16  |->  A#17[(app A#18[(var X#8)] T#19)],
           A#13  |->  A#17[(app A#18 T#19[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(app A#18[(var X#8)] T#19[(letrec {E#2} in T#5[S#3])])])
    -ucp1->                       (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(app A#18[(var X#8)] T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#17[(app A#18[(var X#8)] T#19[(letrec {E#2} in T#5[S#3])])])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#17[(app A#18[(var X#8)] T#19[(letrec {E#2} in T#5[S#3])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= T#16[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
       ;X#6= (\ X#7.S#11)
       ;E#19
       ;EE#14[X#8,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#17= T#16[(letrec {E#2} in T#5[S#3])]
       ;X#6= (\ X#7.S#11)
       ;E#19
       ;EE#14[X#8,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#4,A#12}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#17=T#16;X#6=(\ X#7.S#11);E#19;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           E#10  |->  {X#17=T#16[(letrec {E#2} in T#5[S#3])];E#19},
           E#18  |->  {X#6=(\ X#7.S#11);E#19;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|}}

and instantiated rules:

                                  (letrec {X#17=T#16[(letrec {E#2} in T#5[S#3])];X#6=(\ X#7.S#11);E#19;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -ucp1->                       (letrec {X#17=T#16[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];X#6=(\ X#7.S#11);E#19;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#17=T#16[(letrec {E#2} in T#5[S#3])];X#6=(\ X#7.S#11);E#19;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#17=T#16[(letrec {E#2} in T#5[S#3])];X#6=(\ X#7.S#11);E#19;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#20[A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]]
       ;E#10
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#20[A#22[(app A#23[(\ X#7.S#11)] T#24[(letrec {E#2} in T#5[S#3])])]]
       ;E#10
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#21,A#19,T#16,T#4,A#12,A#20}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#22[(app A#23[[.]] T#24[(letrec {E#2} in T#5[S#3])])]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#11);X#8=A#20[A#22[(app A#23[(var X#9)] T#24)]];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#20[[.2]]},
           X#17         |->  X#8,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;VV#15|X#9,(var X#6)|},
           A#19         |->  A#20,
           T#16         |->  A#20[A#22[(app A#23[(var X#9)] T#24)]],
           T#21         |->  A#22[(app A#23[(var X#9)] T#24)],
           A#12         |->  A#22[(app A#23 T#24[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);X#8=A#20[A#22[(app A#23[(var X#9)] T#24[(letrec {E#2} in T#5[S#3])])]];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -ucp1->                       (letrec {X#6=(\ X#7.S#11);X#8=A#20[A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);X#8=A#20[A#22[(app A#23[(var X#9)] T#24[(letrec {E#2} in T#5[S#3])])]];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);X#8=A#20[A#22[(app A#23[(\ X#7.S#11)] T#24[(letrec {E#2} in T#5[S#3])])]];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#20[(app A#21[A#12[(var X#9)]] T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#10
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#20[(app A#21[A#12[(\ X#7.S#11)]] T#22[(letrec {E#2} in T#5[S#3])])]
       ;E#10
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#19,T#16,T#4,A#12}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[A#12[(var X#9)]] T#22)];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#20[(app A#21[[.2]] T#22[(letrec {E#2} in T#5[S#3])])]},
           X#17         |->  X#8,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;VV#15|X#9,(var X#6)|},
           T#16         |->  A#20[(app A#21[A#12[(var X#9)]] T#22)],
           A#19         |->  A#20[(app A#21 T#22[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[A#12[(var X#9)]] T#22[(letrec {E#2} in T#5[S#3])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -ucp1->                       (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[A#12[(var X#9)]] T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[A#12[(var X#9)]] T#22[(letrec {E#2} in T#5[S#3])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[A#12[(\ X#7.S#11)]] T#22[(letrec {E#2} in T#5[S#3])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#20[(app A#21[(var X#9)] T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#10
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#20[(app A#21[(\ X#7.S#11)] T#22[(letrec {E#2} in T#5[S#3])])]
       ;E#10
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#16,T#4,A#12}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#20[(app A#21[[.]] T#22[(letrec {E#2} in T#5[S#3])])]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[(var X#9)] T#22)];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#17         |->  X#8,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;VV#15|X#9,(var X#6)|},
           A#19         |->  [.],
           T#16         |->  A#20[(app A#21[(var X#9)] T#22)],
           A#12         |->  A#20[(app A#21 T#22[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[(var X#9)] T#22[(letrec {E#2} in T#5[S#3])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -ucp1->                       (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[(var X#9)] T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[(var X#9)] T#22[(letrec {E#2} in T#5[S#3])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);X#8=A#20[(app A#21[(\ X#7.S#11)] T#22[(letrec {E#2} in T#5[S#3])])];E#10;VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#10
       ;EE#21[X#20,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;X#8= A#22[(app A#23[(var X#20)] T#24[(letrec {E#2} in T#5[S#3])])]
       ;E#10
       ;EE#21[X#20,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#19,T#16,T#4,A#12}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(\ X#7.S#11);X#8=A#22[(app A#23[(var X#20)] T#24)];E#10;EE#21[X#20,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#22[(app A#23[(var X#20)] T#24[(letrec {E#2} in T#5[S#3])])];EE#21[X#20,[.2]]},
           X#17         |->  X#8,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;EE#21[X#20,A#12[(var X#9)]];VV#15|X#9,(var X#6)|},
           T#16         |->  A#22[(app A#23[(var X#20)] T#24)],
           A#19         |->  A#22[(app A#23 T#24[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);X#8=A#22[(app A#23[(var X#20)] T#24[(letrec {E#2} in T#5[S#3])])];E#10;EE#21[X#20,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -ucp1->                       (letrec {X#6=(\ X#7.S#11);X#8=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#10;EE#21[X#20,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);X#8=A#22[(app A#23[(var X#20)] T#24[(letrec {E#2} in T#5[S#3])])];E#10;EE#21[X#20,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);X#8=A#22[(app A#23[(var X#20)] T#24[(letrec {E#2} in T#5[S#3])])];E#10;EE#21[X#20,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#22[X#8,(var X#20)]
       ;EE#23[X#21,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#20= A#24[(app A#25[(var X#21)] T#26[(letrec {E#2} in T#5[S#3])])]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#22[X#8,(var X#20)]
       ;EE#23[X#21,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#19,T#16,T#4,A#12}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26)];X#6=(\ X#7.S#11);E#10;EE#22[X#8,(var X#20)];EE#23[X#21,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {E#2} in T#5[S#3])])];EE#22[[.1],(var X#20)];EE#23[X#21,[.2]]},
           X#17         |->  X#20,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;EE#22[X#8,(var X#20)];EE#23[X#21,A#12[(var X#9)]];VV#15|X#9,(var X#6)|},
           T#16         |->  A#24[(app A#25[(var X#21)] T#26)],
           A#19         |->  A#24[(app A#25 T#26[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#11);E#10;EE#22[X#8,(var X#20)];EE#23[X#21,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -ucp1->                       (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];X#6=(\ X#7.S#11);E#10;EE#22[X#8,(var X#20)];EE#23[X#21,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#11);E#10;EE#22[X#8,(var X#20)];EE#23[X#21,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#11);E#10;EE#22[X#8,(var X#20)];EE#23[X#21,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[A#24[(app A#25[(var X#9)] T#26[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#21[X#8,(var X#20)]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#20= A#22[A#24[(app A#25[(\ X#7.S#11)] T#26[(letrec {E#2} in T#5[S#3])])]]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#21[X#8,(var X#20)]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#23,A#19,T#16,T#4,A#12,A#22}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#24[(app A#25[[.]] T#26[(letrec {E#2} in T#5[S#3])])]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#20=A#22[A#24[(app A#25[(var X#9)] T#26)]];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#20=A#22[[.2]];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|},
           A#19         |->  A#22,
           T#16         |->  A#22[A#24[(app A#25[(var X#9)] T#26)]],
           T#23         |->  A#24[(app A#25[(var X#9)] T#26)],
           A#12         |->  A#24[(app A#25 T#26[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#20=A#22[A#24[(app A#25[(var X#9)] T#26[(letrec {E#2} in T#5[S#3])])]];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -ucp1->                       (letrec {X#20=A#22[A#24[(app A#25[(var X#9)] T#26[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#20=A#22[A#24[(app A#25[(var X#9)] T#26[(letrec {E#2} in T#5[S#3])])]];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#20=A#22[A#24[(app A#25[(\ X#7.S#11)] T#26[(letrec {E#2} in T#5[S#3])])]];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app A#23[A#12[(var X#9)]] T#24[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#21[X#8,(var X#20)]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#20= A#22[(app A#23[A#12[(\ X#7.S#11)]] T#24[(letrec {E#2} in T#5[S#3])])]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#21[X#8,(var X#20)]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#19,T#16,T#4,A#12}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#20=A#22[(app A#23[A#12[(var X#9)]] T#24)];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#20=A#22[(app A#23[[.2]] T#24[(letrec {E#2} in T#5[S#3])])];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|},
           T#16         |->  A#22[(app A#23[A#12[(var X#9)]] T#24)],
           A#19         |->  A#22[(app A#23 T#24[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app A#23[A#12[(var X#9)]] T#24[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -ucp1->                       (letrec {X#20=A#22[(app A#23[A#12[(var X#9)]] T#24[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#20=A#22[(app A#23[A#12[(var X#9)]] T#24[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#20=A#22[(app A#23[A#12[(\ X#7.S#11)]] T#24[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#21[X#8,(var X#20)]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#20= A#22[(app A#23[(\ X#7.S#11)] T#24[(letrec {E#2} in T#5[S#3])])]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#21[X#8,(var X#20)]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#16,T#4,A#12}
   Delta2 = {E#2}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#22[(app A#23[[.]] T#24[(letrec {E#2} in T#5[S#3])])]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#20=A#22[(app A#23[(var X#9)] T#24)];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|},
           A#19         |->  [.],
           T#16         |->  A#22[(app A#23[(var X#9)] T#24)],
           A#12         |->  A#22[(app A#23 T#24[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app A#23[(var X#9)] T#24[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -ucp1->                       (letrec {X#20=A#22[(app A#23[(var X#9)] T#24[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#20=A#22[(app A#23[(var X#9)] T#24[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#20=A#22[(app A#23[(\ X#7.S#11)] T#24[(letrec {E#2} in T#5[S#3])])];X#6=(\ X#7.S#11);E#10;EE#21[X#8,(var X#20)];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#8)
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#16[(var X#1)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#16[(var X#8)]
     )
  )

where

   Delta1 = {A#13,T#5,A#12,A#16}
   Delta2 = {E#2}
   Delta3 = {((var X#1),A#16[[.]]),
             ((var X#8),A#16[[.]]),
             ((letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#16[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#16[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#16[[.]]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#16[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|},
           A#13  |->  A#16,
           T#5   |->  A#16[[.]],
           T#17  |->  [.],
           S#3   |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#16[(var X#8)])
    -ucp1->                       (letrec {X#1=(var X#8);X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#16[(var X#1)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#16[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#16[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#17[(var X#8)]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#16[(var X#1)]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#16[A#17[(var X#8)]]
     )
  )

where

   Delta1 = {A#13,T#5,A#12,A#16}
   Delta2 = {E#2}
   Delta3 = {((var X#1),A#16),
             (A#17[(var X#8)],A#16),
             ((letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#16[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (A#17[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#16[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#16[A#17[[.]]]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#16[A#17[[.]]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|},
           A#13  |->  A#16[A#17],
           T#5   |->  A#16,
           S#3   |->  A#17[(var X#8)]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#16[A#17[(var X#8)]])
    -ucp1->                       (letrec {X#1=A#17[(var X#8)];X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#16[(var X#1)])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#16[A#17[(var X#8)]])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#16[A#17[(var X#8)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#3
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#16[(app A#17[(var X#8)] T#18[(var X#1)])]
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#16[(app A#17[(var X#8)] T#18[S#3])]
     )
  )

where

   Delta1 = {A#13,T#5,A#12}
   Delta2 = {E#2}
   Delta3 = {((var X#1),A#16[(app A#17[(var X#8)] T#18)]),
             (S#3,A#16[(app A#17[(var X#8)] T#18)]),
             ((letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#16[(app A#17[(var X#8)] T#18[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#16[(app A#17[(var X#8)] T#18[[.]])]),
             ((var X#6),[.]),
             ((var X#8),A#16[(app A#17[[.]] T#18[S#3])]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#16[(app A#17[[.]] T#18[S#3])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|},
           T#5   |->  A#16[(app A#17[(var X#8)] T#18)],
           A#13  |->  A#16[(app A#17 T#18[S#3])]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#16[(app A#17[(var X#8)] T#18[S#3])])
    -ucp1->                       (letrec {X#1=S#3;X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#16[(app A#17[(var X#8)] T#18[(var X#1)])])
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#16[(app A#17[(var X#8)] T#18[S#3])])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#16[(app A#17[(var X#8)] T#18[S#3])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#13[(var X#8)]
       ;X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(var X#9)]]
       ;VV#15|X#9,(var X#6)|
     in
        (var X#1)
     )
    ,
     (letrec
        X#6= (\ X#7.S#11)
       ;E#10
       ;EE#14[X#8,A#12[(\ X#7.S#11)]]
       ;VV#15|X#9,(var X#6)|
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#12}
   Delta2 = {E#2}
   Delta3 = {((var X#1),[.]),
             (A#13[(var X#8)],[.]),
             ((letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in (dummy3 )),(letrec {X#1=(dummy3 )} in [.])),
             (A#13[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#9),A#12[[.]]),
             ((var X#6),[.]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,cp-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    and constraints: A#12/= [.]

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])}
      Delta1=  {A#12}
      Delta2=  {E#2}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#5[[.]]),((var X#6),[.]),((var X#8),A#13[[.]]),((var X#9),A#12[[.]]),((var X#6),[.]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           E#2  |->  {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|},
           T#5  |->  [.],
           S#3  |->  A#13[(var X#8)]}

and instantiated rules:

                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -ucp1->                       (letrec {X#1=A#13[(var X#8)];X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in (var X#1))
    ................................................................................
                                  (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(var X#9)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    -SR,cp-e2->                   (letrec {X#6=(\ X#7.S#11);E#10;EE#14[X#8,A#12[(\ X#7.S#11)]];VV#15|X#9,(var X#6)|} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        (letrec {E#7} in T#10[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])
     )
    ,
     (letrec {E#6;E#7} in T#10[(letrec {E#2} in T#5[S#3])])
  )

where

   Delta1 = {T#9,T#4}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             [{E#6},(letrec {E#7} in [.])],
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {E#6;E#7} in S#8)
    and constraints: E#6/= {}, E#7/= {}, ({E#6},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= (letrec {E#6} in (letrec {E#7} in S#8))}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),[{E#6},(letrec {E#7} in [.])],((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4  |->  (letrec {E#6} in (letrec {E#7} in T#10)),
           T#9  |->  (letrec {E#7} in T#10),
           S#8  |->  T#10[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {E#6} in (letrec {E#7} in T#10[(letrec {E#2} in T#5[S#3])]))
    -ucp1->                       (letrec {E#6} in (letrec {E#7} in T#10[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]))
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in T#10[(letrec {E#2} in T#5[S#3])]))
    -SR,llet-in1->                (letrec {E#6;E#7} in T#10[(letrec {E#2} in T#5[S#3])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        (letrec {X#11=T#10[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#13} in S#8)
     )
    ,
     (letrec {X#11=T#10[(letrec {E#2} in T#5[S#3])];E#13;E#6} in S#8)
  )

where

   Delta1 = {T#9,T#4}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             [{E#6},(letrec {X#11=T#10[(letrec {E#2} in T#5[S#3])];E#13} in [.])],
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {E#6;E#7} in S#8)
    and constraints: E#6/= {}, E#7/= {}, ({E#6},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= (letrec {E#6} in (letrec {E#7} in S#8))}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),[{E#6},(letrec {E#7} in [.])],((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in (letrec {X#11=T#10;E#13} in S#8)),
           T#9   |->  (letrec {X#11=T#10;E#13} in S#8),
           E#7   |->  {X#11=T#10[(letrec {E#2} in T#5[S#3])];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {E#6} in (letrec {X#11=T#10[(letrec {E#2} in T#5[S#3])];E#13} in S#8))
    -ucp1->                       (letrec {E#6} in (letrec {X#11=T#10[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#13} in S#8))
    ................................................................................
                                  (letrec {E#6} in (letrec {X#11=T#10[(letrec {E#2} in T#5[S#3])];E#13} in S#8))
    -SR,llet-in1->                (letrec {X#11=T#10[(letrec {E#2} in T#5[S#3])];E#13;E#6} in S#8)
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (letrec {X#1=S#3;E#2} in T#5[(var X#1)]))
    ,
     (letrec {E#2;E#6} in T#5[S#3])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             [{E#6},(letrec {E#2} in [.])],
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {E#6;E#7} in S#8)
    and constraints: E#6/= {}, E#7/= {}, ({E#6},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= (letrec {E#6} in (letrec {E#7} in S#8))}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),[{E#6},(letrec {E#7} in [.])],((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4  |->  (letrec {E#6} in [.]),
           T#9  |->  [.],
           S#8  |->  T#5[S#3],
           E#7  |->  {E#2}}

and instantiated rules:

                                  (letrec {E#6} in (letrec {E#2} in T#5[S#3]))
    -ucp1->                       (letrec {E#6} in (letrec {X#1=S#3;E#2} in T#5[(var X#1)]))
    ................................................................................
                                  (letrec {E#6} in (letrec {E#2} in T#5[S#3]))
    -SR,llet-in1->                (letrec {E#2;E#6} in T#5[S#3])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= T#9[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
       ;E#12
     in
        (letrec {E#7} in S#8)
     )
    ,
     (letrec {X#10=T#9[(letrec {E#2} in T#5[S#3])];E#12;E#7} in S#8)
  )

where

   Delta1 = {T#4}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             [{X#10=T#9[(letrec {E#2} in T#5[S#3])];E#12},(letrec {E#7} in [.])],
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {E#6;E#7} in S#8)
    and constraints: E#6/= {}, E#7/= {}, ({E#6},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= (letrec {E#6} in (letrec {E#7} in S#8))}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),[{E#6},(letrec {E#7} in [.])],((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#10=T#9;E#12} in (letrec {E#7} in S#8)),
           E#6   |->  {X#10=T#9[(letrec {E#2} in T#5[S#3])];E#12},
           E#11  |->  {E#12}}

and instantiated rules:

                                  (letrec {X#10=T#9[(letrec {E#2} in T#5[S#3])];E#12} in (letrec {E#7} in S#8))
    -ucp1->                       (letrec {X#10=T#9[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#12} in (letrec {E#7} in S#8))
    ................................................................................
                                  (letrec {X#10=T#9[(letrec {E#2} in T#5[S#3])];E#12} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {X#10=T#9[(letrec {E#2} in T#5[S#3])];E#12;E#7} in S#8)
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#3;E#6} in (letrec {E#7} in T#9[(var X#1)]))
    ,
     (letrec {E#6;E#7} in T#9[S#3])
  )

where

   Delta1 = {T#5}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),(letrec {E#7} in T#9)),
             (S#3,(letrec {E#7} in T#9)),
             ((letrec {E#6} in (letrec {E#7} in T#9[(dummy3 )])),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             [{E#6},(letrec {E#7} in [.])],
             ((var X#1),(letrec {E#7} in T#9[[.]]))}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {E#6;E#7} in S#8)
    and constraints: E#6/= {}, E#7/= {}, ({E#6},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= (letrec {E#6} in (letrec {E#7} in S#8))}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),[{E#6},(letrec {E#7} in [.])],((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           E#2  |->  {E#6},
           T#5  |->  (letrec {E#7} in T#9),
           S#8  |->  T#9[S#3]}

and instantiated rules:

                                  (letrec {E#6} in (letrec {E#7} in T#9[S#3]))
    -ucp1->                       (letrec {X#1=S#3;E#6} in (letrec {E#7} in T#9[(var X#1)]))
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in T#9[S#3]))
    -SR,llet-in1->                (letrec {E#6;E#7} in T#9[S#3])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#3;E#6} in (letrec {X#10=T#9[(var X#1)];E#12} in S#8))
    ,
     (letrec {X#10=T#9[S#3];E#12;E#6} in S#8)
  )

where

   Delta1 = {T#5}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),(letrec {X#10=T#9;E#12} in S#8)),
             (S#3,(letrec {X#10=T#9;E#12} in S#8)),
             ((letrec {E#6} in (letrec {X#10=T#9[(dummy3 )];E#12} in S#8)),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             [{E#6},(letrec {X#10=T#9[S#3];E#12} in [.])],
             ((var X#1),(letrec {X#10=T#9[[.]];E#12} in S#8))}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {E#6;E#7} in S#8)
    and constraints: E#6/= {}, E#7/= {}, ({E#6},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= (letrec {E#6} in (letrec {E#7} in S#8))}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),[{E#6},(letrec {E#7} in [.])],((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#6},
           T#5   |->  (letrec {X#10=T#9;E#12} in S#8),
           E#7   |->  {X#10=T#9[S#3];E#12},
           E#11  |->  {E#12}}

and instantiated rules:

                                  (letrec {E#6} in (letrec {X#10=T#9[S#3];E#12} in S#8))
    -ucp1->                       (letrec {X#1=S#3;E#6} in (letrec {X#10=T#9[(var X#1)];E#12} in S#8))
    ................................................................................
                                  (letrec {E#6} in (letrec {X#10=T#9[S#3];E#12} in S#8))
    -SR,llet-in1->                (letrec {X#10=T#9[S#3];E#12;E#6} in S#8)
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {E#7} in S#8);E#6} in (var X#1))
    ,
     (letrec {E#6;E#7} in S#8)
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#7} in S#8),[.]),
             ((letrec {E#6} in (dummy3 )),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#8),(letrec {X#1=(dummy3 )} in [.])),
             [{E#6},(letrec {E#7} in [.])],
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-in1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {E#6;E#7} in S#8)
    and constraints: E#6/= {}, E#7/= {}, ({E#6},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= (letrec {E#6} in (letrec {E#7} in S#8))}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),[{E#6},(letrec {E#7} in [.])],((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           E#2  |->  {E#6},
           T#5  |->  [.],
           S#3  |->  (letrec {E#7} in S#8)}

and instantiated rules:

                                  (letrec {E#6} in (letrec {E#7} in S#8))
    -ucp1->                       (letrec {X#1=(letrec {E#7} in S#8);E#6} in (var X#1))
    ................................................................................
                                  (letrec {E#6} in (letrec {E#7} in S#8))
    -SR,llet-in1->                (letrec {E#6;E#7} in S#8)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {E#7} in S#9)
       ;E#8
     in
        A#12[(app A#13[(var X#6)] T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
     )
    ,
     (letrec
        X#6= S#9
       ;E#7
       ;E#8
     in
        A#12[(app A#13[(var X#6)] T#14[(letrec {E#2} in T#5[S#3])])]
     )
  )

where

   Delta1 = {A#10,T#11,T#4}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(app A#13[(var X#6)] T#14[(letrec {E#2} in T#5[S#3])])],(letrec {E#7} in [.])),
             [{E#8},(letrec {E#7} in [.])],
             ((var X#1),T#5[[.]]),
             ((var X#6),A#12[(app A#13[[.]] T#14[(letrec {E#2} in T#5[S#3])])]),
             ((var X#6),A#12[(app A#13[[.]] T#14[(letrec {E#2} in T#5[S#3])])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),T#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#12[(app A#13[(var X#6)] T#14)]),
           T#11  |->  A#12[(app A#13[(var X#6)] T#14)],
           A#10  |->  A#12[(app A#13 T#14[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#12[(app A#13[(var X#6)] T#14[(letrec {E#2} in T#5[S#3])])])
    -ucp1->                       (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#12[(app A#13[(var X#6)] T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])])
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#12[(app A#13[(var X#6)] T#14[(letrec {E#2} in T#5[S#3])])])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#12[(app A#13[(var X#6)] T#14[(letrec {E#2} in T#5[S#3])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {E#7} in T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#6=T#14[(letrec {E#2} in T#5[S#3])];E#7;E#8} in A#10[(var X#6)])
  )

where

   Delta1 = {T#11,T#4}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8},(letrec {E#7} in [.])],
             ((var X#1),T#5[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),T#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(letrec {E#7} in T#14);E#8} in A#10[(var X#6)]),
           X#12  |->  X#6,
           E#13  |->  {E#8},
           T#11  |->  (letrec {E#7} in T#14),
           S#9   |->  T#14[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#7} in T#14[(letrec {E#2} in T#5[S#3])]);E#8} in A#10[(var X#6)])
    -ucp1->                       (letrec {X#6=(letrec {E#7} in T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]);E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in T#14[(letrec {E#2} in T#5[S#3])]);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=T#14[(letrec {E#2} in T#5[S#3])];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {X#15=T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#17} in S#9)
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#15= T#14[(letrec {E#2} in T#5[S#3])]
       ;X#6= S#9
       ;E#17
       ;E#8
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#11,T#4}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#6)],(letrec {X#15=T#14[(letrec {E#2} in T#5[S#3])];E#17} in [.])),
             [{E#8},(letrec {X#15=T#14[(letrec {E#2} in T#5[S#3])];E#17} in [.])],
             ((var X#1),T#5[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),T#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(letrec {X#15=T#14;E#17} in S#9);E#8} in A#10[(var X#6)]),
           X#12  |->  X#6,
           E#13  |->  {E#8},
           T#11  |->  (letrec {X#15=T#14;E#17} in S#9),
           E#7   |->  {X#15=T#14[(letrec {E#2} in T#5[S#3])];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {X#6=(letrec {X#15=T#14[(letrec {E#2} in T#5[S#3])];E#17} in S#9);E#8} in A#10[(var X#6)])
    -ucp1->                       (letrec {X#6=(letrec {X#15=T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#17} in S#9);E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(letrec {X#15=T#14[(letrec {E#2} in T#5[S#3])];E#17} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#15=T#14[(letrec {E#2} in T#5[S#3])];X#6=S#9;E#17;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#6=(letrec {X#1=S#3;E#2} in T#5[(var X#1)]);E#8} in A#10[(var X#6)])
    ,
     (letrec {X#6=T#5[S#3];E#2;E#8} in A#10[(var X#6)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#6)],(letrec {E#2} in [.])),
             [{E#8},(letrec {E#2} in [.])],
             ((var X#1),T#5[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),T#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=[.];E#8} in A#10[(var X#6)]),
           X#12  |->  X#6,
           E#13  |->  {E#8},
           T#11  |->  [.],
           S#9   |->  T#5[S#3],
           E#7   |->  {E#2}}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#2} in T#5[S#3]);E#8} in A#10[(var X#6)])
    -ucp1->                       (letrec {X#6=(letrec {X#1=S#3;E#2} in T#5[(var X#1)]);E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(letrec {E#2} in T#5[S#3]);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=T#5[S#3];E#2;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#12= T#11[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
       ;X#6= (letrec {E#7} in S#9)
       ;E#14
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#12= T#11[(letrec {E#2} in T#5[S#3])]
       ;X#6= S#9
       ;E#14
       ;E#7
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14},(letrec {E#7} in [.])],
             ((var X#1),T#5[[.]]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),T#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#12=T#11;X#6=(letrec {E#7} in S#9);E#14} in A#10[(var X#6)]),
           E#8   |->  {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14},
           E#13  |->  {X#6=(letrec {E#7} in S#9);E#14}}

and instantiated rules:

                                  (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];X#6=(letrec {E#7} in S#9);E#14} in A#10[(var X#6)])
    -ucp1->                       (letrec {X#12=T#11[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];X#6=(letrec {E#7} in S#9);E#14} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];X#6=(letrec {E#7} in S#9);E#14} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];X#6=S#9;E#14;E#7} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(var X#6);X#6=(letrec {E#7} in S#9);E#8} in A#11[(var X#1)])
    ,
     (letrec {X#6=S#9;E#7;E#8} in A#11[(var X#6)])
  )

where

   Delta1 = {A#10,T#5,A#11}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),A#11[[.]]),
             ((var X#6),A#11[[.]]),
             ((letrec {X#6=(letrec {E#7} in S#9);E#8} in A#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(var X#6)],(letrec {E#7} in [.])),
             [{E#8},(letrec {E#7} in [.])],
             ((var X#1),A#11[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),T#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(letrec {E#7} in S#9);E#8},
           A#10  |->  A#11,
           T#5   |->  A#11[[.]],
           T#12  |->  [.],
           S#3   |->  (var X#6)}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#1=(var X#6);X#6=(letrec {E#7} in S#9);E#8} in A#11[(var X#1)])
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#11[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=A#12[(var X#6)];X#6=(letrec {E#7} in S#9);E#8} in A#11[(var X#1)])
    ,
     (letrec {X#6=S#9;E#7;E#8} in A#11[A#12[(var X#6)]])
  )

where

   Delta1 = {A#10,T#5,A#11}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),A#11),
             (A#12[(var X#6)],A#11),
             ((letrec {X#6=(letrec {E#7} in S#9);E#8} in A#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(var X#6)],(letrec {X#1=(dummy3 )} in [.])),
             (A#11[A#12[(var X#6)]],(letrec {E#7} in [.])),
             [{E#8},(letrec {E#7} in [.])],
             ((var X#1),A#11[[.]]),
             ((var X#6),A#11[A#12[[.]]]),
             ((var X#6),A#11[A#12[[.]]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),T#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(letrec {E#7} in S#9);E#8},
           A#10  |->  A#11[A#12],
           T#5   |->  A#11,
           S#3   |->  A#12[(var X#6)]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#11[A#12[(var X#6)]])
    -ucp1->                       (letrec {X#1=A#12[(var X#6)];X#6=(letrec {E#7} in S#9);E#8} in A#11[(var X#1)])
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#11[A#12[(var X#6)]])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#11[A#12[(var X#6)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#3
       ;X#6= (letrec {E#7} in S#9)
       ;E#8
     in
        A#11[(app A#12[(var X#6)] T#13[(var X#1)])]
     )
    ,
     (letrec {X#6=S#9;E#7;E#8} in A#11[(app A#12[(var X#6)] T#13[S#3])])
  )

where

   Delta1 = {A#10,T#5}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),A#11[(app A#12[(var X#6)] T#13)]),
             (S#3,A#11[(app A#12[(var X#6)] T#13)]),
             ((letrec {X#6=(letrec {E#7} in S#9);E#8} in A#11[(app A#12[(var X#6)] T#13[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(app A#12[(var X#6)] T#13[S#3])],(letrec {E#7} in [.])),
             [{E#8},(letrec {E#7} in [.])],
             ((var X#1),A#11[(app A#12[(var X#6)] T#13[[.]])]),
             ((var X#6),A#11[(app A#12[[.]] T#13[S#3])]),
             ((var X#6),A#11[(app A#12[[.]] T#13[S#3])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),T#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(letrec {E#7} in S#9);E#8},
           T#5   |->  A#11[(app A#12[(var X#6)] T#13)],
           A#10  |->  A#11[(app A#12 T#13[S#3])]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#11[(app A#12[(var X#6)] T#13[S#3])])
    -ucp1->                       (letrec {X#1=S#3;X#6=(letrec {E#7} in S#9);E#8} in A#11[(app A#12[(var X#6)] T#13[(var X#1)])])
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#11[(app A#12[(var X#6)] T#13[S#3])])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#11[(app A#12[(var X#6)] T#13[S#3])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=A#10[(var X#6)];X#6=(letrec {E#7} in S#9);E#8} in (var X#1))
    ,
     (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#7}
   Delta3 = {((var X#1),[.]),
             (A#10[(var X#6)],[.]),
             ((letrec {X#6=(letrec {E#7} in S#9);E#8} in (dummy3 )),(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#6)],(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    and constraints: E#7/= {}, (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8},(letrec {E#7} in [.])],((var X#1),T#5[[.]]),((var X#6),A#10[[.]]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           E#2  |->  {X#6=(letrec {E#7} in S#9);E#8},
           T#5  |->  [.],
           S#3  |->  A#10[(var X#6)]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -ucp1->                       (letrec {X#1=A#10[(var X#6)];X#6=(letrec {E#7} in S#9);E#8} in (var X#1))
    ................................................................................
                                  (letrec {X#6=(letrec {E#7} in S#9);E#8} in A#10[(var X#6)])
    -SR,llet-e1->                 (letrec {X#6=S#9;E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {E#8} in S#10)
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#14[(app A#15[(var X#7)] T#16[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
     )
    ,
     (letrec
        X#6= S#10
       ;E#8
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#14[(app A#15[(var X#7)] T#16[(letrec {E#2} in T#5[S#3])])]
     )
  )

where

   Delta1 = {A#11,T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),
             (A#14[(app A#15[(var X#7)] T#16[(letrec {E#2} in T#5[S#3])])],(letrec {E#8} in [.])),
             [{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#14[(app A#15[[.]] T#16[(letrec {E#2} in T#5[S#3])])]),
             ((var X#6),[.]),
             ((var X#7),A#14[(app A#15[[.]] T#16[(letrec {E#2} in T#5[S#3])])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),T#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#14[(app A#15[(var X#7)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#7)] T#16)],
           A#11  |->  A#14[(app A#15 T#16[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#14[(app A#15[(var X#7)] T#16[(letrec {E#2} in T#5[S#3])])])
    -ucp1->                       (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#14[(app A#15[(var X#7)] T#16[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])])
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#14[(app A#15[(var X#7)] T#16[(letrec {E#2} in T#5[S#3])])])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#14[(app A#15[(var X#7)] T#16[(letrec {E#2} in T#5[S#3])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {E#8} in T#16[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#6= T#16[(letrec {E#2} in T#5[S#3])]
       ;E#8
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),T#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(letrec {E#8} in T#16);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)]),
           X#14  |->  X#6,
           E#15  |->  {E#9;EE#12[X#7,(var X#6)]},
           T#13  |->  (letrec {E#8} in T#16),
           S#10  |->  T#16[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#8} in T#16[(letrec {E#2} in T#5[S#3])]);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -ucp1->                       (letrec {X#6=(letrec {E#8} in T#16[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in T#16[(letrec {E#2} in T#5[S#3])]);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=T#16[(letrec {E#2} in T#5[S#3])];E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {X#17=T#16[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#19} in S#10)
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= T#16[(letrec {E#2} in T#5[S#3])]
       ;X#6= S#10
       ;E#19
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {X#17=T#16[(letrec {E#2} in T#5[S#3])];E#19;E#9;EE#12[X#7,(var X#6)]} in [.])),
             (A#11[(var X#7)],(letrec {X#17=T#16[(letrec {E#2} in T#5[S#3])];E#19} in [.])),
             [{E#9;EE#12[X#7,(var X#6)]},(letrec {X#17=T#16[(letrec {E#2} in T#5[S#3])];E#19} in [.])],
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),T#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=(letrec {X#17=T#16;E#19} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)]),
           X#14  |->  X#6,
           E#15  |->  {E#9;EE#12[X#7,(var X#6)]},
           T#13  |->  (letrec {X#17=T#16;E#19} in S#10),
           E#8   |->  {X#17=T#16[(letrec {E#2} in T#5[S#3])];E#19},
           E#18  |->  {E#19}}

and instantiated rules:

                                  (letrec {X#6=(letrec {X#17=T#16[(letrec {E#2} in T#5[S#3])];E#19} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -ucp1->                       (letrec {X#6=(letrec {X#17=T#16[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#19} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#6=(letrec {X#17=T#16[(letrec {E#2} in T#5[S#3])];E#19} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#17=T#16[(letrec {E#2} in T#5[S#3])];X#6=S#10;E#19;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {X#1=S#3;E#2} in T#5[(var X#1)])
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#6=T#5[S#3];E#2;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {E#2;E#9;EE#12[X#7,(var X#6)]} in [.])),
             (A#11[(var X#7)],(letrec {E#2} in [.])),
             [{E#9;EE#12[X#7,(var X#6)]},(letrec {E#2} in [.])],
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),T#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#6=[.];E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)]),
           X#14  |->  X#6,
           E#15  |->  {E#9;EE#12[X#7,(var X#6)]},
           T#13  |->  [.],
           S#10  |->  T#5[S#3],
           E#8   |->  {E#2}}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#2} in T#5[S#3]);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -ucp1->                       (letrec {X#6=(letrec {X#1=S#3;E#2} in T#5[(var X#1)]);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#6=(letrec {E#2} in T#5[S#3]);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=T#5[S#3];E#2;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
       ;X#6= (letrec {E#8} in S#10)
       ;E#16
       ;EE#12[X#7,(var X#6)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {E#2} in T#5[S#3])]
       ;X#6= S#10
       ;E#16
       ;E#8
       ;EE#12[X#7,(var X#6)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16;E#8;EE#12[X#7,(var X#6)]} in [.])),
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),T#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#14=T#13;X#6=(letrec {E#8} in S#10);E#16;EE#12[X#7,(var X#6)]} in A#11[(var X#7)]),
           E#9   |->  {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16},
           E#15  |->  {X#6=(letrec {E#8} in S#10);E#16;EE#12[X#7,(var X#6)]}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];X#6=(letrec {E#8} in S#10);E#16;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -ucp1->                       (letrec {X#14=T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];X#6=(letrec {E#8} in S#10);E#16;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];X#6=(letrec {E#8} in S#10);E#16;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];X#6=S#10;E#16;E#8;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {E#8} in S#10)
       ;X#7= A#17[(app A#18[(var X#6)] T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#9
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#6= S#10
       ;X#7= A#17[(app A#18[(var X#6)] T#19[(letrec {E#2} in T#5[S#3])])]
       ;E#8
       ;E#9
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {X#7=A#17[(app A#18[(var X#6)] T#19[(letrec {E#2} in T#5[S#3])])];E#8;E#9} in [.])),
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#7=A#17[(app A#18[(var X#6)] T#19[(letrec {E#2} in T#5[S#3])])];E#9},(letrec {E#8} in [.])],
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),T#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(letrec {E#8} in S#10);X#7=A#17[(app A#18[(var X#6)] T#19)];E#9} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] T#19[(letrec {E#2} in T#5[S#3])])]},
           X#14         |->  X#7,
           E#15         |->  {X#6=(letrec {E#8} in S#10);E#9},
           T#13         |->  A#17[(app A#18[(var X#6)] T#19)],
           A#16         |->  A#17[(app A#18 T#19[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#8} in S#10);X#7=A#17[(app A#18[(var X#6)] T#19[(letrec {E#2} in T#5[S#3])])];E#9} in A#11[(var X#7)])
    -ucp1->                       (letrec {X#6=(letrec {E#8} in S#10);X#7=A#17[(app A#18[(var X#6)] T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#9} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);X#7=A#17[(app A#18[(var X#6)] T#19[(letrec {E#2} in T#5[S#3])])];E#9} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;X#7=A#17[(app A#18[(var X#6)] T#19[(letrec {E#2} in T#5[S#3])])];E#8;E#9} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (letrec {E#8} in S#10)
       ;X#7= A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#9
       ;EE#18[X#17,(var X#6)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#6= S#10
       ;X#7= A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])]
       ;E#8
       ;E#9
       ;EE#18[X#17,(var X#6)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])];E#8;E#9;EE#18[X#17,(var X#6)]} in [.])),
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])];E#9;EE#18[X#17,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),T#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(letrec {E#8} in S#10);X#7=A#19[(app A#20[(var X#17)] T#21)];E#9;EE#18[X#17,(var X#6)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#6=(letrec {E#8} in S#10);E#9;EE#18[X#17,(var X#6)]},
           T#13         |->  A#19[(app A#20[(var X#17)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#8} in S#10);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])];E#9;EE#18[X#17,(var X#6)]} in A#11[(var X#7)])
    -ucp1->                       (letrec {X#6=(letrec {E#8} in S#10);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#9;EE#18[X#17,(var X#6)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])];E#9;EE#18[X#17,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])];E#8;E#9;EE#18[X#17,(var X#6)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;X#6= (letrec {E#8} in S#10)
       ;E#9
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,(var X#6)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])]
       ;X#6= S#10
       ;E#8
       ;E#9
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,(var X#6)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])];E#8;E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]} in [.])),
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])];E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),T#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23)];X#6=(letrec {E#8} in S#10);E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#6=(letrec {E#8} in S#10);E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]},
           T#13         |->  A#21[(app A#22[(var X#18)] T#23)],
           A#16         |->  A#21[(app A#22 T#23[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])];X#6=(letrec {E#8} in S#10);E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]} in A#11[(var X#7)])
    -ucp1->                       (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];X#6=(letrec {E#8} in S#10);E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])];X#6=(letrec {E#8} in S#10);E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])];X#6=S#10;E#8;E#9;EE#19[X#7,(var X#17)];EE#20[X#18,(var X#6)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[(var X#6)] T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;X#6= (letrec {E#8} in S#10)
       ;E#9
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(var X#6)] T#21[(letrec {E#2} in T#5[S#3])])]
       ;X#6= S#10
       ;E#8
       ;E#9
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {X#17=A#19[(app A#20[(var X#6)] T#21[(letrec {E#2} in T#5[S#3])])];E#8;E#9;EE#18[X#7,(var X#17)]} in [.])),
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{X#17=A#19[(app A#20[(var X#6)] T#21[(letrec {E#2} in T#5[S#3])])];E#9;EE#18[X#7,(var X#17)]},(letrec {E#8} in [.])],
             ((var X#1),T#5[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),T#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app A#20[(var X#6)] T#21)];X#6=(letrec {E#8} in S#10);E#9;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] T#21[(letrec {E#2} in T#5[S#3])])];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#6=(letrec {E#8} in S#10);E#9;EE#18[X#7,(var X#17)]},
           T#13         |->  A#19[(app A#20[(var X#6)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(var X#6)] T#21[(letrec {E#2} in T#5[S#3])])];X#6=(letrec {E#8} in S#10);E#9;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp1->                       (letrec {X#17=A#19[(app A#20[(var X#6)] T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];X#6=(letrec {E#8} in S#10);E#9;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(var X#6)] T#21[(letrec {E#2} in T#5[S#3])])];X#6=(letrec {E#8} in S#10);E#9;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#17=A#19[(app A#20[(var X#6)] T#21[(letrec {E#2} in T#5[S#3])])];X#6=S#10;E#8;E#9;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#7)
       ;X#6= (letrec {E#8} in S#10)
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#13[(var X#1)]
     )
    ,
     (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#13[(var X#7)])
  )

where

   Delta1 = {A#11,T#5,A#13}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),A#13[[.]]),
             ((var X#7),A#13[[.]]),
             ((letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#13[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#7),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),
             (A#13[(var X#7)],(letrec {E#8} in [.])),
             [{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),A#13[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#13[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),T#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]},
           A#11  |->  A#13,
           T#5   |->  A#13[[.]],
           T#14  |->  [.],
           S#3   |->  (var X#7)}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#13[(var X#7)])
    -ucp1->                       (letrec {X#1=(var X#7);X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#13[(var X#1)])
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#13[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#13[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(var X#7)]
       ;X#6= (letrec {E#8} in S#10)
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#13[(var X#1)]
     )
    ,
     (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#13[A#14[(var X#7)]])
  )

where

   Delta1 = {A#11,T#5,A#13}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),A#13),
             (A#14[(var X#7)],A#13),
             ((letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#13[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(var X#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),
             (A#13[A#14[(var X#7)]],(letrec {E#8} in [.])),
             [{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),A#13[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#13[A#14[[.]]]),
             ((var X#6),[.]),
             ((var X#7),A#13[A#14[[.]]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),T#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]},
           A#11  |->  A#13[A#14],
           T#5   |->  A#13,
           S#3   |->  A#14[(var X#7)]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#13[A#14[(var X#7)]])
    -ucp1->                       (letrec {X#1=A#14[(var X#7)];X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#13[(var X#1)])
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#13[A#14[(var X#7)]])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#13[A#14[(var X#7)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#3
       ;X#6= (letrec {E#8} in S#10)
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#13[(app A#14[(var X#7)] T#15[(var X#1)])]
     )
    ,
     (letrec
        X#6= S#10
       ;E#8
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        A#13[(app A#14[(var X#7)] T#15[S#3])]
     )
  )

where

   Delta1 = {A#11,T#5}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),A#13[(app A#14[(var X#7)] T#15)]),
             (S#3,A#13[(app A#14[(var X#7)] T#15)]),
             ((letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#13[(app A#14[(var X#7)] T#15[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),
             (A#13[(app A#14[(var X#7)] T#15[S#3])],(letrec {E#8} in [.])),
             [{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),A#13[(app A#14[(var X#7)] T#15[[.]])]),
             ((var X#6),[.]),
             ((var X#7),A#13[(app A#14[[.]] T#15[S#3])]),
             ((var X#6),[.]),
             ((var X#7),A#13[(app A#14[[.]] T#15[S#3])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),T#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]},
           T#5   |->  A#13[(app A#14[(var X#7)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[S#3])]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#13[(app A#14[(var X#7)] T#15[S#3])])
    -ucp1->                       (letrec {X#1=S#3;X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#13[(app A#14[(var X#7)] T#15[(var X#1)])])
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#13[(app A#14[(var X#7)] T#15[S#3])])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#13[(app A#14[(var X#7)] T#15[S#3])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#11[(var X#7)]
       ;X#6= (letrec {E#8} in S#10)
       ;E#9
       ;EE#12[X#7,(var X#6)]
     in
        (var X#1)
     )
    ,
     (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),[.]),
             (A#11[(var X#7)],[.]),
             ((letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in (dummy3 )),(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(var X#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),
             (A#11[(var X#7)],(letrec {E#8} in [.])),
             [{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],
             ((var X#1),[.]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]]),
             ((var X#6),[.]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,llet-e2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    and constraints: E#8/= {}, ((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])), (A#11[(var X#7)],(letrec {E#8} in [.])), ({E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),((var X#6),(letrec {E#8;E#9;EE#12[X#7,(var X#6)]} in [.])),(A#11[(var X#7)],(letrec {E#8} in [.])),[{E#9;EE#12[X#7,(var X#6)]},(letrec {E#8} in [.])],((var X#1),T#5[[.]]),((var X#6),[.]),((var X#7),A#11[[.]]),((var X#6),[.]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           E#2  |->  {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]},
           T#5  |->  [.],
           S#3  |->  A#11[(var X#7)]}

and instantiated rules:

                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -ucp1->                       (letrec {X#1=A#11[(var X#7)];X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in (var X#1))
    ................................................................................
                                  (letrec {X#6=(letrec {E#8} in S#10);E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    -SR,llet-e2->                 (letrec {X#6=S#10;E#8;E#9;EE#12[X#7,(var X#6)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     A#10[(app (letrec {E#6} in T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#7)]
    ,
     A#10[(letrec {E#6} in (app T#13[(letrec {E#2} in T#5[S#3])] S#7))]
  )

where

   Delta1 = {T#12,T#11,A#9,T#4,A#10}
   Delta2 = {E#2,E#6}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#2,E#6}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {A#9   |->  A#10,
           T#4   |->  A#10[(app (letrec {E#6} in T#13) S#7)],
           T#11  |->  (app (letrec {E#6} in T#13) S#7),
           T#12  |->  (letrec {E#6} in T#13),
           S#8   |->  T#13[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  A#10[(app (letrec {E#6} in T#13[(letrec {E#2} in T#5[S#3])]) S#7)]
    -ucp1->                       A#10[(app (letrec {E#6} in T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#7)]
    ................................................................................
                                  A#10[(app (letrec {E#6} in T#13[(letrec {E#2} in T#5[S#3])]) S#7)]
    -SR,lapp1->                   A#10[(letrec {E#6} in (app T#13[(letrec {E#2} in T#5[S#3])] S#7))]
    

================================================================================
Critical Pair:

  (
     A#10[(app (letrec {X#14=T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#16} in S#8) S#7)]
    ,
     A#10[(letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16} in (app S#8 S#7))]
  )

where

   Delta1 = {T#12,T#11,A#9,T#4,A#10}
   Delta2 = {E#2,E#6}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#2,E#6}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {A#9   |->  A#10,
           T#4   |->  A#10[(app (letrec {X#14=T#13;E#16} in S#8) S#7)],
           T#11  |->  (app (letrec {X#14=T#13;E#16} in S#8) S#7),
           T#12  |->  (letrec {X#14=T#13;E#16} in S#8),
           E#6   |->  {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  A#10[(app (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16} in S#8) S#7)]
    -ucp1->                       A#10[(app (letrec {X#14=T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#16} in S#8) S#7)]
    ................................................................................
                                  A#10[(app (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16} in S#8) S#7)]
    -SR,lapp1->                   A#10[(letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16} in (app S#8 S#7))]
    

================================================================================
Critical Pair:

  (
     A#10[(app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#7)]
    ,
     A#10[(letrec {E#2} in (app T#5[S#3] S#7))]
  )

where

   Delta1 = {T#11,A#9,T#4,A#10}
   Delta2 = {E#2,E#6}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#2} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#2,E#6}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {A#9   |->  A#10,
           T#4   |->  A#10[(app [.] S#7)],
           T#11  |->  (app [.] S#7),
           T#12  |->  [.],
           S#8   |->  T#5[S#3],
           E#6   |->  {E#2}}

and instantiated rules:

                                  A#10[(app (letrec {E#2} in T#5[S#3]) S#7)]
    -ucp1->                       A#10[(app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#7)]
    ................................................................................
                                  A#10[(app (letrec {E#2} in T#5[S#3]) S#7)]
    -SR,lapp1->                   A#10[(letrec {E#2} in (app T#5[S#3] S#7))]
    

================================================================================
Critical Pair:

  (
     A#10[(app (letrec {E#6} in S#8) T#12[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
    ,
     A#10[(letrec {E#6} in (app S#8 T#12[(letrec {E#2} in T#5[S#3])]))]
  )

where

   Delta1 = {T#11,A#9,T#4,A#10}
   Delta2 = {E#2,E#6}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#12[(letrec {E#2} in T#5[S#3])],(letrec {E#6} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#2,E#6}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {A#9   |->  A#10,
           T#4   |->  A#10[(app (letrec {E#6} in S#8) T#12)],
           T#11  |->  (app (letrec {E#6} in S#8) T#12),
           S#7   |->  T#12[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  A#10[(app (letrec {E#6} in S#8) T#12[(letrec {E#2} in T#5[S#3])])]
    -ucp1->                       A#10[(app (letrec {E#6} in S#8) T#12[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
    ................................................................................
                                  A#10[(app (letrec {E#6} in S#8) T#12[(letrec {E#2} in T#5[S#3])])]
    -SR,lapp1->                   A#10[(letrec {E#6} in (app S#8 T#12[(letrec {E#2} in T#5[S#3])]))]
    

================================================================================
Critical Pair:

  (
     A#10[(app A#11[(app (letrec {E#6} in S#8) S#7)] T#12[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
    ,
     A#10[(app A#11[(letrec {E#6} in (app S#8 S#7))] T#12[(letrec {E#2} in T#5[S#3])])]
  )

where

   Delta1 = {A#9,T#4}
   Delta2 = {E#2,E#6}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#2,E#6}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4  |->  A#10[(app A#11[(app (letrec {E#6} in S#8) S#7)] T#12)],
           A#9  |->  A#10[(app A#11 T#12[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  A#10[(app A#11[(app (letrec {E#6} in S#8) S#7)] T#12[(letrec {E#2} in T#5[S#3])])]
    -ucp1->                       A#10[(app A#11[(app (letrec {E#6} in S#8) S#7)] T#12[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
    ................................................................................
                                  A#10[(app A#11[(app (letrec {E#6} in S#8) S#7)] T#12[(letrec {E#2} in T#5[S#3])])]
    -SR,lapp1->                   A#10[(app A#11[(letrec {E#6} in (app S#8 S#7))] T#12[(letrec {E#2} in T#5[S#3])])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#6} in T#11[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#7)
    ,
     (letrec {E#6} in (app T#11[(letrec {E#2} in T#5[S#3])] S#7))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#2,E#6}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#2,E#6}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {A#9   |->  [.],
           T#4   |->  (app (letrec {E#6} in T#11) S#7),
           T#10  |->  (letrec {E#6} in T#11),
           S#8   |->  T#11[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (app (letrec {E#6} in T#11[(letrec {E#2} in T#5[S#3])]) S#7)
    -ucp1->                       (app (letrec {E#6} in T#11[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#7)
    ................................................................................
                                  (app (letrec {E#6} in T#11[(letrec {E#2} in T#5[S#3])]) S#7)
    -SR,lapp1->                   (letrec {E#6} in (app T#11[(letrec {E#2} in T#5[S#3])] S#7))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#12=T#11[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#14} in S#8) S#7)
    ,
     (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14} in (app S#8 S#7))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#2,E#6}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#2,E#6}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {A#9   |->  [.],
           T#4   |->  (app (letrec {X#12=T#11;E#14} in S#8) S#7),
           T#10  |->  (letrec {X#12=T#11;E#14} in S#8),
           E#6   |->  {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14},
           E#13  |->  {E#14}}

and instantiated rules:

                                  (app (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14} in S#8) S#7)
    -ucp1->                       (app (letrec {X#12=T#11[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#14} in S#8) S#7)
    ................................................................................
                                  (app (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14} in S#8) S#7)
    -SR,lapp1->                   (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14} in (app S#8 S#7))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#7)
    ,
     (letrec {E#2} in (app T#5[S#3] S#7))
  )

where

   Delta1 = {T#4}
   Delta2 = {E#2,E#6}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#2} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#2,E#6}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {A#9   |->  [.],
           T#4   |->  (app [.] S#7),
           T#10  |->  [.],
           S#8   |->  T#5[S#3],
           E#6   |->  {E#2}}

and instantiated rules:

                                  (app (letrec {E#2} in T#5[S#3]) S#7)
    -ucp1->                       (app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#7)
    ................................................................................
                                  (app (letrec {E#2} in T#5[S#3]) S#7)
    -SR,lapp1->                   (letrec {E#2} in (app T#5[S#3] S#7))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#6} in S#8) T#10[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])
    ,
     (letrec {E#6} in (app S#8 T#10[(letrec {E#2} in T#5[S#3])]))
  )

where

   Delta1 = {T#4}
   Delta2 = {E#2,E#6}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#10[(letrec {E#2} in T#5[S#3])],(letrec {E#6} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp1-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#9[(app (letrec {E#6} in S#8) S#7)]
    -SR,lapp1->                   A#9[(letrec {E#6} in (app S#8 S#7))]
    and constraints: E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])] =?= A#9[(app (letrec {E#6} in S#8) S#7)]}
      Delta1=  {}
      Delta2=  {E#2,E#6}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {A#9  |->  [.],
           T#4  |->  (app (letrec {E#6} in S#8) T#10),
           S#7  |->  T#10[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (app (letrec {E#6} in S#8) T#10[(letrec {E#2} in T#5[S#3])])
    -ucp1->                       (app (letrec {E#6} in S#8) T#10[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])
    ................................................................................
                                  (app (letrec {E#6} in S#8) T#10[(letrec {E#2} in T#5[S#3])])
    -SR,lapp1->                   (letrec {E#6} in (app S#8 T#10[(letrec {E#2} in T#5[S#3])]))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#12[(app (letrec {E#7} in T#15[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#8)]
     )
    ,
     (letrec
        E#6
     in
        A#12[(letrec {E#7} in (app T#15[(letrec {E#2} in T#5[S#3])] S#8))]
     )
  )

where

   Delta1 = {T#14,T#13,A#10,T#11,T#4,A#12}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#12[(app (letrec {E#7} in T#15) S#8)]),
           A#10  |->  A#12,
           T#11  |->  A#12[(app (letrec {E#7} in T#15) S#8)],
           T#13  |->  (app (letrec {E#7} in T#15) S#8),
           T#14  |->  (letrec {E#7} in T#15),
           S#9   |->  T#15[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {E#6} in A#12[(app (letrec {E#7} in T#15[(letrec {E#2} in T#5[S#3])]) S#8)])
    -ucp1->                       (letrec {E#6} in A#12[(app (letrec {E#7} in T#15[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#8)])
    ................................................................................
                                  (letrec {E#6} in A#12[(app (letrec {E#7} in T#15[(letrec {E#2} in T#5[S#3])]) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#12[(letrec {E#7} in (app T#15[(letrec {E#2} in T#5[S#3])] S#8))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#12[(app (letrec {X#16=T#15[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#18} in S#9) S#8)]
     )
    ,
     (letrec
        E#6
     in
        A#12[(letrec {X#16=T#15[(letrec {E#2} in T#5[S#3])];E#18} in (app S#9 S#8))]
     )
  )

where

   Delta1 = {T#14,T#13,A#10,T#11,T#4,A#12}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#16=T#15[(letrec {E#2} in T#5[S#3])];E#18} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#12[(app (letrec {X#16=T#15;E#18} in S#9) S#8)]),
           A#10  |->  A#12,
           T#11  |->  A#12[(app (letrec {X#16=T#15;E#18} in S#9) S#8)],
           T#13  |->  (app (letrec {X#16=T#15;E#18} in S#9) S#8),
           T#14  |->  (letrec {X#16=T#15;E#18} in S#9),
           E#7   |->  {X#16=T#15[(letrec {E#2} in T#5[S#3])];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {E#6} in A#12[(app (letrec {X#16=T#15[(letrec {E#2} in T#5[S#3])];E#18} in S#9) S#8)])
    -ucp1->                       (letrec {E#6} in A#12[(app (letrec {X#16=T#15[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#18} in S#9) S#8)])
    ................................................................................
                                  (letrec {E#6} in A#12[(app (letrec {X#16=T#15[(letrec {E#2} in T#5[S#3])];E#18} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#12[(letrec {X#16=T#15[(letrec {E#2} in T#5[S#3])];E#18} in (app S#9 S#8))])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in A#12[(app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#8)])
    ,
     (letrec {E#6} in A#12[(letrec {E#2} in (app T#5[S#3] S#8))])
  )

where

   Delta1 = {T#13,A#10,T#11,T#4,A#12}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#2} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#12[(app [.] S#8)]),
           A#10  |->  A#12,
           T#11  |->  A#12[(app [.] S#8)],
           T#13  |->  (app [.] S#8),
           T#14  |->  [.],
           S#9   |->  T#5[S#3],
           E#7   |->  {E#2}}

and instantiated rules:

                                  (letrec {E#6} in A#12[(app (letrec {E#2} in T#5[S#3]) S#8)])
    -ucp1->                       (letrec {E#6} in A#12[(app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#8)])
    ................................................................................
                                  (letrec {E#6} in A#12[(app (letrec {E#2} in T#5[S#3]) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#12[(letrec {E#2} in (app T#5[S#3] S#8))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#12[(app (letrec {E#7} in S#9) T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
     )
    ,
     (letrec
        E#6
     in
        A#12[(letrec {E#7} in (app S#9 T#14[(letrec {E#2} in T#5[S#3])]))]
     )
  )

where

   Delta1 = {T#13,A#10,T#11,T#4,A#12}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#14[(letrec {E#2} in T#5[S#3])],(letrec {E#7} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#12[(app (letrec {E#7} in S#9) T#14)]),
           A#10  |->  A#12,
           T#11  |->  A#12[(app (letrec {E#7} in S#9) T#14)],
           T#13  |->  (app (letrec {E#7} in S#9) T#14),
           S#8   |->  T#14[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {E#6} in A#12[(app (letrec {E#7} in S#9) T#14[(letrec {E#2} in T#5[S#3])])])
    -ucp1->                       (letrec {E#6} in A#12[(app (letrec {E#7} in S#9) T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])])
    ................................................................................
                                  (letrec {E#6} in A#12[(app (letrec {E#7} in S#9) T#14[(letrec {E#2} in T#5[S#3])])])
    -SR,lapp2->                   (letrec {E#6} in A#12[(letrec {E#7} in (app S#9 T#14[(letrec {E#2} in T#5[S#3])]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
     )
    ,
     (letrec
        E#6
     in
        A#12[(app A#13[(letrec {E#7} in (app S#9 S#8))] T#14[(letrec {E#2} in T#5[S#3])])]
     )
  )

where

   Delta1 = {A#10,T#11,T#4}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] T#14)]),
           T#11  |->  A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] T#14)],
           A#10  |->  A#12[(app A#13 T#14[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {E#6} in A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] T#14[(letrec {E#2} in T#5[S#3])])])
    -ucp1->                       (letrec {E#6} in A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] T#14[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])])
    ................................................................................
                                  (letrec {E#6} in A#12[(app A#13[(app (letrec {E#7} in S#9) S#8)] T#14[(letrec {E#2} in T#5[S#3])])])
    -SR,lapp2->                   (letrec {E#6} in A#12[(app A#13[(letrec {E#7} in (app S#9 S#8))] T#14[(letrec {E#2} in T#5[S#3])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        (app (letrec {E#7} in T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#8)
     )
    ,
     (letrec {E#6} in (letrec {E#7} in (app T#13[(letrec {E#2} in T#5[S#3])] S#8)))
  )

where

   Delta1 = {T#12,T#11,T#4}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in (app (letrec {E#7} in T#13) S#8)),
           A#10  |->  [.],
           T#11  |->  (app (letrec {E#7} in T#13) S#8),
           T#12  |->  (letrec {E#7} in T#13),
           S#9   |->  T#13[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {E#6} in (app (letrec {E#7} in T#13[(letrec {E#2} in T#5[S#3])]) S#8))
    -ucp1->                       (letrec {E#6} in (app (letrec {E#7} in T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#8))
    ................................................................................
                                  (letrec {E#6} in (app (letrec {E#7} in T#13[(letrec {E#2} in T#5[S#3])]) S#8))
    -SR,lapp2->                   (letrec {E#6} in (letrec {E#7} in (app T#13[(letrec {E#2} in T#5[S#3])] S#8)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        (app (letrec {X#14=T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#16} in S#9) S#8)
     )
    ,
     (letrec
        E#6
     in
        (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16} in (app S#9 S#8))
     )
  )

where

   Delta1 = {T#12,T#11,T#4}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in (app (letrec {X#14=T#13;E#16} in S#9) S#8)),
           A#10  |->  [.],
           T#11  |->  (app (letrec {X#14=T#13;E#16} in S#9) S#8),
           T#12  |->  (letrec {X#14=T#13;E#16} in S#9),
           E#7   |->  {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {E#6} in (app (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16} in S#9) S#8))
    -ucp1->                       (letrec {E#6} in (app (letrec {X#14=T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#16} in S#9) S#8))
    ................................................................................
                                  (letrec {E#6} in (app (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16} in S#9) S#8))
    -SR,lapp2->                   (letrec {E#6} in (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16} in (app S#9 S#8)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#8))
    ,
     (letrec {E#6} in (letrec {E#2} in (app T#5[S#3] S#8)))
  )

where

   Delta1 = {T#11,T#4}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#2} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in (app [.] S#8)),
           A#10  |->  [.],
           T#11  |->  (app [.] S#8),
           T#12  |->  [.],
           S#9   |->  T#5[S#3],
           E#7   |->  {E#2}}

and instantiated rules:

                                  (letrec {E#6} in (app (letrec {E#2} in T#5[S#3]) S#8))
    -ucp1->                       (letrec {E#6} in (app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#8))
    ................................................................................
                                  (letrec {E#6} in (app (letrec {E#2} in T#5[S#3]) S#8))
    -SR,lapp2->                   (letrec {E#6} in (letrec {E#2} in (app T#5[S#3] S#8)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        (app (letrec {E#7} in S#9) T#12[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])
     )
    ,
     (letrec {E#6} in (letrec {E#7} in (app S#9 T#12[(letrec {E#2} in T#5[S#3])])))
  )

where

   Delta1 = {T#11,T#4}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#12[(letrec {E#2} in T#5[S#3])],(letrec {E#7} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#6} in (app (letrec {E#7} in S#9) T#12)),
           A#10  |->  [.],
           T#11  |->  (app (letrec {E#7} in S#9) T#12),
           S#8   |->  T#12[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {E#6} in (app (letrec {E#7} in S#9) T#12[(letrec {E#2} in T#5[S#3])]))
    -ucp1->                       (letrec {E#6} in (app (letrec {E#7} in S#9) T#12[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]))
    ................................................................................
                                  (letrec {E#6} in (app (letrec {E#7} in S#9) T#12[(letrec {E#2} in T#5[S#3])]))
    -SR,lapp2->                   (letrec {E#6} in (letrec {E#7} in (app S#9 T#12[(letrec {E#2} in T#5[S#3])])))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#12= T#11[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
       ;E#14
     in
        A#10[(app (letrec {E#7} in S#9) S#8)]
     )
    ,
     (letrec
        X#12= T#11[(letrec {E#2} in T#5[S#3])]
       ;E#14
     in
        A#10[(letrec {E#7} in (app S#9 S#8))]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),T#5[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#12=T#11;E#14} in A#10[(app (letrec {E#7} in S#9) S#8)]),
           E#6   |->  {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14},
           E#13  |->  {E#14}}

and instantiated rules:

                                  (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -ucp1->                       (letrec {X#12=T#11[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#14} in A#10[(app (letrec {E#7} in S#9) S#8)])
    ................................................................................
                                  (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {X#12=T#11[(letrec {E#2} in T#5[S#3])];E#14} in A#10[(letrec {E#7} in (app S#9 S#8))])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#3;E#6} in A#11[(app (letrec {E#7} in T#14[(var X#1)]) S#8)])
    ,
     (letrec {E#6} in A#11[(letrec {E#7} in (app T#14[S#3] S#8))])
  )

where

   Delta1 = {T#13,T#12,A#10,T#5,A#11}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),A#11[(app (letrec {E#7} in T#14) S#8)]),
             (S#3,A#11[(app (letrec {E#7} in T#14) S#8)]),
             ((letrec {E#6} in A#11[(app (letrec {E#7} in T#14[(dummy3 )]) S#8)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#11[(app (letrec {E#7} in T#14[[.]]) S#8)])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#6},
           A#10  |->  A#11,
           T#5   |->  A#11[(app (letrec {E#7} in T#14) S#8)],
           T#12  |->  (app (letrec {E#7} in T#14) S#8),
           T#13  |->  (letrec {E#7} in T#14),
           S#9   |->  T#14[S#3]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (letrec {E#7} in T#14[S#3]) S#8)])
    -ucp1->                       (letrec {X#1=S#3;E#6} in A#11[(app (letrec {E#7} in T#14[(var X#1)]) S#8)])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (letrec {E#7} in T#14[S#3]) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#11[(letrec {E#7} in (app T#14[S#3] S#8))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#3
       ;E#6
     in
        A#11[(app (letrec {X#15=T#14[(var X#1)];E#17} in S#9) S#8)]
     )
    ,
     (letrec {E#6} in A#11[(letrec {X#15=T#14[S#3];E#17} in (app S#9 S#8))])
  )

where

   Delta1 = {T#13,T#12,A#10,T#5,A#11}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),A#11[(app (letrec {X#15=T#14;E#17} in S#9) S#8)]),
             (S#3,A#11[(app (letrec {X#15=T#14;E#17} in S#9) S#8)]),
             ((letrec {E#6} in A#11[(app (letrec {X#15=T#14[(dummy3 )];E#17} in S#9) S#8)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#15=T#14[S#3];E#17} in [.])),
             ((var X#1),A#11[(app (letrec {X#15=T#14[[.]];E#17} in S#9) S#8)])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#6},
           A#10  |->  A#11,
           T#5   |->  A#11[(app (letrec {X#15=T#14;E#17} in S#9) S#8)],
           T#12  |->  (app (letrec {X#15=T#14;E#17} in S#9) S#8),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#9),
           E#7   |->  {X#15=T#14[S#3];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (letrec {X#15=T#14[S#3];E#17} in S#9) S#8)])
    -ucp1->                       (letrec {X#1=S#3;E#6} in A#11[(app (letrec {X#15=T#14[(var X#1)];E#17} in S#9) S#8)])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (letrec {X#15=T#14[S#3];E#17} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#11[(letrec {X#15=T#14[S#3];E#17} in (app S#9 S#8))])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {E#7} in S#9);E#6} in A#11[(app (var X#1) S#8)])
    ,
     (letrec {E#6} in A#11[(letrec {E#7} in (app S#9 S#8))])
  )

where

   Delta1 = {T#12,A#10,T#5,A#11}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),A#11[(app [.] S#8)]),
             ((letrec {E#7} in S#9),A#11[(app [.] S#8)]),
             ((letrec {E#6} in A#11[(app (dummy3 ) S#8)]),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#11[(app [.] S#8)])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#6},
           A#10  |->  A#11,
           T#5   |->  A#11[(app [.] S#8)],
           T#12  |->  (app [.] S#8),
           T#13  |->  [.],
           S#3   |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (letrec {E#7} in S#9) S#8)])
    -ucp1->                       (letrec {X#1=(letrec {E#7} in S#9);E#6} in A#11[(app (var X#1) S#8)])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#11[(letrec {E#7} in (app S#9 S#8))])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#3;E#6} in A#11[(app (letrec {E#7} in S#9) T#13[(var X#1)])])
    ,
     (letrec {E#6} in A#11[(letrec {E#7} in (app S#9 T#13[S#3]))])
  )

where

   Delta1 = {T#12,A#10,T#5,A#11}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),A#11[(app (letrec {E#7} in S#9) T#13)]),
             (S#3,A#11[(app (letrec {E#7} in S#9) T#13)]),
             ((letrec {E#6} in A#11[(app (letrec {E#7} in S#9) T#13[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#13[S#3],(letrec {E#7} in [.])),
             ((var X#1),A#11[(app (letrec {E#7} in S#9) T#13[[.]])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#6},
           A#10  |->  A#11,
           T#5   |->  A#11[(app (letrec {E#7} in S#9) T#13)],
           T#12  |->  (app (letrec {E#7} in S#9) T#13),
           S#8   |->  T#13[S#3]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (letrec {E#7} in S#9) T#13[S#3])])
    -ucp1->                       (letrec {X#1=S#3;E#6} in A#11[(app (letrec {E#7} in S#9) T#13[(var X#1)])])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (letrec {E#7} in S#9) T#13[S#3])])
    -SR,lapp2->                   (letrec {E#6} in A#11[(letrec {E#7} in (app S#9 T#13[S#3]))])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(app (letrec {E#7} in S#9) S#8);E#6} in A#11[(var X#1)])
    ,
     (letrec {E#6} in A#11[(letrec {E#7} in (app S#9 S#8))])
  )

where

   Delta1 = {A#10,T#5,A#11}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),A#11[[.]]),
             ((app (letrec {E#7} in S#9) S#8),A#11[[.]]),
             ((letrec {E#6} in A#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#7} in S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#6},
           A#10  |->  A#11,
           T#5   |->  A#11[[.]],
           T#12  |->  [.],
           S#3   |->  (app (letrec {E#7} in S#9) S#8)}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (letrec {E#7} in S#9) S#8)])
    -ucp1->                       (letrec {X#1=(app (letrec {E#7} in S#9) S#8);E#6} in A#11[(var X#1)])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#11[(letrec {E#7} in (app S#9 S#8))])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=A#12[(app (letrec {E#7} in S#9) S#8)];E#6} in A#11[(var X#1)])
    ,
     (letrec {E#6} in A#11[A#12[(letrec {E#7} in (app S#9 S#8))]])
  )

where

   Delta1 = {A#10,T#5,A#11}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),A#11),
             (A#12[(app (letrec {E#7} in S#9) S#8)],A#11),
             ((letrec {E#6} in A#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(app (letrec {E#7} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#6},
           A#10  |->  A#11[A#12],
           T#5   |->  A#11,
           S#3   |->  A#12[(app (letrec {E#7} in S#9) S#8)]}

and instantiated rules:

                                  (letrec {E#6} in A#11[A#12[(app (letrec {E#7} in S#9) S#8)]])
    -ucp1->                       (letrec {X#1=A#12[(app (letrec {E#7} in S#9) S#8)];E#6} in A#11[(var X#1)])
    ................................................................................
                                  (letrec {E#6} in A#11[A#12[(app (letrec {E#7} in S#9) S#8)]])
    -SR,lapp2->                   (letrec {E#6} in A#11[A#12[(letrec {E#7} in (app S#9 S#8))]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#3
       ;E#6
     in
        A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[(var X#1)])]
     )
    ,
     (letrec {E#6} in A#11[(app A#12[(letrec {E#7} in (app S#9 S#8))] T#13[S#3])])
  )

where

   Delta1 = {A#10,T#5}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13)]),
             (S#3,A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13)]),
             ((letrec {E#6} in A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[[.]])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#6},
           T#5   |->  A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13)],
           A#10  |->  A#11[(app A#12 T#13[S#3])]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[S#3])])
    -ucp1->                       (letrec {X#1=S#3;E#6} in A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[(var X#1)])])
    ................................................................................
                                  (letrec {E#6} in A#11[(app A#12[(app (letrec {E#7} in S#9) S#8)] T#13[S#3])])
    -SR,lapp2->                   (letrec {E#6} in A#11[(app A#12[(letrec {E#7} in (app S#9 S#8))] T#13[S#3])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#3;E#6} in (app (letrec {E#7} in T#12[(var X#1)]) S#8))
    ,
     (letrec {E#6} in (letrec {E#7} in (app T#12[S#3] S#8)))
  )

where

   Delta1 = {T#11,T#5}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in T#12) S#8)),
             (S#3,(app (letrec {E#7} in T#12) S#8)),
             ((letrec {E#6} in (app (letrec {E#7} in T#12[(dummy3 )]) S#8)),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in T#12[[.]]) S#8))}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#6},
           A#10  |->  [.],
           T#5   |->  (app (letrec {E#7} in T#12) S#8),
           T#11  |->  (letrec {E#7} in T#12),
           S#9   |->  T#12[S#3]}

and instantiated rules:

                                  (letrec {E#6} in (app (letrec {E#7} in T#12[S#3]) S#8))
    -ucp1->                       (letrec {X#1=S#3;E#6} in (app (letrec {E#7} in T#12[(var X#1)]) S#8))
    ................................................................................
                                  (letrec {E#6} in (app (letrec {E#7} in T#12[S#3]) S#8))
    -SR,lapp2->                   (letrec {E#6} in (letrec {E#7} in (app T#12[S#3] S#8)))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#3;E#6} in (app (letrec {X#13=T#12[(var X#1)];E#15} in S#9) S#8))
    ,
     (letrec {E#6} in (letrec {X#13=T#12[S#3];E#15} in (app S#9 S#8)))
  )

where

   Delta1 = {T#11,T#5}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),(app (letrec {X#13=T#12;E#15} in S#9) S#8)),
             (S#3,(app (letrec {X#13=T#12;E#15} in S#9) S#8)),
             ((letrec {E#6} in (app (letrec {X#13=T#12[(dummy3 )];E#15} in S#9) S#8)),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#13=T#12[S#3];E#15} in [.])),
             ((var X#1),(app (letrec {X#13=T#12[[.]];E#15} in S#9) S#8))}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#6},
           A#10  |->  [.],
           T#5   |->  (app (letrec {X#13=T#12;E#15} in S#9) S#8),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#9),
           E#7   |->  {X#13=T#12[S#3];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {E#6} in (app (letrec {X#13=T#12[S#3];E#15} in S#9) S#8))
    -ucp1->                       (letrec {X#1=S#3;E#6} in (app (letrec {X#13=T#12[(var X#1)];E#15} in S#9) S#8))
    ................................................................................
                                  (letrec {E#6} in (app (letrec {X#13=T#12[S#3];E#15} in S#9) S#8))
    -SR,lapp2->                   (letrec {E#6} in (letrec {X#13=T#12[S#3];E#15} in (app S#9 S#8)))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {E#7} in S#9);E#6} in (app (var X#1) S#8))
    ,
     (letrec {E#6} in (letrec {E#7} in (app S#9 S#8)))
  )

where

   Delta1 = {T#5}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),(app [.] S#8)),
             ((letrec {E#7} in S#9),(app [.] S#8)),
             ((letrec {E#6} in (app (dummy3 ) S#8)),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(app [.] S#8))}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#6},
           A#10  |->  [.],
           T#5   |->  (app [.] S#8),
           T#11  |->  [.],
           S#3   |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {E#6} in (app (letrec {E#7} in S#9) S#8))
    -ucp1->                       (letrec {X#1=(letrec {E#7} in S#9);E#6} in (app (var X#1) S#8))
    ................................................................................
                                  (letrec {E#6} in (app (letrec {E#7} in S#9) S#8))
    -SR,lapp2->                   (letrec {E#6} in (letrec {E#7} in (app S#9 S#8)))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#3;E#6} in (app (letrec {E#7} in S#9) T#11[(var X#1)]))
    ,
     (letrec {E#6} in (letrec {E#7} in (app S#9 T#11[S#3])))
  )

where

   Delta1 = {T#5}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in S#9) T#11)),
             (S#3,(app (letrec {E#7} in S#9) T#11)),
             ((letrec {E#6} in (app (letrec {E#7} in S#9) T#11[(dummy3 )])),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[S#3],(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in S#9) T#11[[.]]))}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#6},
           A#10  |->  [.],
           T#5   |->  (app (letrec {E#7} in S#9) T#11),
           S#8   |->  T#11[S#3]}

and instantiated rules:

                                  (letrec {E#6} in (app (letrec {E#7} in S#9) T#11[S#3]))
    -ucp1->                       (letrec {X#1=S#3;E#6} in (app (letrec {E#7} in S#9) T#11[(var X#1)]))
    ................................................................................
                                  (letrec {E#6} in (app (letrec {E#7} in S#9) T#11[S#3]))
    -SR,lapp2->                   (letrec {E#6} in (letrec {E#7} in (app S#9 T#11[S#3])))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=A#10[(app (letrec {E#7} in S#9) S#8)];E#6} in (var X#1))
    ,
     (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#6,E#7}
   Delta3 = {((var X#1),[.]),
             (A#10[(app (letrec {E#7} in S#9) S#8)],[.]),
             ((letrec {E#6} in (dummy3 )),(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(app (letrec {E#7} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp2-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    and constraints: E#6/= {}, E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])}
      Delta1=  {}
      Delta2=  {E#2,E#6,E#7}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#5[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           E#2  |->  {E#6},
           T#5  |->  [.],
           S#3  |->  A#10[(app (letrec {E#7} in S#9) S#8)]}

and instantiated rules:

                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -ucp1->                       (letrec {X#1=A#10[(app (letrec {E#7} in S#9) S#8)];E#6} in (var X#1))
    ................................................................................
                                  (letrec {E#6} in A#10[(app (letrec {E#7} in S#9) S#8)])
    -SR,lapp2->                   (letrec {E#6} in A#10[(letrec {E#7} in (app S#9 S#8))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]
     in
        A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
     )
    ,
     (letrec
        E#7
       ;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]
     in
        A#14[(app A#15[(var X#6)] T#16[(letrec {E#2} in T#5[S#3])])]
     )
  )

where

   Delta1 = {A#11,T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#14[(app A#15[[.]] T#16[(letrec {E#2} in T#5[S#3])])]),
             ((var X#6),A#14[(app A#15[[.]] T#16[(letrec {E#2} in T#5[S#3])])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#6)] T#16)],
           A#11  |->  A#14[(app A#15 T#16[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16[(letrec {E#2} in T#5[S#3])])])
    -ucp1->                       (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])])
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#14[(app A#15[(var X#6)] T#16[(letrec {E#2} in T#5[S#3])])])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#14[(app A#15[(var X#6)] T#16[(letrec {E#2} in T#5[S#3])])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
       ;E#16
       ;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {E#2} in T#5[S#3])]
       ;E#16
       ;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  (letrec {X#14=T#13;E#16;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)]),
           E#7   |->  {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16},
           E#15  |->  {E#16;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#14=T#13[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#16;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#14=T#13[(letrec {E#2} in T#5[S#3])];E#16;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#17[(app (letrec {E#8} in T#20[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#9)]
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#17[(letrec {E#8} in (app T#20[(letrec {E#2} in T#5[S#3])] S#9))]
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#19,T#18,A#16,T#13,T#4,A#17}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#17[(app (letrec {E#8} in T#20) S#9)];E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  A#17,
           T#13         |->  A#17[(app (letrec {E#8} in T#20) S#9)],
           T#18         |->  (app (letrec {E#8} in T#20) S#9),
           T#19         |->  (letrec {E#8} in T#20),
           S#10         |->  T#20[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {X#6=A#17[(app (letrec {E#8} in T#20[(letrec {E#2} in T#5[S#3])]) S#9)];E#7} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#6=A#17[(app (letrec {E#8} in T#20[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#9)];E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#17[(app (letrec {E#8} in T#20[(letrec {E#2} in T#5[S#3])]) S#9)];E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=A#17[(letrec {E#8} in (app T#20[(letrec {E#2} in T#5[S#3])] S#9))];E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#17[(app (letrec {X#21=T#20[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#23} in S#10) S#9)]
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#17[(letrec {X#21=T#20[(letrec {E#2} in T#5[S#3])];E#23} in (app S#10 S#9))]
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#19,T#18,A#16,T#13,T#4,A#17}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {X#21=T#20[(letrec {E#2} in T#5[S#3])];E#23} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#17[(app (letrec {X#21=T#20;E#23} in S#10) S#9)];E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  A#17,
           T#13         |->  A#17[(app (letrec {X#21=T#20;E#23} in S#10) S#9)],
           T#18         |->  (app (letrec {X#21=T#20;E#23} in S#10) S#9),
           T#19         |->  (letrec {X#21=T#20;E#23} in S#10),
           E#8          |->  {X#21=T#20[(letrec {E#2} in T#5[S#3])];E#23},
           E#22         |->  {E#23}}

and instantiated rules:

                                  (letrec {X#6=A#17[(app (letrec {X#21=T#20[(letrec {E#2} in T#5[S#3])];E#23} in S#10) S#9)];E#7} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#6=A#17[(app (letrec {X#21=T#20[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#23} in S#10) S#9)];E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#17[(app (letrec {X#21=T#20[(letrec {E#2} in T#5[S#3])];E#23} in S#10) S#9)];E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=A#17[(letrec {X#21=T#20[(letrec {E#2} in T#5[S#3])];E#23} in (app S#10 S#9))];E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#17[(app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#9)]
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec {X#6=A#17[(letrec {E#2} in (app T#5[S#3] S#9))];E#7} in A#11[(var X#6)])
  )

where

   Delta1 = {T#18,A#16,T#13,T#4,A#17}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#2} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#17[(app [.] S#9)];E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  A#17,
           T#13         |->  A#17[(app [.] S#9)],
           T#18         |->  (app [.] S#9),
           T#19         |->  [.],
           S#10         |->  T#5[S#3],
           E#8          |->  {E#2}}

and instantiated rules:

                                  (letrec {X#6=A#17[(app (letrec {E#2} in T#5[S#3]) S#9)];E#7} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#6=A#17[(app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#9)];E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#17[(app (letrec {E#2} in T#5[S#3]) S#9)];E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=A#17[(letrec {E#2} in (app T#5[S#3] S#9))];E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#17[(app (letrec {E#8} in S#10) T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#17[(letrec {E#8} in (app S#10 T#19[(letrec {E#2} in T#5[S#3])]))]
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#18,A#16,T#13,T#4,A#17}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#19[(letrec {E#2} in T#5[S#3])],(letrec {E#8} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#17[(app (letrec {E#8} in S#10) T#19)];E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  A#17,
           T#13         |->  A#17[(app (letrec {E#8} in S#10) T#19)],
           T#18         |->  (app (letrec {E#8} in S#10) T#19),
           S#9          |->  T#19[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {X#6=A#17[(app (letrec {E#8} in S#10) T#19[(letrec {E#2} in T#5[S#3])])];E#7} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#6=A#17[(app (letrec {E#8} in S#10) T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#17[(app (letrec {E#8} in S#10) T#19[(letrec {E#2} in T#5[S#3])])];E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=A#17[(letrec {E#8} in (app S#10 T#19[(letrec {E#2} in T#5[S#3])]))];E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#17[(app A#18[(app (letrec {E#8} in S#10) S#9)] T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#17[(app A#18[(letrec {E#8} in (app S#10 S#9))] T#19[(letrec {E#2} in T#5[S#3])])]
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#17[(app A#18[(app (letrec {E#8} in S#10) S#9)] T#19)];E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] T#19[(letrec {E#2} in T#5[S#3])])]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           T#13         |->  A#17[(app A#18[(app (letrec {E#8} in S#10) S#9)] T#19)],
           A#16         |->  A#17[(app A#18 T#19[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=A#17[(app A#18[(app (letrec {E#8} in S#10) S#9)] T#19[(letrec {E#2} in T#5[S#3])])];E#7} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#6=A#17[(app A#18[(app (letrec {E#8} in S#10) S#9)] T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#17[(app A#18[(app (letrec {E#8} in S#10) S#9)] T#19[(letrec {E#2} in T#5[S#3])])];E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=A#17[(app A#18[(letrec {E#8} in (app S#10 S#9))] T#19[(letrec {E#2} in T#5[S#3])])];E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (app (letrec {E#8} in T#18[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#9)
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= (letrec {E#8} in (app T#18[(letrec {E#2} in T#5[S#3])] S#9))
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#17,T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(app (letrec {E#8} in T#18) S#9);E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  [.],
           T#13         |->  (app (letrec {E#8} in T#18) S#9),
           T#17         |->  (letrec {E#8} in T#18),
           S#10         |->  T#18[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {X#6=(app (letrec {E#8} in T#18[(letrec {E#2} in T#5[S#3])]) S#9);E#7} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#6=(app (letrec {E#8} in T#18[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#9);E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(app (letrec {E#8} in T#18[(letrec {E#2} in T#5[S#3])]) S#9);E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=(letrec {E#8} in (app T#18[(letrec {E#2} in T#5[S#3])] S#9));E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (app (letrec {X#19=T#18[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#21} in S#10) S#9)
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= (letrec {X#19=T#18[(letrec {E#2} in T#5[S#3])];E#21} in (app S#10 S#9))
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#17,T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {X#19=T#18[(letrec {E#2} in T#5[S#3])];E#21} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(app (letrec {X#19=T#18;E#21} in S#10) S#9);E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  [.],
           T#13         |->  (app (letrec {X#19=T#18;E#21} in S#10) S#9),
           T#17         |->  (letrec {X#19=T#18;E#21} in S#10),
           E#8          |->  {X#19=T#18[(letrec {E#2} in T#5[S#3])];E#21},
           E#20         |->  {E#21}}

and instantiated rules:

                                  (letrec {X#6=(app (letrec {X#19=T#18[(letrec {E#2} in T#5[S#3])];E#21} in S#10) S#9);E#7} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#6=(app (letrec {X#19=T#18[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#21} in S#10) S#9);E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(app (letrec {X#19=T#18[(letrec {E#2} in T#5[S#3])];E#21} in S#10) S#9);E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=(letrec {X#19=T#18[(letrec {E#2} in T#5[S#3])];E#21} in (app S#10 S#9));E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#9)
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec {X#6=(letrec {E#2} in (app T#5[S#3] S#9));E#7} in A#11[(var X#6)])
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#2} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(app [.] S#9);E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  [.],
           T#13         |->  (app [.] S#9),
           T#17         |->  [.],
           S#10         |->  T#5[S#3],
           E#8          |->  {E#2}}

and instantiated rules:

                                  (letrec {X#6=(app (letrec {E#2} in T#5[S#3]) S#9);E#7} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#6=(app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#9);E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(app (letrec {E#2} in T#5[S#3]) S#9);E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=(letrec {E#2} in (app T#5[S#3] S#9));E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= (app (letrec {E#8} in S#10) T#17[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])
       ;E#7
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= (letrec {E#8} in (app S#10 T#17[(letrec {E#2} in T#5[S#3])]))
       ;E#7
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#17[(letrec {E#2} in T#5[S#3])],(letrec {E#8} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=(app (letrec {E#8} in S#10) T#17);E#7} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#6,
           E#15         |->  {E#7},
           A#16         |->  [.],
           T#13         |->  (app (letrec {E#8} in S#10) T#17),
           S#9          |->  T#17[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {X#6=(app (letrec {E#8} in S#10) T#17[(letrec {E#2} in T#5[S#3])]);E#7} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#6=(app (letrec {E#8} in S#10) T#17[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]);E#7} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=(app (letrec {E#8} in S#10) T#17[(letrec {E#2} in T#5[S#3])]);E#7} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=(letrec {E#8} in (app S#10 T#17[(letrec {E#2} in T#5[S#3])]));E#7} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#6= A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#7
       ;EE#18[X#17,(app (letrec {E#8} in S#10) S#9)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#6= A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])]
       ;E#7
       ;EE#18[X#17,(letrec {E#8} in (app S#10 S#9))]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#6=A#19[(app A#20[(var X#17)] T#21)];E#7;EE#18[X#17,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])];EE#18[X#17,[.2]]},
           X#14         |->  X#6,
           E#15         |->  {E#7;EE#18[X#17,(app (letrec {E#8} in S#10) S#9)]},
           T#13         |->  A#19[(app A#20[(var X#17)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])];E#7;EE#18[X#17,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#7;EE#18[X#17,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])];E#7;EE#18[X#17,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#6=A#19[(app A#20[(var X#17)] T#21[(letrec {E#2} in T#5[S#3])])];E#7;EE#18[X#17,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#7
       ;EE#19[X#6,(var X#17)]
       ;EE#20[X#18,(app (letrec {E#8} in S#10) S#9)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])]
       ;E#7
       ;EE#19[X#6,(var X#17)]
       ;EE#20[X#18,(letrec {E#8} in (app S#10 S#9))]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23)];E#7;EE#19[X#6,(var X#17)];EE#20[X#18,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#19[X#6,(var X#17)];EE#20[X#18,(app (letrec {E#8} in S#10) S#9)]},
           T#13         |->  A#21[(app A#22[(var X#18)] T#23)],
           A#16         |->  A#21[(app A#22 T#23[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])];E#7;EE#19[X#6,(var X#17)];EE#20[X#18,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#7;EE#19[X#6,(var X#17)];EE#20[X#18,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])];E#7;EE#19[X#6,(var X#17)];EE#20[X#18,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {E#2} in T#5[S#3])])];E#7;EE#19[X#6,(var X#17)];EE#20[X#18,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app (letrec {E#8} in T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#9)]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#19[(letrec {E#8} in (app T#22[(letrec {E#2} in T#5[S#3])] S#9))]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#21,T#20,A#16,T#13,T#4,A#19}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app (letrec {E#8} in T#22) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[(app (letrec {E#8} in T#22) S#9)],
           T#20         |->  (app (letrec {E#8} in T#22) S#9),
           T#21         |->  (letrec {E#8} in T#22),
           S#10         |->  T#22[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app (letrec {E#8} in T#22[(letrec {E#2} in T#5[S#3])]) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#17=A#19[(app (letrec {E#8} in T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#19[(app (letrec {E#8} in T#22[(letrec {E#2} in T#5[S#3])]) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=A#19[(letrec {E#8} in (app T#22[(letrec {E#2} in T#5[S#3])] S#9))];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app (letrec {X#23=T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#25} in S#10) S#9)]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#19[(letrec {X#23=T#22[(letrec {E#2} in T#5[S#3])];E#25} in (app S#10 S#9))]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#21,T#20,A#16,T#13,T#4,A#19}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {X#23=T#22[(letrec {E#2} in T#5[S#3])];E#25} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app (letrec {X#23=T#22;E#25} in S#10) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[(app (letrec {X#23=T#22;E#25} in S#10) S#9)],
           T#20         |->  (app (letrec {X#23=T#22;E#25} in S#10) S#9),
           T#21         |->  (letrec {X#23=T#22;E#25} in S#10),
           E#8          |->  {X#23=T#22[(letrec {E#2} in T#5[S#3])];E#25},
           E#24         |->  {E#25}}

and instantiated rules:

                                  (letrec {X#17=A#19[(app (letrec {X#23=T#22[(letrec {E#2} in T#5[S#3])];E#25} in S#10) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#17=A#19[(app (letrec {X#23=T#22[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#25} in S#10) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#19[(app (letrec {X#23=T#22[(letrec {E#2} in T#5[S#3])];E#25} in S#10) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=A#19[(letrec {X#23=T#22[(letrec {E#2} in T#5[S#3])];E#25} in (app S#10 S#9))];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#9)]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#19[(letrec {E#2} in (app T#5[S#3] S#9))]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#20,A#16,T#13,T#4,A#19}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#2} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app [.] S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[(app [.] S#9)],
           T#20         |->  (app [.] S#9),
           T#21         |->  [.],
           S#10         |->  T#5[S#3],
           E#8          |->  {E#2}}

and instantiated rules:

                                  (letrec {X#17=A#19[(app (letrec {E#2} in T#5[S#3]) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#17=A#19[(app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#19[(app (letrec {E#2} in T#5[S#3]) S#9)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=A#19[(letrec {E#2} in (app T#5[S#3] S#9))];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app (letrec {E#8} in S#10) T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#19[(letrec {E#8} in (app S#10 T#21[(letrec {E#2} in T#5[S#3])]))]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#20,A#16,T#13,T#4,A#19}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#21[(letrec {E#2} in T#5[S#3])],(letrec {E#8} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app (letrec {E#8} in S#10) T#21)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[(app (letrec {E#8} in S#10) T#21)],
           T#20         |->  (app (letrec {E#8} in S#10) T#21),
           S#9          |->  T#21[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app (letrec {E#8} in S#10) T#21[(letrec {E#2} in T#5[S#3])])];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#17=A#19[(app (letrec {E#8} in S#10) T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#19[(app (letrec {E#8} in S#10) T#21[(letrec {E#2} in T#5[S#3])])];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=A#19[(letrec {E#8} in (app S#10 T#21[(letrec {E#2} in T#5[S#3])]))];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[(app (letrec {E#8} in S#10) S#9)] T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(letrec {E#8} in (app S#10 S#9))] T#21[(letrec {E#2} in T#5[S#3])])]
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=A#19[(app A#20[(app (letrec {E#8} in S#10) S#9)] T#21)];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] T#21[(letrec {E#2} in T#5[S#3])])];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           T#13         |->  A#19[(app A#20[(app (letrec {E#8} in S#10) S#9)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[(letrec {E#2} in T#5[S#3])])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(app (letrec {E#8} in S#10) S#9)] T#21[(letrec {E#2} in T#5[S#3])])];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#17=A#19[(app A#20[(app (letrec {E#8} in S#10) S#9)] T#21[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(app (letrec {E#8} in S#10) S#9)] T#21[(letrec {E#2} in T#5[S#3])])];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=A#19[(app A#20[(letrec {E#8} in (app S#10 S#9))] T#21[(letrec {E#2} in T#5[S#3])])];E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (app (letrec {E#8} in T#20[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#9)
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= (letrec {E#8} in (app T#20[(letrec {E#2} in T#5[S#3])] S#9))
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#19,T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=(app (letrec {E#8} in T#20) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  (app (letrec {E#8} in T#20) S#9),
           T#19         |->  (letrec {E#8} in T#20),
           S#10         |->  T#20[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {X#17=(app (letrec {E#8} in T#20[(letrec {E#2} in T#5[S#3])]) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#17=(app (letrec {E#8} in T#20[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=(app (letrec {E#8} in T#20[(letrec {E#2} in T#5[S#3])]) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=(letrec {E#8} in (app T#20[(letrec {E#2} in T#5[S#3])] S#9));E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (app (letrec {X#21=T#20[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#23} in S#10) S#9)
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= (letrec {X#21=T#20[(letrec {E#2} in T#5[S#3])];E#23} in (app S#10 S#9))
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#19,T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {X#21=T#20[(letrec {E#2} in T#5[S#3])];E#23} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=(app (letrec {X#21=T#20;E#23} in S#10) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  (app (letrec {X#21=T#20;E#23} in S#10) S#9),
           T#19         |->  (letrec {X#21=T#20;E#23} in S#10),
           E#8          |->  {X#21=T#20[(letrec {E#2} in T#5[S#3])];E#23},
           E#22         |->  {E#23}}

and instantiated rules:

                                  (letrec {X#17=(app (letrec {X#21=T#20[(letrec {E#2} in T#5[S#3])];E#23} in S#10) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#17=(app (letrec {X#21=T#20[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])];E#23} in S#10) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=(app (letrec {X#21=T#20[(letrec {E#2} in T#5[S#3])];E#23} in S#10) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=(letrec {X#21=T#20[(letrec {E#2} in T#5[S#3])];E#23} in (app S#10 S#9));E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#9)
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= (letrec {E#2} in (app T#5[S#3] S#9))
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#2} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=(app [.] S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  (app [.] S#9),
           T#19         |->  [.],
           S#10         |->  T#5[S#3],
           E#8          |->  {E#2}}

and instantiated rules:

                                  (letrec {X#17=(app (letrec {E#2} in T#5[S#3]) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#17=(app (letrec {X#1=S#3;E#2} in T#5[(var X#1)]) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=(app (letrec {E#2} in T#5[S#3]) S#9);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=(letrec {E#2} in (app T#5[S#3] S#9));E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (app (letrec {E#8} in S#10) T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])])
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
    ,
     (letrec
        X#17= (letrec {E#8} in (app S#10 T#19[(letrec {E#2} in T#5[S#3])]))
       ;E#7
       ;EE#18[X#6,(var X#17)]
     in
        A#11[(var X#6)]
     )
  )

where

   Delta1 = {T#13,T#4}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),T#5),
             (S#3,T#5),
             ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (T#19[(letrec {E#2} in T#5[S#3])],(letrec {E#8} in [.])),
             ((var X#1),T#5[[.]]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4          |->  (letrec {X#17=(app (letrec {E#8} in S#10) T#19);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {E#7;EE#18[X#6,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  (app (letrec {E#8} in S#10) T#19),
           S#9          |->  T#19[(letrec {E#2} in T#5[S#3])]}

and instantiated rules:

                                  (letrec {X#17=(app (letrec {E#8} in S#10) T#19[(letrec {E#2} in T#5[S#3])]);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#17=(app (letrec {E#8} in S#10) T#19[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    ................................................................................
                                  (letrec {X#17=(app (letrec {E#8} in S#10) T#19[(letrec {E#2} in T#5[S#3])]);E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {X#17=(letrec {E#8} in (app S#10 T#19[(letrec {E#2} in T#5[S#3])]));E#7;EE#18[X#6,(var X#17)]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (var X#6)
       ;E#7
       ;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]
     in
        A#13[(var X#1)]
     )
    ,
     (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#13[(var X#6)])
  )

where

   Delta1 = {A#11,T#5,A#13}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),A#13[[.]]),
             ((var X#6),A#13[[.]]),
             ((letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#13[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),A#13[[.]]),
             ((var X#6),A#13[[.]]),
             ((var X#6),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]},
           A#11  |->  A#13,
           T#5   |->  A#13[[.]],
           T#14  |->  [.],
           S#3   |->  (var X#6)}

and instantiated rules:

                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#13[(var X#6)])
    -ucp1->                       (letrec {X#1=(var X#6);E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#13[(var X#1)])
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#13[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#13[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#14[(var X#6)]
       ;E#7
       ;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]
     in
        A#13[(var X#1)]
     )
    ,
     (letrec
        E#7
       ;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]
     in
        A#13[A#14[(var X#6)]]
     )
  )

where

   Delta1 = {A#11,T#5,A#13}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),A#13),
             (A#14[(var X#6)],A#13),
             ((letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#13[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(var X#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),A#13[[.]]),
             ((var X#6),A#13[A#14[[.]]]),
             ((var X#6),A#13[A#14[[.]]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]},
           A#11  |->  A#13[A#14],
           T#5   |->  A#13,
           S#3   |->  A#14[(var X#6)]}

and instantiated rules:

                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#13[A#14[(var X#6)]])
    -ucp1->                       (letrec {X#1=A#14[(var X#6)];E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#13[(var X#1)])
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#13[A#14[(var X#6)]])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#13[A#14[(var X#6)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#3
       ;E#7
       ;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]
     in
        A#13[(app A#14[(var X#6)] T#15[(var X#1)])]
     )
    ,
     (letrec
        E#7
       ;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]
     in
        A#13[(app A#14[(var X#6)] T#15[S#3])]
     )
  )

where

   Delta1 = {A#11,T#5}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),A#13[(app A#14[(var X#6)] T#15)]),
             (S#3,A#13[(app A#14[(var X#6)] T#15)]),
             ((letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#13[(app A#14[(var X#6)] T#15[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#3,(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),A#13[(app A#14[(var X#6)] T#15[[.]])]),
             ((var X#6),A#13[(app A#14[[.]] T#15[S#3])]),
             ((var X#6),A#13[(app A#14[[.]] T#15[S#3])])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4   |->  [.],
           E#2   |->  {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]},
           T#5   |->  A#13[(app A#14[(var X#6)] T#15)],
           A#11  |->  A#13[(app A#14 T#15[S#3])]}

and instantiated rules:

                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#13[(app A#14[(var X#6)] T#15[S#3])])
    -ucp1->                       (letrec {X#1=S#3;E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#13[(app A#14[(var X#6)] T#15[(var X#1)])])
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#13[(app A#14[(var X#6)] T#15[S#3])])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#13[(app A#14[(var X#6)] T#15[S#3])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#11[(var X#6)]
       ;E#7
       ;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]
     in
        (var X#1)
     )
    ,
     (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
  )

where

   Delta1 = {}
   Delta2 = {E#2,E#8}
   Delta3 = {((var X#1),[.]),
             (A#11[(var X#6)],[.]),
             ((letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in (dummy3 )),(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(var X#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#1),[.]),
             ((var X#6),A#11[[.]]),
             ((var X#6),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp1-> . -SR,lapp3-> with input rules:

                                  T#4[(letrec {E#2} in T#5[S#3])]
    -ucp1->                       T#4[(letrec {X#1=S#3;E#2} in T#5[(var X#1)])]
    and constraints: E#2/= {}, ((var X#1),T#5), (S#3,T#5), ((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])), (S#3,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#4[(letrec {E#2} in T#5[S#3])]
        =?=
        (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#2,E#8}
      Delta3=  {((var X#1),T#5),(S#3,T#5),((letrec {E#2} in T#5[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),(S#3,(letrec {X#1=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#1),T#5[[.]]),((var X#6),A#11[[.]]),((var X#6),A#11[[.]])}


and found solution:

    Sol = {T#4  |->  [.],
           E#2  |->  {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]},
           T#5  |->  [.],
           S#3  |->  A#11[(var X#6)]}

and instantiated rules:

                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -ucp1->                       (letrec {X#1=A#11[(var X#6)];E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in (var X#1))
    ................................................................................
                                  (letrec {E#7;EE#12[X#6,(app (letrec {E#8} in S#10) S#9)]} in A#11[(var X#6)])
    -SR,lapp3->                   (letrec {E#7;EE#12[X#6,(letrec {E#8} in (app S#10 S#9))]} in A#11[(var X#6)])
    

================================================================================
Critical Pair:

  (
     A#12[(app (\ X#8.S#10) T#14[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
    ,
     A#12[(letrec {X#8=T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#10)]
  )

where

   Delta1 = {T#13,A#11,T#6,A#12}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)],(\ X#8.[.])),
             (T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {X#8=[.]} in S#10)),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  A#11[(app (\ X#8.S#10) S#9)]
    -SR,lbeta1->                  A#11[(letrec {X#8=S#9} in S#10)]
    and constraints: (S#9,(\ X#8.[.])), (S#9,(letrec {X#8=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)] =?= A#11[(app (\ X#8.S#10) S#9)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#9,(\ X#8.[.])),(S#9,(letrec {X#8=[.]} in S#10)),((var X#2),T#7[[.]])}


and found solution:

    Sol = {A#11  |->  A#12,
           T#6   |->  A#12[(app (\ X#8.S#10) T#14)],
           T#13  |->  (app (\ X#8.S#10) T#14),
           S#9   |->  T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  A#12[(app (\ X#8.S#10) T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
    -ucp2->                       A#12[(app (\ X#8.S#10) T#14[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
    ................................................................................
                                  A#12[(app (\ X#8.S#10) T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
    -SR,lbeta1->                  A#12[(letrec {X#8=T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#10)]
    

================================================================================
Critical Pair:

  (
     A#12[(app A#13[(app (\ X#8.S#10) S#9)] T#14[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
    ,
     A#12[(app A#13[(letrec {X#8=S#9} in S#10)] T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
  )

where

   Delta1 = {A#11,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#9,(\ X#8.[.])),
             (S#9,(letrec {X#8=[.]} in S#10)),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  A#11[(app (\ X#8.S#10) S#9)]
    -SR,lbeta1->                  A#11[(letrec {X#8=S#9} in S#10)]
    and constraints: (S#9,(\ X#8.[.])), (S#9,(letrec {X#8=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)] =?= A#11[(app (\ X#8.S#10) S#9)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#9,(\ X#8.[.])),(S#9,(letrec {X#8=[.]} in S#10)),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  A#12[(app A#13[(app (\ X#8.S#10) S#9)] T#14)],
           A#11  |->  A#12[(app A#13 T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  A#12[(app A#13[(app (\ X#8.S#10) S#9)] T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
    -ucp2->                       A#12[(app A#13[(app (\ X#8.S#10) S#9)] T#14[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
    ................................................................................
                                  A#12[(app A#13[(app (\ X#8.S#10) S#9)] T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
    -SR,lbeta1->                  A#12[(app A#13[(letrec {X#8=S#9} in S#10)] T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
    

================================================================================
Critical Pair:

  (
     (app (\ X#8.S#10) T#12[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])
    ,
     (letrec {X#8=T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#10)
  )

where

   Delta1 = {T#6}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)],(\ X#8.[.])),
             (T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {X#8=[.]} in S#10)),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  A#11[(app (\ X#8.S#10) S#9)]
    -SR,lbeta1->                  A#11[(letrec {X#8=S#9} in S#10)]
    and constraints: (S#9,(\ X#8.[.])), (S#9,(letrec {X#8=[.]} in S#10))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)] =?= A#11[(app (\ X#8.S#10) S#9)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#9,(\ X#8.[.])),(S#9,(letrec {X#8=[.]} in S#10)),((var X#2),T#7[[.]])}


and found solution:

    Sol = {A#11  |->  [.],
           T#6   |->  (app (\ X#8.S#10) T#12),
           S#9   |->  T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (app (\ X#8.S#10) T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)])
    -ucp2->                       (app (\ X#8.S#10) T#12[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])
    ................................................................................
                                  (app (\ X#8.S#10) T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)])
    -SR,lbeta1->                  (letrec {X#8=T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#10)
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        A#14[(app (\ X#8.S#11) T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
     )
    ,
     (letrec
        E#9
     in
        A#14[(letrec {X#8=T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#11)]
     )
  )

where

   Delta1 = {T#15,A#12,T#13,T#6,A#14}
   Delta2 = {E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)],(\ X#8.[.])),
             (T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {X#8=[.]} in S#11)),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])
    -SR,lbeta2->                  (letrec {E#9} in A#12[(letrec {X#8=S#10} in S#11)])
    and constraints: E#9/= {}, (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#9} in A#14[(app (\ X#8.S#11) T#16)]),
           A#12  |->  A#14,
           T#13  |->  A#14[(app (\ X#8.S#11) T#16)],
           T#15  |->  (app (\ X#8.S#11) T#16),
           S#10  |->  T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#9} in A#14[(app (\ X#8.S#11) T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -ucp2->                       (letrec {E#9} in A#14[(app (\ X#8.S#11) T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#9} in A#14[(app (\ X#8.S#11) T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -SR,lbeta2->                  (letrec {E#9} in A#14[(letrec {X#8=T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        A#14[(app A#15[(app (\ X#8.S#11) S#10)] T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
     )
    ,
     (letrec
        E#9
     in
        A#14[(app A#15[(letrec {X#8=S#10} in S#11)] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#13,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])
    -SR,lbeta2->                  (letrec {E#9} in A#12[(letrec {X#8=S#10} in S#11)])
    and constraints: E#9/= {}, (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#9} in A#14[(app A#15[(app (\ X#8.S#11) S#10)] T#16)]),
           T#13  |->  A#14[(app A#15[(app (\ X#8.S#11) S#10)] T#16)],
           A#12  |->  A#14[(app A#15 T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {E#9} in A#14[(app A#15[(app (\ X#8.S#11) S#10)] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -ucp2->                       (letrec {E#9} in A#14[(app A#15[(app (\ X#8.S#11) S#10)] T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#9} in A#14[(app A#15[(app (\ X#8.S#11) S#10)] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -SR,lbeta2->                  (letrec {E#9} in A#14[(app A#15[(letrec {X#8=S#10} in S#11)] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
     in
        (app (\ X#8.S#11) T#14[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])
     )
    ,
     (letrec
        E#9
     in
        (letrec {X#8=T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#11)
     )
  )

where

   Delta1 = {T#13,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)],(\ X#8.[.])),
             (T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {X#8=[.]} in S#11)),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])
    -SR,lbeta2->                  (letrec {E#9} in A#12[(letrec {X#8=S#10} in S#11)])
    and constraints: E#9/= {}, (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#9} in (app (\ X#8.S#11) T#14)),
           A#12  |->  [.],
           T#13  |->  (app (\ X#8.S#11) T#14),
           S#10  |->  T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#9} in (app (\ X#8.S#11) T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)]))
    -ucp2->                       (letrec {E#9} in (app (\ X#8.S#11) T#14[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]))
    ................................................................................
                                  (letrec {E#9} in (app (\ X#8.S#11) T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)]))
    -SR,lbeta2->                  (letrec {E#9} in (letrec {X#8=T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#11))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
       ;E#16
     in
        A#12[(app (\ X#8.S#11) S#10)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)]
       ;E#16
     in
        A#12[(letrec {X#8=S#10} in S#11)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])
    -SR,lbeta2->                  (letrec {E#9} in A#12[(letrec {X#8=S#10} in S#11)])
    and constraints: E#9/= {}, (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#14=T#13;E#16} in A#12[(app (\ X#8.S#11) S#10)]),
           E#9   |->  {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16} in A#12[(app (\ X#8.S#11) S#10)])
    -ucp2->                       (letrec {X#14=T#13[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#16} in A#12[(app (\ X#8.S#11) S#10)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16} in A#12[(app (\ X#8.S#11) S#10)])
    -SR,lbeta2->                  (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16} in A#12[(letrec {X#8=S#10} in S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#13} in A#12[(app (\ X#8.S#11) S#10)])
    ,
     (letrec {X#1=T#7[S#4];E#13} in A#12[(letrec {X#8=S#10} in S#11)])
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#13} in A#12[(app (\ X#8.S#11) S#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#10,(\ X#8.[.])),
             (S#10,(letrec {X#8=[.]} in S#11)),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])
    -SR,lbeta2->                  (letrec {E#9} in A#12[(letrec {X#8=S#10} in S#11)])
    and constraints: E#9/= {}, (S#10,(\ X#8.[.])), (S#10,(letrec {X#8=[.]} in S#11))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9} in A#12[(app (\ X#8.S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(\ X#8.[.])),(S#10,(letrec {X#8=[.]} in S#11)),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6  |->  [.],
           S#5  |->  A#12[(app (\ X#8.S#11) S#10)],
           E#9  |->  {X#1=T#7[S#4];E#13},
           E#3  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#1=T#7[S#4];E#13} in A#12[(app (\ X#8.S#11) S#10)])
    -ucp2->                       (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#13} in A#12[(app (\ X#8.S#11) S#10)])
    ................................................................................
                                  (letrec {X#1=T#7[S#4];E#13} in A#12[(app (\ X#8.S#11) S#10)])
    -SR,lbeta2->                  (letrec {X#1=T#7[S#4];E#13} in A#12[(letrec {X#8=S#10} in S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#10
       ;EE#14[X#8,(app (\ X#9.S#12) S#11)]
     in
        A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
     )
    ,
     (letrec
        E#10
       ;EE#14[X#8,(letrec {X#9=S#11} in S#12)]
     in
        A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#13,T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#16[(app A#17[[.]] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])]),
             ((var X#8),A#16[(app A#17[[.]] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#8)] T#18)],
           A#13  |->  A#16[(app A#17 T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -ucp2->                       (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
       ;E#18
       ;EE#14[X#8,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)]
       ;E#18
       ;EE#14[X#8,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#16=T#15;E#18;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)]),
           E#10  |->  {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18},
           E#17  |->  {E#18;EE#14[X#8,(app (\ X#9.S#12) S#11)]}}

and instantiated rules:

                                  (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#18;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#19[(app (\ X#9.S#12) T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#19[(letrec {X#9=T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#12)]
       ;E#10
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#6,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)],(\ X#9.[.])),
             (T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {X#9=[.]} in S#12)),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#19[(app (\ X#9.S#12) T#21)];E#10} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#8,
           E#17         |->  {E#10},
           A#18         |->  A#19,
           T#15         |->  A#19[(app (\ X#9.S#12) T#21)],
           T#20         |->  (app (\ X#9.S#12) T#21),
           S#11         |->  T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=A#19[(app (\ X#9.S#12) T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#8=A#19[(app (\ X#9.S#12) T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#19[(app (\ X#9.S#12) T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#19[(letrec {X#9=T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#12)];E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#19[(app A#20[(app (\ X#9.S#12) S#11)] T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#19[(app A#20[(letrec {X#9=S#11} in S#12)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;E#10
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#19[(app A#20[(app (\ X#9.S#12) S#11)] T#21)];E#10} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])]},
           X#16         |->  X#8,
           E#17         |->  {E#10},
           T#15         |->  A#19[(app A#20[(app (\ X#9.S#12) S#11)] T#21)],
           A#18         |->  A#19[(app A#20 T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=A#19[(app A#20[(app (\ X#9.S#12) S#11)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#8=A#19[(app A#20[(app (\ X#9.S#12) S#11)] T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#19[(app A#20[(app (\ X#9.S#12) S#11)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#19[(app A#20[(letrec {X#9=S#11} in S#12)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (app (\ X#9.S#12) T#19[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= (letrec {X#9=T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#12)
       ;E#10
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)],(\ X#9.[.])),
             (T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {X#9=[.]} in S#12)),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=(app (\ X#9.S#12) T#19);E#10} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#8,
           E#17         |->  {E#10},
           A#18         |->  [.],
           T#15         |->  (app (\ X#9.S#12) T#19),
           S#11         |->  T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=(app (\ X#9.S#12) T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)]);E#10} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#8=(app (\ X#9.S#12) T#19[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]);E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (\ X#9.S#12) T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)]);E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=(letrec {X#9=T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#12);E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;E#10
       ;EE#20[X#19,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;E#10
       ;EE#20[X#19,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#21[(app A#22[(var X#19)] T#23)];E#10;EE#20[X#19,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];EE#20[X#19,[.2]]},
           X#16         |->  X#8,
           E#17         |->  {E#10;EE#20[X#19,(app (\ X#9.S#12) S#11)]},
           T#15         |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;EE#20[X#19,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];E#10;EE#20[X#19,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;EE#20[X#19,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;EE#20[X#19,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;E#10
       ;EE#21[X#8,(var X#19)]
       ;EE#22[X#20,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;E#10
       ;EE#21[X#8,(var X#19)]
       ;EE#22[X#20,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];E#10;EE#21[X#8,(var X#19)];EE#22[X#20,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {E#10;EE#21[X#8,(var X#19)];EE#22[X#20,(app (\ X#9.S#12) S#11)]},
           T#15         |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;EE#21[X#8,(var X#19)];EE#22[X#20,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];E#10;EE#21[X#8,(var X#19)];EE#22[X#20,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;EE#21[X#8,(var X#19)];EE#22[X#20,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;EE#21[X#8,(var X#19)];EE#22[X#20,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app (\ X#9.S#12) T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;E#10
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(letrec {X#9=T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#12)]
       ;E#10
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#6,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)],(\ X#9.[.])),
             (T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {X#9=[.]} in S#12)),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app (\ X#9.S#12) T#23)];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#10;EE#20[X#8,(var X#19)]},
           A#18         |->  A#21,
           T#15         |->  A#21[(app (\ X#9.S#12) T#23)],
           T#22         |->  (app (\ X#9.S#12) T#23),
           S#11         |->  T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app (\ X#9.S#12) T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#19=A#21[(app (\ X#9.S#12) T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app (\ X#9.S#12) T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#19=A#21[(letrec {X#9=T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#12)];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(app (\ X#9.S#12) S#11)] T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;E#10
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(letrec {X#9=S#11} in S#12)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;E#10
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app A#22[(app (\ X#9.S#12) S#11)] T#23)];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#10;EE#20[X#8,(var X#19)]},
           T#15         |->  A#21[(app A#22[(app (\ X#9.S#12) S#11)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(app (\ X#9.S#12) S#11)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#19=A#21[(app A#22[(app (\ X#9.S#12) S#11)] T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(app (\ X#9.S#12) S#11)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#19=A#21[(app A#22[(letrec {X#9=S#11} in S#12)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (app (\ X#9.S#12) T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])
       ;E#10
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= (letrec {X#9=T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#12)
       ;E#10
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)],(\ X#9.[.])),
             (T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {X#9=[.]} in S#12)),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=(app (\ X#9.S#12) T#21);E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#10;EE#20[X#8,(var X#19)]},
           A#18         |->  [.],
           T#15         |->  (app (\ X#9.S#12) T#21),
           S#11         |->  T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#19=(app (\ X#9.S#12) T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]);E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#19=(app (\ X#9.S#12) T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]);E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=(app (\ X#9.S#12) T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]);E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#19=(letrec {X#9=T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]} in S#12);E#10;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= T#7[(var X#2)]
       ;X#2= S#4
       ;E#15
       ;EE#14[X#8,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#1= T#7[S#4]
       ;E#15
       ;EE#14[X#8,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#15;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#8)],
           E#10  |->  {X#1=T#7[S#4];E#15},
           E#3   |->  {E#15;EE#14[X#8,(app (\ X#9.S#12) S#11)]}}

and instantiated rules:

                                  (letrec {X#1=T#7[S#4];E#15;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#15;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#1=T#7[S#4];E#15;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#1=T#7[S#4];E#15;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#9.S#12)
       ;X#8= A#16[(app (var X#2) S#11)]
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec {X#8=A#16[(letrec {X#9=S#11} in S#12)];E#10} in A#13[(var X#8)])
  )

where

   Delta1 = {T#17,A#15,T#7,A#16}
   Delta2 = {}
   Delta3 = {((var X#2),A#16[(app [.] S#11)]),
             ((\ X#9.S#12),A#16[(app [.] S#11)]),
             ((letrec {X#8=A#16[(app (dummy3 ) S#11)];E#10} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((\ X#9.S#12),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#16[(app [.] S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#10},
           A#15         |->  A#16,
           T#7          |->  A#16[(app [.] S#11)],
           T#17         |->  (app [.] S#11),
           T#18         |->  [.],
           S#4          |->  (\ X#9.S#12)}

and instantiated rules:

                                  (letrec {X#8=A#16[(app (\ X#9.S#12) S#11)];E#10} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=(\ X#9.S#12);X#8=A#16[(app (var X#2) S#11)];E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#16[(app (\ X#9.S#12) S#11)];E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#16[(letrec {X#9=S#11} in S#12)];E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= A#16[(app (\ X#9.S#12) T#18[(var X#2)])]
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec {X#8=A#16[(letrec {X#9=T#18[S#4]} in S#12)];E#10} in A#13[(var X#8)])
  )

where

   Delta1 = {T#17,A#15,T#7,A#16}
   Delta2 = {}
   Delta3 = {((var X#2),A#16[(app (\ X#9.S#12) T#18)]),
             (S#4,A#16[(app (\ X#9.S#12) T#18)]),
             ((letrec {X#8=A#16[(app (\ X#9.S#12) T#18[(dummy3 )])];E#10} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#18[S#4],(\ X#9.[.])),
             (T#18[S#4],(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#16[(app (\ X#9.S#12) T#18[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#10},
           A#15         |->  A#16,
           T#7          |->  A#16[(app (\ X#9.S#12) T#18)],
           T#17         |->  (app (\ X#9.S#12) T#18),
           S#11         |->  T#18[S#4]}

and instantiated rules:

                                  (letrec {X#8=A#16[(app (\ X#9.S#12) T#18[S#4])];E#10} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=S#4;X#8=A#16[(app (\ X#9.S#12) T#18[(var X#2)])];E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#16[(app (\ X#9.S#12) T#18[S#4])];E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#16[(letrec {X#9=T#18[S#4]} in S#12)];E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (app (\ X#9.S#12) S#11)
       ;X#8= A#16[(var X#2)]
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec {X#8=A#16[(letrec {X#9=S#11} in S#12)];E#10} in A#13[(var X#8)])
  )

where

   Delta1 = {A#15,T#7,A#16}
   Delta2 = {}
   Delta3 = {((var X#2),A#16[[.]]),
             ((app (\ X#9.S#12) S#11),A#16[[.]]),
             ((letrec {X#8=A#16[(dummy3 )];E#10} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((app (\ X#9.S#12) S#11),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#16[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#10},
           A#15         |->  A#16,
           T#7          |->  A#16[[.]],
           T#17         |->  [.],
           S#4          |->  (app (\ X#9.S#12) S#11)}

and instantiated rules:

                                  (letrec {X#8=A#16[(app (\ X#9.S#12) S#11)];E#10} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=(app (\ X#9.S#12) S#11);X#8=A#16[(var X#2)];E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#16[(app (\ X#9.S#12) S#11)];E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#16[(letrec {X#9=S#11} in S#12)];E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= A#17[(app (\ X#9.S#12) S#11)]
       ;X#8= A#16[(var X#2)]
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec {X#8=A#16[A#17[(letrec {X#9=S#11} in S#12)]];E#10} in A#13[(var X#8)])
  )

where

   Delta1 = {A#15,T#7,A#16}
   Delta2 = {}
   Delta3 = {((var X#2),A#16),
             (A#17[(app (\ X#9.S#12) S#11)],A#16),
             ((letrec {X#8=A#16[(dummy3 )];E#10} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#17[(app (\ X#9.S#12) S#11)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#16[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#16[A#17[[.2]]]},
           X#1          |->  X#8,
           E#3          |->  {E#10},
           A#15         |->  A#16[A#17],
           T#7          |->  A#16,
           S#4          |->  A#17[(app (\ X#9.S#12) S#11)]}

and instantiated rules:

                                  (letrec {X#8=A#16[A#17[(app (\ X#9.S#12) S#11)]];E#10} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=A#17[(app (\ X#9.S#12) S#11)];X#8=A#16[(var X#2)];E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#16[A#17[(app (\ X#9.S#12) S#11)]];E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#16[A#17[(letrec {X#9=S#11} in S#12)]];E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= A#16[(app A#17[(app (\ X#9.S#12) S#11)] T#18[(var X#2)])]
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#16[(app A#17[(letrec {X#9=S#11} in S#12)] T#18[S#4])]
       ;E#10
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7}
   Delta2 = {}
   Delta3 = {((var X#2),A#16[(app A#17[(app (\ X#9.S#12) S#11)] T#18)]),
             (S#4,A#16[(app A#17[(app (\ X#9.S#12) S#11)] T#18)]),
             ((letrec {X#8=A#16[(app A#17[(app (\ X#9.S#12) S#11)] T#18[(dummy3 )])];E#10} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#16[(app A#17[(app (\ X#9.S#12) S#11)] T#18[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[S#4])]},
           X#1          |->  X#8,
           E#3          |->  {E#10},
           T#7          |->  A#16[(app A#17[(app (\ X#9.S#12) S#11)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[S#4])]}

and instantiated rules:

                                  (letrec {X#8=A#16[(app A#17[(app (\ X#9.S#12) S#11)] T#18[S#4])];E#10} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=S#4;X#8=A#16[(app A#17[(app (\ X#9.S#12) S#11)] T#18[(var X#2)])];E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#16[(app A#17[(app (\ X#9.S#12) S#11)] T#18[S#4])];E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#16[(app A#17[(letrec {X#9=S#11} in S#12)] T#18[S#4])];E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#2=(\ X#9.S#12);X#8=(app (var X#2) S#11);E#10} in A#13[(var X#8)])
    ,
     (letrec {X#8=(letrec {X#9=S#11} in S#12);E#10} in A#13[(var X#8)])
  )

where

   Delta1 = {T#7}
   Delta2 = {}
   Delta3 = {((var X#2),(app [.] S#11)),
             ((\ X#9.S#12),(app [.] S#11)),
             ((letrec {X#8=(app (dummy3 ) S#11);E#10} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((\ X#9.S#12),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),(app [.] S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#8,
           E#3          |->  {E#10},
           A#15         |->  [.],
           T#7          |->  (app [.] S#11),
           T#16         |->  [.],
           S#4          |->  (\ X#9.S#12)}

and instantiated rules:

                                  (letrec {X#8=(app (\ X#9.S#12) S#11);E#10} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=(\ X#9.S#12);X#8=(app (var X#2) S#11);E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (\ X#9.S#12) S#11);E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=(letrec {X#9=S#11} in S#12);E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= (app (\ X#9.S#12) T#16[(var X#2)])
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec {X#8=(letrec {X#9=T#16[S#4]} in S#12);E#10} in A#13[(var X#8)])
  )

where

   Delta1 = {T#7}
   Delta2 = {}
   Delta3 = {((var X#2),(app (\ X#9.S#12) T#16)),
             (S#4,(app (\ X#9.S#12) T#16)),
             ((letrec {X#8=(app (\ X#9.S#12) T#16[(dummy3 )]);E#10} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#16[S#4],(\ X#9.[.])),
             (T#16[S#4],(letrec {X#9=[.]} in S#12)),
             ((var X#2),(app (\ X#9.S#12) T#16[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#8,
           E#3          |->  {E#10},
           A#15         |->  [.],
           T#7          |->  (app (\ X#9.S#12) T#16),
           S#11         |->  T#16[S#4]}

and instantiated rules:

                                  (letrec {X#8=(app (\ X#9.S#12) T#16[S#4]);E#10} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=S#4;X#8=(app (\ X#9.S#12) T#16[(var X#2)]);E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (\ X#9.S#12) T#16[S#4]);E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=(letrec {X#9=T#16[S#4]} in S#12);E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= A#15[(app (\ X#9.S#12) S#11)]
       ;X#8= (var X#2)
       ;E#10
     in
        A#13[(var X#8)]
     )
    ,
     (letrec {X#8=A#15[(letrec {X#9=S#11} in S#12)];E#10} in A#13[(var X#8)])
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             (A#15[(app (\ X#9.S#12) S#11)],[.]),
             ((letrec {X#8=(dummy3 );E#10} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#15[(app (\ X#9.S#12) S#11)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#10},
           T#7          |->  [.],
           S#4          |->  A#15[(app (\ X#9.S#12) S#11)]}

and instantiated rules:

                                  (letrec {X#8=A#15[(app (\ X#9.S#12) S#11)];E#10} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=A#15[(app (\ X#9.S#12) S#11)];X#8=(var X#2);E#10} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#15[(app (\ X#9.S#12) S#11)];E#10} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#15[(letrec {X#9=S#11} in S#12)];E#10} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#16)
       ;X#8= A#18[(var X#2)]
       ;E#10
       ;EE#17[X#16,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#18[(var X#16)]
       ;E#10
       ;EE#17[X#16,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7,A#18}
   Delta2 = {}
   Delta3 = {((var X#2),A#18[[.]]),
             ((var X#16),A#18[[.]]),
             ((letrec {X#8=A#18[(dummy3 )];E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#16),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#18[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#18[(var X#16)];EE#17[X#16,[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]},
           A#15         |->  A#18,
           T#7          |->  A#18[[.]],
           T#19         |->  [.],
           S#4          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#8=A#18[(var X#16)];E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=(var X#16);X#8=A#18[(var X#2)];E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#18[(var X#16)];E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#18[(var X#16)];E#10;EE#17[X#16,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= A#19[(var X#16)]
       ;X#8= A#18[(var X#2)]
       ;E#10
       ;EE#17[X#16,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#18[A#19[(var X#16)]]
       ;E#10
       ;EE#17[X#16,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7,A#18}
   Delta2 = {}
   Delta3 = {((var X#2),A#18),
             (A#19[(var X#16)],A#18),
             ((letrec {X#8=A#18[(dummy3 )];E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#19[(var X#16)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#18[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#18[A#19[(var X#16)]];EE#17[X#16,[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]},
           A#15         |->  A#18[A#19],
           T#7          |->  A#18,
           S#4          |->  A#19[(var X#16)]}

and instantiated rules:

                                  (letrec {X#8=A#18[A#19[(var X#16)]];E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=A#19[(var X#16)];X#8=A#18[(var X#2)];E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#18[A#19[(var X#16)]];E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#18[A#19[(var X#16)]];E#10;EE#17[X#16,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= A#18[(app A#19[(var X#16)] T#20[(var X#2)])]
       ;E#10
       ;EE#17[X#16,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#18[(app A#19[(var X#16)] T#20[S#4])]
       ;E#10
       ;EE#17[X#16,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7}
   Delta2 = {}
   Delta3 = {((var X#2),A#18[(app A#19[(var X#16)] T#20)]),
             (S#4,A#18[(app A#19[(var X#16)] T#20)]),
             ((letrec {X#8=A#18[(app A#19[(var X#16)] T#20[(dummy3 )])];E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#18[(app A#19[(var X#16)] T#20[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[S#4])];EE#17[X#16,[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]},
           T#7          |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#4])]}

and instantiated rules:

                                  (letrec {X#8=A#18[(app A#19[(var X#16)] T#20[S#4])];E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=S#4;X#8=A#18[(app A#19[(var X#16)] T#20[(var X#2)])];E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#18[(app A#19[(var X#16)] T#20[S#4])];E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#18[(app A#19[(var X#16)] T#20[S#4])];E#10;EE#17[X#16,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= A#15[(var X#16)]
       ;X#8= (var X#2)
       ;E#10
       ;EE#17[X#16,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#15[(var X#16)]
       ;E#10
       ;EE#17[X#16,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             (A#15[(var X#16)],[.]),
             ((letrec {X#8=(dummy3 );E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#15[(var X#16)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#15[(var X#16)];EE#17[X#16,[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]},
           T#7          |->  [.],
           S#4          |->  A#15[(var X#16)]}

and instantiated rules:

                                  (letrec {X#8=A#15[(var X#16)];E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=A#15[(var X#16)];X#8=(var X#2);E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#15[(var X#16)];E#10;EE#17[X#16,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#8=A#15[(var X#16)];E#10;EE#17[X#16,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(var X#2)]
       ;X#2= (var X#17)
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#20[(var X#17)]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7,A#20}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[[.]]),
             ((var X#17),A#20[[.]]),
             ((letrec {X#16=A#20[(dummy3 )];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#20[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#20[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#1          |->  X#16,
           E#3          |->  {E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]},
           A#15         |->  A#20,
           T#7          |->  A#20[[.]],
           T#21         |->  [.],
           S#4          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#16=A#20[(var X#17)];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#20[(var X#2)];X#2=(var X#17);E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#20[(var X#17)];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=A#20[(var X#17)];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(var X#2)]
       ;X#2= A#21[(var X#17)]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#20[A#21[(var X#17)]]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7,A#20}
   Delta2 = {}
   Delta3 = {((var X#2),A#20),
             (A#21[(var X#17)],A#20),
             ((letrec {X#16=A#20[(dummy3 )];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#21[(var X#17)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#20[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#20[A#21[(var X#17)]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#1          |->  X#16,
           E#3          |->  {E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]},
           A#15         |->  A#20[A#21],
           T#7          |->  A#20,
           S#4          |->  A#21[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#21[(var X#17)]];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#20[(var X#2)];X#2=A#21[(var X#17)];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#20[A#21[(var X#17)]];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=A#20[A#21[(var X#17)]];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(var X#2)])]
       ;X#2= S#4
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[S#4])]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7}
   Delta2 = {}
   Delta3 = {((var X#2),A#20[(app A#21[(var X#17)] T#22)]),
             (S#4,A#20[(app A#21[(var X#17)] T#22)]),
             ((letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(dummy3 )])];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#20[(app A#21[(var X#17)] T#22[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[S#4])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#1          |->  X#16,
           E#3          |->  {E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]},
           T#7          |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[S#4])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#4])];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(var X#2)])];X#2=S#4;E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#4])];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#4])];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#2)
       ;X#2= A#15[(var X#17)]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(app (\ X#9.S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#15[(var X#17)]
       ;E#10
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(letrec {X#9=S#11} in S#12)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             (A#15[(var X#17)],[.]),
             ((letrec {X#16=(dummy3 );E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#15[(var X#17)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#15[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#1          |->  X#16,
           E#3          |->  {E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]},
           T#7          |->  [.],
           S#4          |->  A#15[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#15[(var X#17)];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=(var X#2);X#2=A#15[(var X#17)];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#15[(var X#17)];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=A#15[(var X#17)];E#10;EE#18[X#8,(var X#16)];EE#19[X#17,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (var X#2) S#11)]
       ;X#2= (\ X#9.S#12)
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#9=S#11} in S#12)]
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#19,A#15,T#7,A#18}
   Delta2 = {}
   Delta3 = {((var X#2),A#18[(app [.] S#11)]),
             ((\ X#9.S#12),A#18[(app [.] S#11)]),
             ((letrec {X#16=A#18[(app (dummy3 ) S#11)];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((\ X#9.S#12),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#18[(app [.] S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#10;EE#17[X#8,(var X#16)]},
           A#15         |->  A#18,
           T#7          |->  A#18[(app [.] S#11)],
           T#19         |->  (app [.] S#11),
           T#20         |->  [.],
           S#4          |->  (\ X#9.S#12)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#9.S#12) S#11)];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#18[(app (var X#2) S#11)];X#2=(\ X#9.S#12);E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#9.S#12) S#11)];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#9=S#11} in S#12)];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (\ X#9.S#12) T#20[(var X#2)])]
       ;X#2= S#4
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#9=T#20[S#4]} in S#12)]
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#19,A#15,T#7,A#18}
   Delta2 = {}
   Delta3 = {((var X#2),A#18[(app (\ X#9.S#12) T#20)]),
             (S#4,A#18[(app (\ X#9.S#12) T#20)]),
             ((letrec {X#16=A#18[(app (\ X#9.S#12) T#20[(dummy3 )])];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#20[S#4],(\ X#9.[.])),
             (T#20[S#4],(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#18[(app (\ X#9.S#12) T#20[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#10;EE#17[X#8,(var X#16)]},
           A#15         |->  A#18,
           T#7          |->  A#18[(app (\ X#9.S#12) T#20)],
           T#19         |->  (app (\ X#9.S#12) T#20),
           S#11         |->  T#20[S#4]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#9.S#12) T#20[S#4])];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#18[(app (\ X#9.S#12) T#20[(var X#2)])];X#2=S#4;E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#9.S#12) T#20[S#4])];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#9=T#20[S#4]} in S#12)];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(var X#2)]
       ;X#2= (app (\ X#9.S#12) S#11)
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#9=S#11} in S#12)]
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7,A#18}
   Delta2 = {}
   Delta3 = {((var X#2),A#18[[.]]),
             ((app (\ X#9.S#12) S#11),A#18[[.]]),
             ((letrec {X#16=A#18[(dummy3 )];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((app (\ X#9.S#12) S#11),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#18[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#10;EE#17[X#8,(var X#16)]},
           A#15         |->  A#18,
           T#7          |->  A#18[[.]],
           T#19         |->  [.],
           S#4          |->  (app (\ X#9.S#12) S#11)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#9.S#12) S#11)];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#18[(var X#2)];X#2=(app (\ X#9.S#12) S#11);E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#9.S#12) S#11)];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#9=S#11} in S#12)];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(var X#2)]
       ;X#2= A#19[(app (\ X#9.S#12) S#11)]
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#18[A#19[(letrec {X#9=S#11} in S#12)]]
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7,A#18}
   Delta2 = {}
   Delta3 = {((var X#2),A#18),
             (A#19[(app (\ X#9.S#12) S#11)],A#18),
             ((letrec {X#16=A#18[(dummy3 )];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#19[(app (\ X#9.S#12) S#11)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#18[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#18[A#19[[.2]]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#10;EE#17[X#8,(var X#16)]},
           A#15         |->  A#18[A#19],
           T#7          |->  A#18,
           S#4          |->  A#19[(app (\ X#9.S#12) S#11)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#19[(app (\ X#9.S#12) S#11)]];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#18[(var X#2)];X#2=A#19[(app (\ X#9.S#12) S#11)];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#18[A#19[(app (\ X#9.S#12) S#11)]];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=A#18[A#19[(letrec {X#9=S#11} in S#12)]];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(app (\ X#9.S#12) S#11)] T#20[(var X#2)])]
       ;X#2= S#4
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {X#9=S#11} in S#12)] T#20[S#4])]
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7}
   Delta2 = {}
   Delta3 = {((var X#2),A#18[(app A#19[(app (\ X#9.S#12) S#11)] T#20)]),
             (S#4,A#18[(app A#19[(app (\ X#9.S#12) S#11)] T#20)]),
             ((letrec {X#16=A#18[(app A#19[(app (\ X#9.S#12) S#11)] T#20[(dummy3 )])];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),A#18[(app A#19[(app (\ X#9.S#12) S#11)] T#20[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[S#4])];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#10;EE#17[X#8,(var X#16)]},
           T#7          |->  A#18[(app A#19[(app (\ X#9.S#12) S#11)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#4])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (\ X#9.S#12) S#11)] T#20[S#4])];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#18[(app A#19[(app (\ X#9.S#12) S#11)] T#20[(var X#2)])];X#2=S#4;E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (\ X#9.S#12) S#11)] T#20[S#4])];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(app A#19[(letrec {X#9=S#11} in S#12)] T#20[S#4])];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (var X#2) S#11)
       ;X#2= (\ X#9.S#12)
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (letrec {X#9=S#11} in S#12)
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {}
   Delta3 = {((var X#2),(app [.] S#11)),
             ((\ X#9.S#12),(app [.] S#11)),
             ((letrec {X#16=(app (dummy3 ) S#11);E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((\ X#9.S#12),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),(app [.] S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#10;EE#17[X#8,(var X#16)]},
           A#15         |->  [.],
           T#7          |->  (app [.] S#11),
           T#18         |->  [.],
           S#4          |->  (\ X#9.S#12)}

and instantiated rules:

                                  (letrec {X#16=(app (\ X#9.S#12) S#11);E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=(app (var X#2) S#11);X#2=(\ X#9.S#12);E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(app (\ X#9.S#12) S#11);E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(letrec {X#9=S#11} in S#12);E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (\ X#9.S#12) T#18[(var X#2)])
       ;X#2= S#4
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (letrec {X#9=T#18[S#4]} in S#12)
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {}
   Delta3 = {((var X#2),(app (\ X#9.S#12) T#18)),
             (S#4,(app (\ X#9.S#12) T#18)),
             ((letrec {X#16=(app (\ X#9.S#12) T#18[(dummy3 )]);E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#18[S#4],(\ X#9.[.])),
             (T#18[S#4],(letrec {X#9=[.]} in S#12)),
             ((var X#2),(app (\ X#9.S#12) T#18[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#10;EE#17[X#8,(var X#16)]},
           A#15         |->  [.],
           T#7          |->  (app (\ X#9.S#12) T#18),
           S#11         |->  T#18[S#4]}

and instantiated rules:

                                  (letrec {X#16=(app (\ X#9.S#12) T#18[S#4]);E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=(app (\ X#9.S#12) T#18[(var X#2)]);X#2=S#4;E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(app (\ X#9.S#12) T#18[S#4]);E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=(letrec {X#9=T#18[S#4]} in S#12);E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#2)
       ;X#2= A#15[(app (\ X#9.S#12) S#11)]
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#15[(letrec {X#9=S#11} in S#12)]
       ;E#10
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             (A#15[(app (\ X#9.S#12) S#11)],[.]),
             ((letrec {X#16=(dummy3 );E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#15[(app (\ X#9.S#12) S#11)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(\ X#9.[.])),
             (S#11,(letrec {X#9=[.]} in S#12)),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lbeta3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {E#10;EE#14[X#8,(letrec {X#9=S#11} in S#12)]} in A#13[(var X#8)])
    and constraints: (S#11,(\ X#9.[.])), (S#11,(letrec {X#9=[.]} in S#12))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#10;EE#14[X#8,(app (\ X#9.S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(\ X#9.[.])),(S#11,(letrec {X#9=[.]} in S#12)),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#15[[.2]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#10;EE#17[X#8,(var X#16)]},
           T#7          |->  [.],
           S#4          |->  A#15[(app (\ X#9.S#12) S#11)]}

and instantiated rules:

                                  (letrec {X#16=A#15[(app (\ X#9.S#12) S#11)];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=(var X#2);X#2=A#15[(app (\ X#9.S#12) S#11)];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#15[(app (\ X#9.S#12) S#11)];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lbeta3->                  (letrec {X#16=A#15[(letrec {X#9=S#11} in S#12)];E#10;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (\ X#9.S#11)
       ;E#10
     in
        A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
     )
    ,
     (letrec
        X#8= (\ X#9.S#11)
       ;E#10
     in
        A#14[(app A#15[(\ X#9.S#11)] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#13,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#14[(app A#15[[.]] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])
    -SR,cp-in1->                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(\ X#9.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(\ X#9.S#11);E#10} in A#14[(app A#15[(var X#8)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#8)] T#16)],
           A#12  |->  A#14[(app A#15 T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(\ X#9.S#11);E#10} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -ucp2->                       (letrec {X#8=(\ X#9.S#11);E#10} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#11);E#10} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -SR,cp-in1->                  (letrec {X#8=(\ X#9.S#11);E#10} in A#14[(app A#15[(\ X#9.S#11)] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
       ;X#8= (\ X#9.S#11)
       ;E#16
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)]
       ;X#8= (\ X#9.S#11)
       ;E#16
     in
        A#12[(\ X#9.S#11)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])
    -SR,cp-in1->                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(\ X#9.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#14=T#13;X#8=(\ X#9.S#11);E#16} in A#12[(var X#8)]),
           E#10  |->  {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16},
           E#15  |->  {X#8=(\ X#9.S#11);E#16}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(\ X#9.S#11);E#16} in A#12[(var X#8)])
    -ucp2->                       (letrec {X#14=T#13[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];X#8=(\ X#9.S#11);E#16} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(\ X#9.S#11);E#16} in A#12[(var X#8)])
    -SR,cp-in1->                  (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(\ X#9.S#11);E#16} in A#12[(\ X#9.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#2=(\ X#9.S#11);X#8=(var X#2);E#10} in A#12[(var X#8)])
    ,
     (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(\ X#9.S#11)])
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((\ X#9.S#11),[.]),
             ((letrec {X#8=(dummy3 );E#10} in A#12[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((\ X#9.S#11),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])
    -SR,cp-in1->                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(\ X#9.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6  |->  [.],
           S#5  |->  A#12[(var X#8)],
           X#1  |->  X#8,
           E#3  |->  {E#10},
           T#7  |->  [.],
           S#4  |->  (\ X#9.S#11)}

and instantiated rules:

                                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])
    -ucp2->                       (letrec {X#2=(\ X#9.S#11);X#8=(var X#2);E#10} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])
    -SR,cp-in1->                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(\ X#9.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=T#7[(var X#2)];X#2=S#4;X#8=(\ X#9.S#11);E#13} in A#12[(var X#8)])
    ,
     (letrec {X#1=T#7[S#4];X#8=(\ X#9.S#11);E#13} in A#12[(\ X#9.S#11)])
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];X#8=(\ X#9.S#11);E#13} in A#12[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-in1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])
    -SR,cp-in1->                  (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(\ X#9.S#11)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#8)],
           E#10  |->  {X#1=T#7[S#4];E#13},
           E#3   |->  {X#8=(\ X#9.S#11);E#13}}

and instantiated rules:

                                  (letrec {X#1=T#7[S#4];X#8=(\ X#9.S#11);E#13} in A#12[(var X#8)])
    -ucp2->                       (letrec {X#1=T#7[(var X#2)];X#2=S#4;X#8=(\ X#9.S#11);E#13} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#1=T#7[S#4];X#8=(\ X#9.S#11);E#13} in A#12[(var X#8)])
    -SR,cp-in1->                  (letrec {X#1=T#7[S#4];X#8=(\ X#9.S#11);E#13} in A#12[(\ X#9.S#11)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (\ X#9.S#12)
       ;E#11
       ;VV#14|X#10,(var X#8)|
     in
        A#16[(app A#17[(var X#10)] T#18[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
     )
    ,
     (letrec
        X#8= (\ X#9.S#12)
       ;E#11
       ;VV#14|X#10,(var X#8)|
     in
        A#16[(app A#17[(\ X#9.S#12)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#13,T#15,T#6}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#16[(app A#17[[.]] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#16[(app A#17[(var X#10)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#10)] T#18)],
           A#13  |->  A#16[(app A#17 T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#16[(app A#17[(var X#10)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -ucp2->                       (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#16[(app A#17[(var X#10)] T#18[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#16[(app A#17[(var X#10)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#16[(app A#17[(\ X#9.S#12)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
       ;X#8= (\ X#9.S#12)
       ;E#18
       ;VV#14|X#10,(var X#8)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)]
       ;X#8= (\ X#9.S#12)
       ;E#18
       ;VV#14|X#10,(var X#8)|
     in
        A#13[(\ X#9.S#12)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6   |->  (letrec {X#16=T#15;X#8=(\ X#9.S#12);E#18;VV#14|X#10,(var X#8)|} in A#13[(var X#10)]),
           E#11  |->  {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18},
           E#17  |->  {X#8=(\ X#9.S#12);E#18;VV#14|X#10,(var X#8)|}}

and instantiated rules:

                                  (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(\ X#9.S#12);E#18;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -ucp2->                       (letrec {X#16=T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];X#8=(\ X#9.S#12);E#18;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(\ X#9.S#12);E#18;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(\ X#9.S#12);E#18;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#9.S#12)
       ;X#8= (var X#2)
       ;E#11
       ;VV#14|X#10,(var X#8)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((\ X#9.S#12),[.]),
             ((letrec {X#8=(dummy3 );E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((\ X#9.S#12),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6  |->  [.],
           S#5  |->  A#13[(var X#10)],
           X#1  |->  X#8,
           E#3  |->  {E#11;VV#14|X#10,(var X#8)|},
           T#7  |->  [.],
           S#4  |->  (\ X#9.S#12)}

and instantiated rules:

                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -ucp2->                       (letrec {X#2=(\ X#9.S#12);X#8=(var X#2);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= T#7[(var X#2)]
       ;X#2= S#4
       ;X#8= (\ X#9.S#12)
       ;E#15
       ;VV#14|X#10,(var X#8)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#1= T#7[S#4]
       ;X#8= (\ X#9.S#12)
       ;E#15
       ;VV#14|X#10,(var X#8)|
     in
        A#13[(\ X#9.S#12)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];X#8=(\ X#9.S#12);E#15;VV#14|X#10,(var X#8)|} in A#13[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#10)],
           E#11  |->  {X#1=T#7[S#4];E#15},
           E#3   |->  {X#8=(\ X#9.S#12);E#15;VV#14|X#10,(var X#8)|}}

and instantiated rules:

                                  (letrec {X#1=T#7[S#4];X#8=(\ X#9.S#12);E#15;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -ucp2->                       (letrec {X#1=T#7[(var X#2)];X#2=S#4;X#8=(\ X#9.S#12);E#15;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#1=T#7[S#4];X#8=(\ X#9.S#12);E#15;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#1=T#7[S#4];X#8=(\ X#9.S#12);E#15;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#2)
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#13[(var X#10)]
     )
    ,
     (letrec {X#10=(var X#8);X#8=(\ X#9.S#12);E#11} in A#13[(\ X#9.S#12)])
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#8),[.]),
             ((letrec {X#10=(dummy3 );X#8=(\ X#9.S#12);E#11} in A#13[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           VV#14|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11},
           T#7          |->  [.],
           S#4          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#10=(var X#8);X#8=(\ X#9.S#12);E#11} in A#13[(var X#10)])
    -ucp2->                       (letrec {X#10=(var X#2);X#2=(var X#8);X#8=(\ X#9.S#12);E#11} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#8);X#8=(\ X#9.S#12);E#11} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#10=(var X#8);X#8=(\ X#9.S#12);E#11} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#2)
       ;X#2= (var X#16)
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;VV#17|X#16,(var X#8)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#10= (var X#16)
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;VV#17|X#16,(var X#8)|
     in
        A#13[(\ X#9.S#12)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#16),[.]),
             ((letrec {X#10=(dummy3 );X#8=(\ X#9.S#12);E#11;VV#17|X#16,(var X#8)|} in A#13[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#16),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           VV#14|.1,.2| |-> {[.1]=(var X#16);VV#17|X#16,[.2]|},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;VV#17|X#16,(var X#8)|},
           T#7          |->  [.],
           S#4          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#10=(var X#16);X#8=(\ X#9.S#12);E#11;VV#17|X#16,(var X#8)|} in A#13[(var X#10)])
    -ucp2->                       (letrec {X#10=(var X#2);X#2=(var X#16);X#8=(\ X#9.S#12);E#11;VV#17|X#16,(var X#8)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#10=(var X#16);X#8=(\ X#9.S#12);E#11;VV#17|X#16,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#10=(var X#16);X#8=(\ X#9.S#12);E#11;VV#17|X#16,(var X#8)|} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#2)
       ;X#2= (var X#17)
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;VV#18|X#10,(var X#16)|
       ;VV#19|X#17,(var X#8)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#16= (var X#17)
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;VV#18|X#10,(var X#16)|
       ;VV#19|X#17,(var X#8)|
     in
        A#13[(\ X#9.S#12)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#17),[.]),
             ((letrec {X#16=(dummy3 );X#8=(\ X#9.S#12);E#11;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|} in A#13[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           VV#14|.1,.2| |-> {X#16=(var X#17);VV#18|[.1],(var X#16)|;VV#19|X#17,[.2]|},
           X#1          |->  X#16,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|},
           T#7          |->  [.],
           S#4          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#16=(var X#17);X#8=(\ X#9.S#12);E#11;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|} in A#13[(var X#10)])
    -ucp2->                       (letrec {X#16=(var X#2);X#2=(var X#17);X#8=(\ X#9.S#12);E#11;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#16=(var X#17);X#8=(\ X#9.S#12);E#11;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#16=(var X#17);X#8=(\ X#9.S#12);E#11;VV#18|X#10,(var X#16)|;VV#19|X#17,(var X#8)|} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#2)
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;VV#17|X#10,(var X#16)|
     in
        A#13[(var X#10)]
     )
    ,
     (letrec
        X#16= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;VV#17|X#10,(var X#16)|
     in
        A#13[(\ X#9.S#12)]
     )
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#8),[.]),
             ((letrec {X#16=(dummy3 );X#8=(\ X#9.S#12);E#11;VV#17|X#10,(var X#16)|} in A#13[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#13[[.]]),
             ((var X#8),[.])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-in2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(\ X#9.S#12)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;VV#14|X#10,(var X#8)|} in A#13[(var X#10)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#13[[.]]),((var X#8),[.])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#10)],
           VV#14|.1,.2| |-> {X#16=[.2];VV#17|[.1],(var X#16)|},
           X#1          |->  X#16,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;VV#17|X#10,(var X#16)|},
           T#7          |->  [.],
           S#4          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#16=(var X#8);X#8=(\ X#9.S#12);E#11;VV#17|X#10,(var X#16)|} in A#13[(var X#10)])
    -ucp2->                       (letrec {X#16=(var X#2);X#2=(var X#8);X#8=(\ X#9.S#12);E#11;VV#17|X#10,(var X#16)|} in A#13[(var X#10)])
    ................................................................................
                                  (letrec {X#16=(var X#8);X#8=(\ X#9.S#12);E#11;VV#17|X#10,(var X#16)|} in A#13[(var X#10)])
    -SR,cp-in2->                  (letrec {X#16=(var X#8);X#8=(\ X#9.S#12);E#11;VV#17|X#10,(var X#16)|} in A#13[(\ X#9.S#12)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (\ X#9.S#12)
       ;E#11
       ;EE#15[X#10,A#13[(var X#8)]]
     in
        A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
     )
    ,
     (letrec
        X#8= (\ X#9.S#12)
       ;E#11
       ;EE#15[X#10,A#13[(\ X#9.S#12)]]
     in
        A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#14,T#16,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#17[(app A#18[[.]] T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)])]),
             ((var X#10),A#17[(app A#18[[.]] T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)])])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#17[(app A#18[(var X#10)] T#19)]),
           T#16  |->  A#17[(app A#18[(var X#10)] T#19)],
           A#14  |->  A#17[(app A#18 T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -ucp2->                       (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#17[(app A#18[(var X#10)] T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
       ;X#8= (\ X#9.S#12)
       ;E#19
       ;EE#15[X#10,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)]
       ;X#8= (\ X#9.S#12)
       ;E#19
       ;EE#15[X#10,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#17=T#16;X#8=(\ X#9.S#12);E#19;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)]),
           E#11  |->  {X#17=T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#19},
           E#18  |->  {X#8=(\ X#9.S#12);E#19;EE#15[X#10,A#13[(var X#8)]]}}

and instantiated rules:

                                  (letrec {X#17=T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(\ X#9.S#12);E#19;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#17=T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];X#8=(\ X#9.S#12);E#19;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(\ X#9.S#12);E#19;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(\ X#9.S#12);E#19;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[A#22[(app A#23[(\ X#9.S#12)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#21,A#19,T#16,T#6,A#13,A#20}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#22[(app A#23[[.]] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#20[A#22[(app A#23[(var X#8)] T#24)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {[.1]=A#20[[.2]]},
           X#17         |->  X#10,
           E#18         |->  {X#8=(\ X#9.S#12);E#11},
           A#19         |->  A#20,
           T#16         |->  A#20[A#22[(app A#23[(var X#8)] T#24)]],
           T#21         |->  A#22[(app A#23[(var X#8)] T#24)],
           A#13         |->  A#22[(app A#23 T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#20[A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#20[A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#20[A#22[(app A#23[(\ X#9.S#12)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[(app A#21[A#13[(var X#8)]] T#22[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[(app A#21[A#13[(\ X#9.S#12)]] T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,T#16,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#20[(app A#21[A#13[(var X#8)]] T#22)];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {[.1]=A#20[(app A#21[[.2]] T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)])]},
           X#17         |->  X#10,
           E#18         |->  {X#8=(\ X#9.S#12);E#11},
           T#16         |->  A#20[(app A#21[A#13[(var X#8)]] T#22)],
           A#19         |->  A#20[(app A#21 T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#20[(app A#21[A#13[(var X#8)]] T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#20[(app A#21[A#13[(var X#8)]] T#22[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[(app A#21[A#13[(var X#8)]] T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#20[(app A#21[A#13[(\ X#9.S#12)]] T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#20[(app A#21[(var X#8)] T#22[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#20[(app A#21[(\ X#9.S#12)] T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#16,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#20[(app A#21[[.]] T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#20[(app A#21[(var X#8)] T#22)];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#17         |->  X#10,
           E#18         |->  {X#8=(\ X#9.S#12);E#11},
           A#19         |->  [.],
           T#16         |->  A#20[(app A#21[(var X#8)] T#22)],
           A#13         |->  A#20[(app A#21 T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#20[(app A#21[(var X#8)] T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#20[(app A#21[(var X#8)] T#22[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#20[(app A#21[(var X#8)] T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#20[(app A#21[(\ X#9.S#12)] T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#20,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#20,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,T#16,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#22[(app A#23[(var X#20)] T#24)];X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(var X#8)]]} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {[.1]=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];EE#21[X#20,[.2]]},
           X#17         |->  X#10,
           E#18         |->  {X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(var X#8)]]},
           T#16         |->  A#22[(app A#23[(var X#20)] T#24)],
           A#19         |->  A#22[(app A#23 T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(var X#8)]]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#22[(app A#23[(var X#20)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#20,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#21,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#20= A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#22[X#10,(var X#20)]
       ;EE#23[X#21,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,T#16,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26)];X#8=(\ X#9.S#12);E#11;EE#22[X#10,(var X#20)];EE#23[X#21,A#13[(var X#8)]]} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])];EE#22[[.1],(var X#20)];EE#23[X#21,[.2]]},
           X#17         |->  X#20,
           E#18         |->  {X#8=(\ X#9.S#12);E#11;EE#22[X#10,(var X#20)];EE#23[X#21,A#13[(var X#8)]]},
           T#16         |->  A#24[(app A#25[(var X#21)] T#26)],
           A#19         |->  A#24[(app A#25 T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#22[X#10,(var X#20)];EE#23[X#21,A#13[(var X#8)]]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#22[X#10,(var X#20)];EE#23[X#21,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#22[X#10,(var X#20)];EE#23[X#21,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#20=A#24[(app A#25[(var X#21)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#22[X#10,(var X#20)];EE#23[X#21,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[A#24[(app A#25[(var X#8)] T#26[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#10,(var X#20)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#20= A#22[A#24[(app A#25[(\ X#9.S#12)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#10,(var X#20)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#23,A#19,T#16,T#6,A#13,A#22}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#24[(app A#25[[.]] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#20=A#22[A#24[(app A#25[(var X#8)] T#26)]];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {X#20=A#22[[.2]];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]},
           A#19         |->  A#22,
           T#16         |->  A#22[A#24[(app A#25[(var X#8)] T#26)]],
           T#23         |->  A#24[(app A#25[(var X#8)] T#26)],
           A#13         |->  A#24[(app A#25 T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#20=A#22[A#24[(app A#25[(var X#8)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#20=A#22[A#24[(app A#25[(var X#8)] T#26[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#20=A#22[A#24[(app A#25[(var X#8)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#20=A#22[A#24[(app A#25[(\ X#9.S#12)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app A#23[A#13[(var X#8)]] T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#10,(var X#20)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#20= A#22[(app A#23[A#13[(\ X#9.S#12)]] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#10,(var X#20)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#19,T#16,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#20=A#22[(app A#23[A#13[(var X#8)]] T#24)];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {X#20=A#22[(app A#23[[.2]] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]},
           T#16         |->  A#22[(app A#23[A#13[(var X#8)]] T#24)],
           A#19         |->  A#22[(app A#23 T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app A#23[A#13[(var X#8)]] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#20=A#22[(app A#23[A#13[(var X#8)]] T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#20=A#22[(app A#23[A#13[(var X#8)]] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#20=A#22[(app A#23[A#13[(\ X#9.S#12)]] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#20= A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#10,(var X#20)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#20= A#22[(app A#23[(\ X#9.S#12)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#21[X#10,(var X#20)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#16,T#6,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#22[(app A#23[[.]] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#20=A#22[(app A#23[(var X#8)] T#24)];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)]),
           EE#15[.1,.2] |-> {X#20=[.2];EE#21[[.1],(var X#20)]},
           X#17         |->  X#20,
           E#18         |->  {X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]},
           A#19         |->  [.],
           T#16         |->  A#22[(app A#23[(var X#8)] T#24)],
           A#13         |->  A#22[(app A#23 T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#20=A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#20=A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#20=A#22[(app A#23[(var X#8)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#20=A#22[(app A#23[(\ X#9.S#12)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#12);E#11;EE#21[X#10,(var X#20)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#9.S#12)
       ;X#8= (var X#2)
       ;E#11
       ;EE#15[X#10,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#8= (\ X#9.S#12)
       ;E#11
       ;EE#15[X#10,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((\ X#9.S#12),[.]),
             ((letrec {X#8=(dummy3 );E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((\ X#9.S#12),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6  |->  [.],
           S#5  |->  A#14[(var X#10)],
           X#1  |->  X#8,
           E#3  |->  {E#11;EE#15[X#10,A#13[(var X#8)]]},
           T#7  |->  [.],
           S#4  |->  (\ X#9.S#12)}

and instantiated rules:

                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#2=(\ X#9.S#12);X#8=(var X#2);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= T#7[(var X#2)]
       ;X#2= S#4
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#15[X#10,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#1= T#7[S#4]
       ;X#8= (\ X#9.S#12)
       ;E#16
       ;EE#15[X#10,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];X#8=(\ X#9.S#12);E#16;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#14[(var X#10)],
           E#11  |->  {X#1=T#7[S#4];E#16},
           E#3   |->  {X#8=(\ X#9.S#12);E#16;EE#15[X#10,A#13[(var X#8)]]}}

and instantiated rules:

                                  (letrec {X#1=T#7[S#4];X#8=(\ X#9.S#12);E#16;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#1=T#7[(var X#2)];X#2=S#4;X#8=(\ X#9.S#12);E#16;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#1=T#7[S#4];X#8=(\ X#9.S#12);E#16;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#1=T#7[S#4];X#8=(\ X#9.S#12);E#16;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#17[A#19[(var X#2)]]
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#17[A#19[(\ X#9.S#12)]]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#18,A#16,T#7,A#13,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#17[A#19[[.]]]),
             ((var X#8),A#17[A#19[[.]]]),
             ((letrec {X#10=A#17[A#19[(dummy3 )]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#17[A#19[[.]]]),
             ((var X#8),A#19[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11},
           A#16         |->  A#17,
           T#7          |->  A#17[A#19[[.]]],
           A#13         |->  A#19,
           T#18         |->  A#19[[.]],
           T#20         |->  [.],
           S#4          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#10=A#17[A#19[(var X#8)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#17[A#19[(var X#2)]];X#2=(var X#8);X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#17[A#19[(var X#8)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#17[A#19[(\ X#9.S#12)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#17[A#19[(var X#2)]]
       ;X#2= A#20[(var X#8)]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#17[A#19[A#20[(\ X#9.S#12)]]]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#18,A#16,T#7,A#13,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#17[A#19]),
             (A#20[(var X#8)],A#17[A#19]),
             ((letrec {X#10=A#17[A#19[(dummy3 )]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#20[(var X#8)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#17[A#19[[.]]]),
             ((var X#8),A#19[A#20[[.]]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11},
           A#16         |->  A#17,
           T#7          |->  A#17[A#19],
           A#13         |->  A#19[A#20],
           T#18         |->  A#19,
           S#4          |->  A#20[(var X#8)]}

and instantiated rules:

                                  (letrec {X#10=A#17[A#19[A#20[(var X#8)]]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#17[A#19[(var X#2)]];X#2=A#20[(var X#8)];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#17[A#19[A#20[(var X#8)]]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#17[A#19[A#20[(\ X#9.S#12)]]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#17[A#19[(app A#20[(var X#8)] T#21[(var X#2)])]]
       ;X#2= S#4
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#17[A#19[(app A#20[(\ X#9.S#12)] T#21[S#4])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#18,A#16,T#7,A#13,A#17}
   Delta2 = {}
   Delta3 = {((var X#2),A#17[A#19[(app A#20[(var X#8)] T#21)]]),
             (S#4,A#17[A#19[(app A#20[(var X#8)] T#21)]]),
             ((letrec {X#10=A#17[A#19[(app A#20[(var X#8)] T#21[(dummy3 )])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#17[A#19[(app A#20[(var X#8)] T#21[[.]])]]),
             ((var X#8),A#19[(app A#20[[.]] T#21[S#4])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11},
           A#16         |->  A#17,
           T#7          |->  A#17[A#19[(app A#20[(var X#8)] T#21)]],
           T#18         |->  A#19[(app A#20[(var X#8)] T#21)],
           A#13         |->  A#19[(app A#20 T#21[S#4])]}

and instantiated rules:

                                  (letrec {X#10=A#17[A#19[(app A#20[(var X#8)] T#21[S#4])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#17[A#19[(app A#20[(var X#8)] T#21[(var X#2)])]];X#2=S#4;X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#17[A#19[(app A#20[(var X#8)] T#21[S#4])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#17[A#19[(app A#20[(\ X#9.S#12)] T#21[S#4])]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#17[(var X#2)]
       ;X#2= A#13[(var X#8)]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#17[A#13[(\ X#9.S#12)]]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#16,T#7,A#13,A#17}
   Delta2 = {}
   Delta3 = {((var X#2),A#17[[.]]),
             (A#13[(var X#8)],A#17[[.]]),
             ((letrec {X#10=A#17[(dummy3 )];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#13[(var X#8)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#17[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11},
           A#16         |->  A#17,
           T#7          |->  A#17[[.]],
           T#18         |->  [.],
           S#4          |->  A#13[(var X#8)]}

and instantiated rules:

                                  (letrec {X#10=A#17[A#13[(var X#8)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#17[(var X#2)];X#2=A#13[(var X#8)];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#17[A#13[(var X#8)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#17[A#13[(\ X#9.S#12)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#17[(var X#2)]
       ;X#2= A#18[A#13[(var X#8)]]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#17[A#18[A#13[(\ X#9.S#12)]]]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#16,T#7,A#13,A#17}
   Delta2 = {}
   Delta3 = {((var X#2),A#17),
             (A#18[A#13[(var X#8)]],A#17),
             ((letrec {X#10=A#17[(dummy3 )];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#18[A#13[(var X#8)]],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#17[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=A#17[A#18[[.2]]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11},
           A#16         |->  A#17[A#18],
           T#7          |->  A#17,
           S#4          |->  A#18[A#13[(var X#8)]]}

and instantiated rules:

                                  (letrec {X#10=A#17[A#18[A#13[(var X#8)]]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#17[(var X#2)];X#2=A#18[A#13[(var X#8)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#17[A#18[A#13[(var X#8)]]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#17[A#18[A#13[(\ X#9.S#12)]]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#17[(app A#18[A#13[(var X#8)]] T#19[(var X#2)])]
       ;X#2= S#4
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#17[(app A#18[A#13[(\ X#9.S#12)]] T#19[S#4])]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#16,T#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),A#17[(app A#18[A#13[(var X#8)]] T#19)]),
             (S#4,A#17[(app A#18[A#13[(var X#8)]] T#19)]),
             ((letrec {X#10=A#17[(app A#18[A#13[(var X#8)]] T#19[(dummy3 )])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#17[(app A#18[A#13[(var X#8)]] T#19[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] T#19[S#4])]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11},
           T#7          |->  A#17[(app A#18[A#13[(var X#8)]] T#19)],
           A#16         |->  A#17[(app A#18 T#19[S#4])]}

and instantiated rules:

                                  (letrec {X#10=A#17[(app A#18[A#13[(var X#8)]] T#19[S#4])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#17[(app A#18[A#13[(var X#8)]] T#19[(var X#2)])];X#2=S#4;X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#17[(app A#18[A#13[(var X#8)]] T#19[S#4])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#17[(app A#18[A#13[(\ X#9.S#12)]] T#19[S#4])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#17[(var X#2)]
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec {X#10=A#17[(\ X#9.S#12)];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
  )

where

   Delta1 = {T#7,A#13,A#17}
   Delta2 = {}
   Delta3 = {((var X#2),A#17[[.]]),
             ((var X#8),A#17[[.]]),
             ((letrec {X#10=A#17[(dummy3 )];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#17[[.]]),
             ((var X#8),A#17[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11},
           A#16         |->  [.],
           A#13         |->  A#17,
           T#7          |->  A#17[[.]],
           T#18         |->  [.],
           S#4          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#10=A#17[(var X#8)];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#17[(var X#2)];X#2=(var X#8);X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#17[(var X#8)];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#17[(\ X#9.S#12)];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#17[(var X#2)]
       ;X#2= A#18[(var X#8)]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#17[A#18[(\ X#9.S#12)]]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#7,A#13,A#17}
   Delta2 = {}
   Delta3 = {((var X#2),A#17),
             (A#18[(var X#8)],A#17),
             ((letrec {X#10=A#17[(dummy3 )];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#18[(var X#8)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#17[[.]]),
             ((var X#8),A#17[A#18[[.]]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11},
           A#16         |->  [.],
           A#13         |->  A#17[A#18],
           T#7          |->  A#17,
           S#4          |->  A#18[(var X#8)]}

and instantiated rules:

                                  (letrec {X#10=A#17[A#18[(var X#8)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#17[(var X#2)];X#2=A#18[(var X#8)];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#17[A#18[(var X#8)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#17[A#18[(\ X#9.S#12)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#17[(app A#18[(var X#8)] T#19[(var X#2)])]
       ;X#2= S#4
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#17[(app A#18[(\ X#9.S#12)] T#19[S#4])]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),A#17[(app A#18[(var X#8)] T#19)]),
             (S#4,A#17[(app A#18[(var X#8)] T#19)]),
             ((letrec {X#10=A#17[(app A#18[(var X#8)] T#19[(dummy3 )])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#17[(app A#18[(var X#8)] T#19[[.]])]),
             ((var X#8),A#17[(app A#18[[.]] T#19[S#4])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11},
           A#16         |->  [.],
           T#7          |->  A#17[(app A#18[(var X#8)] T#19)],
           A#13         |->  A#17[(app A#18 T#19[S#4])]}

and instantiated rules:

                                  (letrec {X#10=A#17[(app A#18[(var X#8)] T#19[S#4])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#17[(app A#18[(var X#8)] T#19[(var X#2)])];X#2=S#4;X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#17[(app A#18[(var X#8)] T#19[S#4])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#17[(app A#18[(\ X#9.S#12)] T#19[S#4])];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#2)
       ;X#2= A#16[A#13[(var X#8)]]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#16[A#13[(\ X#9.S#12)]]
       ;X#8= (\ X#9.S#12)
       ;E#11
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             (A#16[A#13[(var X#8)]],[.]),
             ((letrec {X#10=(dummy3 );X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#16[A#13[(var X#8)]],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11},
           T#7          |->  [.],
           S#4          |->  A#16[A#13[(var X#8)]]}

and instantiated rules:

                                  (letrec {X#10=A#16[A#13[(var X#8)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=(var X#2);X#2=A#16[A#13[(var X#8)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#16[A#13[(var X#8)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#16[A#13[(\ X#9.S#12)]];X#8=(\ X#9.S#12);E#11} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#19[(var X#2)]
       ;X#2= (var X#17)
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#17,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#19[(var X#17)]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#17,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#16,T#7,A#13,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[[.]]),
             ((var X#17),A#19[[.]]),
             ((letrec {X#10=A#19[(dummy3 )];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=A#19[(var X#17)];EE#18[X#17,[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]},
           A#16         |->  A#19,
           T#7          |->  A#19[[.]],
           T#20         |->  [.],
           S#4          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#10=A#19[(var X#17)];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#19[(var X#2)];X#2=(var X#17);X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#19[(var X#17)];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#19[(var X#17)];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#19[(var X#2)]
       ;X#2= A#20[(var X#17)]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#17,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#19[A#20[(var X#17)]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#17,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#16,T#7,A#13,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19),
             (A#20[(var X#17)],A#19),
             ((letrec {X#10=A#19[(dummy3 )];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#20[(var X#17)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=A#19[A#20[(var X#17)]];EE#18[X#17,[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]},
           A#16         |->  A#19[A#20],
           T#7          |->  A#19,
           S#4          |->  A#20[(var X#17)]}

and instantiated rules:

                                  (letrec {X#10=A#19[A#20[(var X#17)]];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#19[(var X#2)];X#2=A#20[(var X#17)];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#19[A#20[(var X#17)]];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#19[A#20[(var X#17)]];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#19[(app A#20[(var X#17)] T#21[(var X#2)])]
       ;X#2= S#4
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#17,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#19[(app A#20[(var X#17)] T#21[S#4])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#17,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#16,T#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[(app A#20[(var X#17)] T#21)]),
             (S#4,A#19[(app A#20[(var X#17)] T#21)]),
             ((letrec {X#10=A#19[(app A#20[(var X#17)] T#21[(dummy3 )])];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[(app A#20[(var X#17)] T#21[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] T#21[S#4])];EE#18[X#17,[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]},
           T#7          |->  A#19[(app A#20[(var X#17)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[S#4])]}

and instantiated rules:

                                  (letrec {X#10=A#19[(app A#20[(var X#17)] T#21[S#4])];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=A#19[(app A#20[(var X#17)] T#21[(var X#2)])];X#2=S#4;X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#19[(app A#20[(var X#17)] T#21[S#4])];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#19[(app A#20[(var X#17)] T#21[S#4])];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#2)
       ;X#2= A#16[(var X#17)]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#17,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#10= A#16[(var X#17)]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#17,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             (A#16[(var X#17)],[.]),
             ((letrec {X#10=(dummy3 );X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#16[(var X#17)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {[.1]=A#16[(var X#17)];EE#18[X#17,[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]},
           T#7          |->  [.],
           S#4          |->  A#16[(var X#17)]}

and instantiated rules:

                                  (letrec {X#10=A#16[(var X#17)];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#10=(var X#2);X#2=A#16[(var X#17)];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#16[(var X#17)];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#10=A#16[(var X#17)];X#8=(\ X#9.S#12);E#11;EE#18[X#17,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(var X#2)]
       ;X#2= (var X#18)
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#20[X#18,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= A#21[(var X#18)]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#20[X#18,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#16,T#7,A#13,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),A#21[[.]]),
             ((var X#18),A#21[[.]]),
             ((letrec {X#17=A#21[(dummy3 )];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#18),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#21[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=A#21[(var X#18)];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#1          |->  X#17,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]},
           A#16         |->  A#21,
           T#7          |->  A#21[[.]],
           T#22         |->  [.],
           S#4          |->  (var X#18)}

and instantiated rules:

                                  (letrec {X#17=A#21[(var X#18)];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#17=A#21[(var X#2)];X#2=(var X#18);X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=A#21[(var X#18)];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=A#21[(var X#18)];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(var X#2)]
       ;X#2= A#22[(var X#18)]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#20[X#18,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= A#21[A#22[(var X#18)]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#20[X#18,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#16,T#7,A#13,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),A#21),
             (A#22[(var X#18)],A#21),
             ((letrec {X#17=A#21[(dummy3 )];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#22[(var X#18)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#21[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=A#21[A#22[(var X#18)]];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#1          |->  X#17,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]},
           A#16         |->  A#21[A#22],
           T#7          |->  A#21,
           S#4          |->  A#22[(var X#18)]}

and instantiated rules:

                                  (letrec {X#17=A#21[A#22[(var X#18)]];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#17=A#21[(var X#2)];X#2=A#22[(var X#18)];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=A#21[A#22[(var X#18)]];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=A#21[A#22[(var X#18)]];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(var X#2)])]
       ;X#2= S#4
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#20[X#18,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[S#4])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#20[X#18,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#16,T#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),A#21[(app A#22[(var X#18)] T#23)]),
             (S#4,A#21[(app A#22[(var X#18)] T#23)]),
             ((letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(dummy3 )])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#21[(app A#22[(var X#18)] T#23[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] T#23[S#4])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#1          |->  X#17,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]},
           T#7          |->  A#21[(app A#22[(var X#18)] T#23)],
           A#16         |->  A#21[(app A#22 T#23[S#4])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[S#4])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(var X#2)])];X#2=S#4;X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[S#4])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[S#4])];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#2)
       ;X#2= A#16[(var X#18)]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#20[X#18,A#13[(var X#8)]]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= A#16[(var X#18)]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#19[X#10,(var X#17)]
       ;EE#20[X#18,A#13[(\ X#9.S#12)]]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             (A#16[(var X#18)],[.]),
             ((letrec {X#17=(dummy3 );X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#16[(var X#18)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=A#16[(var X#18)];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#1          |->  X#17,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]},
           T#7          |->  [.],
           S#4          |->  A#16[(var X#18)]}

and instantiated rules:

                                  (letrec {X#17=A#16[(var X#18)];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#17=(var X#2);X#2=A#16[(var X#18)];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=A#16[(var X#18)];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=A#16[(var X#18)];X#8=(\ X#9.S#12);E#11;EE#19[X#10,(var X#17)];EE#20[X#18,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[A#21[(var X#2)]]
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(\ X#9.S#12)]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#20,A#16,T#7,A#13,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[A#21[[.]]]),
             ((var X#8),A#19[A#21[[.]]]),
             ((letrec {X#17=A#19[A#21[(dummy3 )]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[A#21[[.]]]),
             ((var X#8),A#21[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]},
           A#16         |->  A#19,
           T#7          |->  A#19[A#21[[.]]],
           A#13         |->  A#21,
           T#20         |->  A#21[[.]],
           T#22         |->  [.],
           S#4          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(var X#8)]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#17=A#19[A#21[(var X#2)]];X#2=(var X#8);X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(var X#8)]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(\ X#9.S#12)]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[A#21[(var X#2)]]
       ;X#2= A#22[(var X#8)]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= A#19[A#21[A#22[(\ X#9.S#12)]]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#20,A#16,T#7,A#13,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[A#21]),
             (A#22[(var X#8)],A#19[A#21]),
             ((letrec {X#17=A#19[A#21[(dummy3 )]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#22[(var X#8)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[A#21[[.]]]),
             ((var X#8),A#21[A#22[[.]]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]},
           A#16         |->  A#19,
           T#7          |->  A#19[A#21],
           A#13         |->  A#21[A#22],
           T#20         |->  A#21,
           S#4          |->  A#22[(var X#8)]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[A#22[(var X#8)]]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#17=A#19[A#21[(var X#2)]];X#2=A#22[(var X#8)];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[A#22[(var X#8)]]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[A#22[(\ X#9.S#12)]]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[A#21[(app A#22[(var X#8)] T#23[(var X#2)])]]
       ;X#2= S#4
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(app A#22[(\ X#9.S#12)] T#23[S#4])]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#20,A#16,T#7,A#13,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[A#21[(app A#22[(var X#8)] T#23)]]),
             (S#4,A#19[A#21[(app A#22[(var X#8)] T#23)]]),
             ((letrec {X#17=A#19[A#21[(app A#22[(var X#8)] T#23[(dummy3 )])]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[A#21[(app A#22[(var X#8)] T#23[[.]])]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[S#4])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]},
           A#16         |->  A#19,
           T#7          |->  A#19[A#21[(app A#22[(var X#8)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#13         |->  A#21[(app A#22 T#23[S#4])]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#8)] T#23[S#4])]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#17=A#19[A#21[(app A#22[(var X#8)] T#23[(var X#2)])]];X#2=S#4;X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#8)] T#23[S#4])]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(app A#22[(\ X#9.S#12)] T#23[S#4])]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(var X#2)]
       ;X#2= A#13[(var X#8)]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= A#19[A#13[(\ X#9.S#12)]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#16,T#7,A#13,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[[.]]),
             (A#13[(var X#8)],A#19[[.]]),
             ((letrec {X#17=A#19[(dummy3 )];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#13[(var X#8)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]},
           A#16         |->  A#19,
           T#7          |->  A#19[[.]],
           T#20         |->  [.],
           S#4          |->  A#13[(var X#8)]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#13[(var X#8)]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#17=A#19[(var X#2)];X#2=A#13[(var X#8)];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=A#19[A#13[(var X#8)]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#13[(\ X#9.S#12)]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(var X#2)]
       ;X#2= A#20[A#13[(var X#8)]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= A#19[A#20[A#13[(\ X#9.S#12)]]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#16,T#7,A#13,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19),
             (A#20[A#13[(var X#8)]],A#19),
             ((letrec {X#17=A#19[(dummy3 )];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#20[A#13[(var X#8)]],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=A#19[A#20[[.2]]];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]},
           A#16         |->  A#19[A#20],
           T#7          |->  A#19,
           S#4          |->  A#20[A#13[(var X#8)]]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#20[A#13[(var X#8)]]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#17=A#19[(var X#2)];X#2=A#20[A#13[(var X#8)]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=A#19[A#20[A#13[(var X#8)]]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#20[A#13[(\ X#9.S#12)]]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[A#13[(var X#8)]] T#21[(var X#2)])]
       ;X#2= S#4
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[A#13[(\ X#9.S#12)]] T#21[S#4])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#16,T#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[(app A#20[A#13[(var X#8)]] T#21)]),
             (S#4,A#19[(app A#20[A#13[(var X#8)]] T#21)]),
             ((letrec {X#17=A#19[(app A#20[A#13[(var X#8)]] T#21[(dummy3 )])];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[(app A#20[A#13[(var X#8)]] T#21[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] T#21[S#4])];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]},
           T#7          |->  A#19[(app A#20[A#13[(var X#8)]] T#21)],
           A#16         |->  A#19[(app A#20 T#21[S#4])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[A#13[(var X#8)]] T#21[S#4])];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#17=A#19[(app A#20[A#13[(var X#8)]] T#21[(var X#2)])];X#2=S#4;X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[A#13[(var X#8)]] T#21[S#4])];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[A#13[(\ X#9.S#12)]] T#21[S#4])];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(var X#2)]
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= A#19[(\ X#9.S#12)]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#7,A#13,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[[.]]),
             ((var X#8),A#19[[.]]),
             ((letrec {X#17=A#19[(dummy3 )];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[[.]]),
             ((var X#8),A#19[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]},
           A#16         |->  [.],
           A#13         |->  A#19,
           T#7          |->  A#19[[.]],
           T#20         |->  [.],
           S#4          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#17=A#19[(var X#8)];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#17=A#19[(var X#2)];X#2=(var X#8);X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=A#19[(var X#8)];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(\ X#9.S#12)];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(var X#2)]
       ;X#2= A#20[(var X#8)]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= A#19[A#20[(\ X#9.S#12)]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#7,A#13,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19),
             (A#20[(var X#8)],A#19),
             ((letrec {X#17=A#19[(dummy3 )];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#20[(var X#8)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[[.]]),
             ((var X#8),A#19[A#20[[.]]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]},
           A#16         |->  [.],
           A#13         |->  A#19[A#20],
           T#7          |->  A#19,
           S#4          |->  A#20[(var X#8)]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#20[(var X#8)]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#17=A#19[(var X#2)];X#2=A#20[(var X#8)];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=A#19[A#20[(var X#8)]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#20[(\ X#9.S#12)]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[(var X#8)] T#21[(var X#2)])]
       ;X#2= S#4
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(\ X#9.S#12)] T#21[S#4])]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {T#7,A#13}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[(app A#20[(var X#8)] T#21)]),
             (S#4,A#19[(app A#20[(var X#8)] T#21)]),
             ((letrec {X#17=A#19[(app A#20[(var X#8)] T#21[(dummy3 )])];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[(app A#20[(var X#8)] T#21[[.]])]),
             ((var X#8),A#19[(app A#20[[.]] T#21[S#4])]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]},
           A#16         |->  [.],
           T#7          |->  A#19[(app A#20[(var X#8)] T#21)],
           A#13         |->  A#19[(app A#20 T#21[S#4])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(var X#8)] T#21[S#4])];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#17=A#19[(app A#20[(var X#8)] T#21[(var X#2)])];X#2=S#4;X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(var X#8)] T#21[S#4])];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[(\ X#9.S#12)] T#21[S#4])];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (var X#2)
       ;X#2= A#16[A#13[(var X#8)]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
    ,
     (letrec
        X#17= A#16[A#13[(\ X#9.S#12)]]
       ;X#8= (\ X#9.S#12)
       ;E#11
       ;EE#18[X#10,(var X#17)]
     in
        A#14[(var X#10)]
     )
  )

where

   Delta1 = {A#13}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             (A#16[A#13[(var X#8)]],[.]),
             ((letrec {X#17=(dummy3 );X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#16[A#13[(var X#8)]],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#10),A#14[[.]]),
             ((var X#10),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(\ X#9.S#12)]]} in A#14[(var X#10)])
    and constraints: A#13/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#12);E#11;EE#15[X#10,A#13[(var X#8)]]} in A#14[(var X#10)])}
      Delta1=  {A#13}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#10),A#14[[.]]),((var X#10),A#14[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#14[(var X#10)],
           EE#15[.1,.2] |-> {X#17=A#16[[.2]];EE#18[[.1],(var X#17)]},
           X#1          |->  X#17,
           E#3          |->  {X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]},
           T#7          |->  [.],
           S#4          |->  A#16[A#13[(var X#8)]]}

and instantiated rules:

                                  (letrec {X#17=A#16[A#13[(var X#8)]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -ucp2->                       (letrec {X#17=(var X#2);X#2=A#16[A#13[(var X#8)]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    ................................................................................
                                  (letrec {X#17=A#16[A#13[(var X#8)]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    -SR,cp-e1->                   (letrec {X#17=A#16[A#13[(\ X#9.S#12)]];X#8=(\ X#9.S#12);E#11;EE#18[X#10,(var X#17)]} in A#14[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (\ X#9.S#13)
       ;E#12
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#19[(app A#20[(var X#10)] T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
     )
    ,
     (letrec
        X#8= (\ X#9.S#13)
       ;E#12
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#19[(app A#20[(var X#10)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#15,T#18,T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#19[(app A#20[[.]] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#19[(app A#20[[.]] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#19[(app A#20[(var X#10)] T#21)]),
           T#18  |->  A#19[(app A#20[(var X#10)] T#21)],
           A#15  |->  A#19[(app A#20 T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#19[(app A#20[(var X#10)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -ucp2->                       (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#19[(app A#20[(var X#10)] T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#19[(app A#20[(var X#10)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#19[(app A#20[(var X#10)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= T#18[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
       ;X#8= (\ X#9.S#13)
       ;E#21
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)]
       ;X#8= (\ X#9.S#13)
       ;E#21
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#19=T#18;X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           E#12  |->  {X#19=T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#21},
           E#20  |->  {X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|}}

and instantiated rules:

                                  (letrec {X#19=T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=T#18[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(\ X#9.S#13);E#21;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[A#24[(app A#25[(\ X#9.S#13)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#23,A#21,T#18,T#6,A#14,A#22}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#24[(app A#25[[.]] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#22[A#24[(app A#25[(var X#11)] T#26)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {[.1]=A#22[[.2]]},
           X#19         |->  X#10,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           A#21         |->  A#22,
           T#18         |->  A#22[A#24[(app A#25[(var X#11)] T#26)]],
           T#23         |->  A#24[(app A#25[(var X#11)] T#26)],
           A#14         |->  A#24[(app A#25 T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#22[A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[A#24[(app A#25[(\ X#9.S#13)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(app A#23[A#14[(var X#11)]] T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(app A#23[A#14[(\ X#9.S#13)]] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,T#18,T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#22[(app A#23[A#14[(var X#11)]] T#24)];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {[.1]=A#22[(app A#23[[.2]] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]},
           X#19         |->  X#10,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           T#18         |->  A#22[(app A#23[A#14[(var X#11)]] T#24)],
           A#21         |->  A#22[(app A#23 T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[(app A#23[A#14[(var X#11)]] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#22[(app A#23[A#14[(var X#11)]] T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(app A#23[A#14[(var X#11)]] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[(app A#23[A#14[(\ X#9.S#13)]] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#22[(app A#23[(var X#11)] T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#22[(app A#23[(\ X#9.S#13)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#18,T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#22[(app A#23[[.]] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#22[(app A#23[(var X#11)] T#24)];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#19         |->  X#10,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           A#21         |->  [.],
           T#18         |->  A#22[(app A#23[(var X#11)] T#24)],
           A#14         |->  A#22[(app A#23 T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#22[(app A#23[(var X#11)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#22[(app A#23[(var X#11)] T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#22[(app A#23[(var X#11)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#22[(app A#23[(\ X#9.S#13)] T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#24[(app A#25[(var X#22)] T#26[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#22,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#24[(app A#25[(var X#22)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#22,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,T#18,T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#10=A#24[(app A#25[(var X#22)] T#26)];X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {[.1]=A#24[(app A#25[(var X#22)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])];EE#23[X#22,[.2]]},
           X#19         |->  X#10,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           T#18         |->  A#24[(app A#25[(var X#22)] T#26)],
           A#21         |->  A#24[(app A#25 T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#10=A#24[(app A#25[(var X#22)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#24[(app A#25[(var X#22)] T#26[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#24[(app A#25[(var X#22)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#24[(app A#25[(var X#22)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#22,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#22= A#26[(app A#27[(var X#23)] T#28[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#24[X#10,(var X#22)]
       ;EE#25[X#23,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#22= A#26[(app A#27[(var X#23)] T#28[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#24[X#10,(var X#22)]
       ;EE#25[X#23,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,T#18,T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#22=A#26[(app A#27[(var X#23)] T#28)];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {X#22=A#26[(app A#27[(var X#23)] T#28[(letrec {X#1=T#7[S#4];E#3} in S#5)])];EE#24[[.1],(var X#22)];EE#25[X#23,[.2]]},
           X#19         |->  X#22,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           T#18         |->  A#26[(app A#27[(var X#23)] T#28)],
           A#21         |->  A#26[(app A#27 T#28[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#22=A#26[(app A#27[(var X#23)] T#28[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#22=A#26[(app A#27[(var X#23)] T#28[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#22=A#26[(app A#27[(var X#23)] T#28[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#22=A#26[(app A#27[(var X#23)] T#28[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#24[X#10,(var X#22)];EE#25[X#23,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#22= A#24[A#26[(app A#27[(var X#11)] T#28[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#22= A#24[A#26[(app A#27[(\ X#9.S#13)] T#28[(letrec {X#1=T#7[S#4];E#3} in S#5)])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#25,A#21,T#18,T#6,A#14,A#24}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#26[(app A#27[[.]] T#28[(letrec {X#1=T#7[S#4];E#3} in S#5)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#22=A#24[A#26[(app A#27[(var X#11)] T#28)]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {X#22=A#24[[.2]];EE#23[[.1],(var X#22)]},
           X#19         |->  X#22,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|},
           A#21         |->  A#24,
           T#18         |->  A#24[A#26[(app A#27[(var X#11)] T#28)]],
           T#25         |->  A#26[(app A#27[(var X#11)] T#28)],
           A#14         |->  A#26[(app A#27 T#28[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#22=A#24[A#26[(app A#27[(var X#11)] T#28[(letrec {X#1=T#7[S#4];E#3} in S#5)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#22=A#24[A#26[(app A#27[(var X#11)] T#28[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#22=A#24[A#26[(app A#27[(var X#11)] T#28[(letrec {X#1=T#7[S#4];E#3} in S#5)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#22=A#24[A#26[(app A#27[(\ X#9.S#13)] T#28[(letrec {X#1=T#7[S#4];E#3} in S#5)])]];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#22= A#24[(app A#25[A#14[(var X#11)]] T#26[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#22= A#24[(app A#25[A#14[(\ X#9.S#13)]] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#21,T#18,T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#22=A#24[(app A#25[A#14[(var X#11)]] T#26)];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {X#22=A#24[(app A#25[[.2]] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])];EE#23[[.1],(var X#22)]},
           X#19         |->  X#22,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|},
           T#18         |->  A#24[(app A#25[A#14[(var X#11)]] T#26)],
           A#21         |->  A#24[(app A#25 T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#22=A#24[(app A#25[A#14[(var X#11)]] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#22=A#24[(app A#25[A#14[(var X#11)]] T#26[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#22=A#24[(app A#25[A#14[(var X#11)]] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#22=A#24[(app A#25[A#14[(\ X#9.S#13)]] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#22= A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#22= A#24[(app A#25[(\ X#9.S#13)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#23[X#10,(var X#22)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#18,T#6,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#24[(app A#25[[.]] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#22=A#24[(app A#25[(var X#11)] T#26)];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),
           EE#16[.1,.2] |-> {X#22=[.2];EE#23[[.1],(var X#22)]},
           X#19         |->  X#22,
           E#20         |->  {X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|},
           A#21         |->  [.],
           T#18         |->  A#24[(app A#25[(var X#11)] T#26)],
           A#14         |->  A#24[(app A#25 T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#22=A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#22=A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#22=A#24[(app A#25[(var X#11)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#22=A#24[(app A#25[(\ X#9.S#13)] T#26[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(\ X#9.S#13);E#12;EE#23[X#10,(var X#22)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (\ X#9.S#13)
       ;X#8= (var X#2)
       ;E#12
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#8= (\ X#9.S#13)
       ;E#12
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((\ X#9.S#13),[.]),
             ((letrec {X#8=(dummy3 );E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((\ X#9.S#13),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6  |->  [.],
           S#5  |->  A#15[(var X#10)],
           X#1  |->  X#8,
           E#3  |->  {E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           T#7  |->  [.],
           S#4  |->  (\ X#9.S#13)}

and instantiated rules:

                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#2=(\ X#9.S#13);X#8=(var X#2);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= T#7[(var X#2)]
       ;X#2= S#4
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#1= T#7[S#4]
       ;X#8= (\ X#9.S#13)
       ;E#18
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#15[(var X#10)],
           E#12  |->  {X#1=T#7[S#4];E#18},
           E#3   |->  {X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|}}

and instantiated rules:

                                  (letrec {X#1=T#7[S#4];X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#1=T#7[(var X#2)];X#2=S#4;X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#1=T#7[S#4];X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#1=T#7[S#4];X#8=(\ X#9.S#13);E#18;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= (var X#2)
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#16[X#10,A#14[(var X#11)]]
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#11= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#8),[.]),
             ((letrec {X#11=(dummy3 );X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]]} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=[.2]},
           X#1          |->  X#11,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]]},
           T#7          |->  [.],
           S#4          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#11=(var X#8);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]]} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#11=(var X#2);X#2=(var X#8);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]]} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#11=(var X#8);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]]} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#11=(var X#8);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]]} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= (var X#2)
       ;X#2= (var X#19)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#11= (var X#19)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#20|X#19,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#19),[.]),
             ((letrec {X#11=(dummy3 );X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#19),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {[.1]=(var X#19);VV#20|X#19,[.2]|},
           X#1          |->  X#11,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#19,(var X#8)|},
           T#7          |->  [.],
           S#4          |->  (var X#19)}

and instantiated rules:

                                  (letrec {X#11=(var X#19);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#11=(var X#2);X#2=(var X#19);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#11=(var X#19);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#11=(var X#19);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#20|X#19,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#2)
       ;X#2= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#21|X#11,(var X#19)|
       ;VV#22|X#20,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#20),[.]),
             ((letrec {X#19=(dummy3 );X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#20),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=(var X#20);VV#21|[.1],(var X#19)|;VV#22|X#20,[.2]|},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|},
           T#7          |->  [.],
           S#4          |->  (var X#20)}

and instantiated rules:

                                  (letrec {X#19=(var X#20);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=(var X#2);X#2=(var X#20);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#20);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#20);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#21|X#11,(var X#19)|;VV#22|X#20,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#2)
       ;X#2= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#16[X#10,A#14[(var X#11)]]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= (var X#8)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#16[X#10,A#14[(\ X#9.S#13)]]
       ;VV#20|X#11,(var X#19)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             ((var X#8),[.]),
             ((letrec {X#19=(dummy3 );X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           VV#17|.1,.2| |-> {X#19=[.2];VV#20|[.1],(var X#19)|},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#11,(var X#19)|},
           T#7          |->  [.],
           S#4          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#19=(var X#8);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=(var X#2);X#2=(var X#8);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=(var X#8);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=(var X#8);X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#20|X#11,(var X#19)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#19[A#21[(var X#2)]]
       ;X#2= (var X#11)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#19[A#21[(\ X#9.S#13)]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#20,A#18,T#7,A#14,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[A#21[[.]]]),
             ((var X#11),A#19[A#21[[.]]]),
             ((letrec {X#10=A#19[A#21[(dummy3 )]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#11),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[A#21[[.]]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#21[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           A#18         |->  A#19,
           T#7          |->  A#19[A#21[[.]]],
           A#14         |->  A#21,
           T#20         |->  A#21[[.]],
           T#22         |->  [.],
           S#4          |->  (var X#11)}

and instantiated rules:

                                  (letrec {X#10=A#19[A#21[(var X#11)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#19[A#21[(var X#2)]];X#2=(var X#11);X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#19[A#21[(var X#11)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#19[A#21[(\ X#9.S#13)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#19[A#21[(var X#2)]]
       ;X#2= A#22[(var X#11)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#19[A#21[A#22[(\ X#9.S#13)]]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#20,A#18,T#7,A#14,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[A#21]),
             (A#22[(var X#11)],A#19[A#21]),
             ((letrec {X#10=A#19[A#21[(dummy3 )]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#22[(var X#11)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[A#21[[.]]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#21[A#22[[.]]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           A#18         |->  A#19,
           T#7          |->  A#19[A#21],
           A#14         |->  A#21[A#22],
           T#20         |->  A#21,
           S#4          |->  A#22[(var X#11)]}

and instantiated rules:

                                  (letrec {X#10=A#19[A#21[A#22[(var X#11)]]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#19[A#21[(var X#2)]];X#2=A#22[(var X#11)];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#19[A#21[A#22[(var X#11)]]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#19[A#21[A#22[(\ X#9.S#13)]]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#19[A#21[(app A#22[(var X#11)] T#23[(var X#2)])]]
       ;X#2= S#4
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#19[A#21[(app A#22[(\ X#9.S#13)] T#23[S#4])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#20,A#18,T#7,A#14,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[A#21[(app A#22[(var X#11)] T#23)]]),
             (S#4,A#19[A#21[(app A#22[(var X#11)] T#23)]]),
             ((letrec {X#10=A#19[A#21[(app A#22[(var X#11)] T#23[(dummy3 )])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[A#21[(app A#22[(var X#11)] T#23[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#21[(app A#22[[.]] T#23[S#4])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           A#18         |->  A#19,
           T#7          |->  A#19[A#21[(app A#22[(var X#11)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#11)] T#23)],
           A#14         |->  A#21[(app A#22 T#23[S#4])]}

and instantiated rules:

                                  (letrec {X#10=A#19[A#21[(app A#22[(var X#11)] T#23[S#4])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#19[A#21[(app A#22[(var X#11)] T#23[(var X#2)])]];X#2=S#4;X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#19[A#21[(app A#22[(var X#11)] T#23[S#4])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#19[A#21[(app A#22[(\ X#9.S#13)] T#23[S#4])]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#19[(var X#2)]
       ;X#2= A#14[(var X#11)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#19[A#14[(\ X#9.S#13)]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#18,T#7,A#14,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[[.]]),
             (A#14[(var X#11)],A#19[[.]]),
             ((letrec {X#10=A#19[(dummy3 )];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#14[(var X#11)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           A#18         |->  A#19,
           T#7          |->  A#19[[.]],
           T#20         |->  [.],
           S#4          |->  A#14[(var X#11)]}

and instantiated rules:

                                  (letrec {X#10=A#19[A#14[(var X#11)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#19[(var X#2)];X#2=A#14[(var X#11)];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#19[A#14[(var X#11)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#19[A#14[(\ X#9.S#13)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#19[(var X#2)]
       ;X#2= A#20[A#14[(var X#11)]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#19[A#20[A#14[(\ X#9.S#13)]]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#18,T#7,A#14,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19),
             (A#20[A#14[(var X#11)]],A#19),
             ((letrec {X#10=A#19[(dummy3 )];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#20[A#14[(var X#11)]],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=A#19[A#20[[.2]]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           A#18         |->  A#19[A#20],
           T#7          |->  A#19,
           S#4          |->  A#20[A#14[(var X#11)]]}

and instantiated rules:

                                  (letrec {X#10=A#19[A#20[A#14[(var X#11)]]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#19[(var X#2)];X#2=A#20[A#14[(var X#11)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#19[A#20[A#14[(var X#11)]]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#19[A#20[A#14[(\ X#9.S#13)]]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#19[(app A#20[A#14[(var X#11)]] T#21[(var X#2)])]
       ;X#2= S#4
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#19[(app A#20[A#14[(\ X#9.S#13)]] T#21[S#4])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#18,T#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[(app A#20[A#14[(var X#11)]] T#21)]),
             (S#4,A#19[(app A#20[A#14[(var X#11)]] T#21)]),
             ((letrec {X#10=A#19[(app A#20[A#14[(var X#11)]] T#21[(dummy3 )])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[(app A#20[A#14[(var X#11)]] T#21[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[S#4])]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           T#7          |->  A#19[(app A#20[A#14[(var X#11)]] T#21)],
           A#18         |->  A#19[(app A#20 T#21[S#4])]}

and instantiated rules:

                                  (letrec {X#10=A#19[(app A#20[A#14[(var X#11)]] T#21[S#4])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#19[(app A#20[A#14[(var X#11)]] T#21[(var X#2)])];X#2=S#4;X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#19[(app A#20[A#14[(var X#11)]] T#21[S#4])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#19[(app A#20[A#14[(\ X#9.S#13)]] T#21[S#4])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#19[(var X#2)]
       ;X#2= (var X#11)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#19[(\ X#9.S#13)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#7,A#14,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[[.]]),
             ((var X#11),A#19[[.]]),
             ((letrec {X#10=A#19[(dummy3 )];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#11),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#19[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           A#18         |->  [.],
           A#14         |->  A#19,
           T#7          |->  A#19[[.]],
           T#20         |->  [.],
           S#4          |->  (var X#11)}

and instantiated rules:

                                  (letrec {X#10=A#19[(var X#11)];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#19[(var X#2)];X#2=(var X#11);X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#19[(var X#11)];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#19[(\ X#9.S#13)];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#19[(var X#2)]
       ;X#2= A#20[(var X#11)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#19[A#20[(\ X#9.S#13)]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#7,A#14,A#19}
   Delta2 = {}
   Delta3 = {((var X#2),A#19),
             (A#20[(var X#11)],A#19),
             ((letrec {X#10=A#19[(dummy3 )];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#20[(var X#11)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#19[A#20[[.]]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           A#18         |->  [.],
           A#14         |->  A#19[A#20],
           T#7          |->  A#19,
           S#4          |->  A#20[(var X#11)]}

and instantiated rules:

                                  (letrec {X#10=A#19[A#20[(var X#11)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#19[(var X#2)];X#2=A#20[(var X#11)];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#19[A#20[(var X#11)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#19[A#20[(\ X#9.S#13)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#19[(app A#20[(var X#11)] T#21[(var X#2)])]
       ;X#2= S#4
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#19[(app A#20[(\ X#9.S#13)] T#21[S#4])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),A#19[(app A#20[(var X#11)] T#21)]),
             (S#4,A#19[(app A#20[(var X#11)] T#21)]),
             ((letrec {X#10=A#19[(app A#20[(var X#11)] T#21[(dummy3 )])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#19[(app A#20[(var X#11)] T#21[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#19[(app A#20[[.]] T#21[S#4])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           A#18         |->  [.],
           T#7          |->  A#19[(app A#20[(var X#11)] T#21)],
           A#14         |->  A#19[(app A#20 T#21[S#4])]}

and instantiated rules:

                                  (letrec {X#10=A#19[(app A#20[(var X#11)] T#21[S#4])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#19[(app A#20[(var X#11)] T#21[(var X#2)])];X#2=S#4;X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#19[(app A#20[(var X#11)] T#21[S#4])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#19[(app A#20[(\ X#9.S#13)] T#21[S#4])];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#2)
       ;X#2= A#18[A#14[(var X#11)]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#18[A#14[(\ X#9.S#13)]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             (A#18[A#14[(var X#11)]],[.]),
             ((letrec {X#10=(dummy3 );X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#18[A#14[(var X#11)]],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|},
           T#7          |->  [.],
           S#4          |->  A#18[A#14[(var X#11)]]}

and instantiated rules:

                                  (letrec {X#10=A#18[A#14[(var X#11)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=(var X#2);X#2=A#18[A#14[(var X#11)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#18[A#14[(var X#11)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#18[A#14[(\ X#9.S#13)]];X#8=(\ X#9.S#13);E#12;VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#21[(var X#2)]
       ;X#2= (var X#19)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#19,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#21[(var X#19)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#19,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#18,T#7,A#14,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),A#21[[.]]),
             ((var X#19),A#21[[.]]),
             ((letrec {X#10=A#21[(dummy3 )];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#19),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#21[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=A#21[(var X#19)];EE#20[X#19,[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           A#18         |->  A#21,
           T#7          |->  A#21[[.]],
           T#22         |->  [.],
           S#4          |->  (var X#19)}

and instantiated rules:

                                  (letrec {X#10=A#21[(var X#19)];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#21[(var X#2)];X#2=(var X#19);X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#21[(var X#19)];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#21[(var X#19)];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#21[(var X#2)]
       ;X#2= A#22[(var X#19)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#19,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#21[A#22[(var X#19)]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#19,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#18,T#7,A#14,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),A#21),
             (A#22[(var X#19)],A#21),
             ((letrec {X#10=A#21[(dummy3 )];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#22[(var X#19)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#21[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=A#21[A#22[(var X#19)]];EE#20[X#19,[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           A#18         |->  A#21[A#22],
           T#7          |->  A#21,
           S#4          |->  A#22[(var X#19)]}

and instantiated rules:

                                  (letrec {X#10=A#21[A#22[(var X#19)]];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#21[(var X#2)];X#2=A#22[(var X#19)];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#21[A#22[(var X#19)]];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#21[A#22[(var X#19)]];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= A#21[(app A#22[(var X#19)] T#23[(var X#2)])]
       ;X#2= S#4
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#19,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#21[(app A#22[(var X#19)] T#23[S#4])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#19,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#18,T#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),A#21[(app A#22[(var X#19)] T#23)]),
             (S#4,A#21[(app A#22[(var X#19)] T#23)]),
             ((letrec {X#10=A#21[(app A#22[(var X#19)] T#23[(dummy3 )])];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#21[(app A#22[(var X#19)] T#23[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[S#4])];EE#20[X#19,[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           T#7          |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[S#4])]}

and instantiated rules:

                                  (letrec {X#10=A#21[(app A#22[(var X#19)] T#23[S#4])];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=A#21[(app A#22[(var X#19)] T#23[(var X#2)])];X#2=S#4;X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#21[(app A#22[(var X#19)] T#23[S#4])];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#21[(app A#22[(var X#19)] T#23[S#4])];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#10= (var X#2)
       ;X#2= A#18[(var X#19)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#19,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#10= A#18[(var X#19)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#19,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             (A#18[(var X#19)],[.]),
             ((letrec {X#10=(dummy3 );X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#18[(var X#19)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {[.1]=A#18[(var X#19)];EE#20[X#19,[.2]]},
           X#1          |->  X#10,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           T#7          |->  [.],
           S#4          |->  A#18[(var X#19)]}

and instantiated rules:

                                  (letrec {X#10=A#18[(var X#19)];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#10=(var X#2);X#2=A#18[(var X#19)];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#10=A#18[(var X#19)];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#10=A#18[(var X#19)];X#8=(\ X#9.S#13);E#12;EE#20[X#19,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(var X#2)]
       ;X#2= (var X#20)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#22[X#20,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= A#23[(var X#20)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#22[X#20,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#18,T#7,A#14,A#23}
   Delta2 = {}
   Delta3 = {((var X#2),A#23[[.]]),
             ((var X#20),A#23[[.]]),
             ((letrec {X#19=A#23[(dummy3 )];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#20),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#23[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=A#23[(var X#20)];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           A#18         |->  A#23,
           T#7          |->  A#23[[.]],
           T#24         |->  [.],
           S#4          |->  (var X#20)}

and instantiated rules:

                                  (letrec {X#19=A#23[(var X#20)];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=A#23[(var X#2)];X#2=(var X#20);X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=A#23[(var X#20)];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=A#23[(var X#20)];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(var X#2)]
       ;X#2= A#24[(var X#20)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#22[X#20,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= A#23[A#24[(var X#20)]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#22[X#20,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#18,T#7,A#14,A#23}
   Delta2 = {}
   Delta3 = {((var X#2),A#23),
             (A#24[(var X#20)],A#23),
             ((letrec {X#19=A#23[(dummy3 )];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#24[(var X#20)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#23[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=A#23[A#24[(var X#20)]];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           A#18         |->  A#23[A#24],
           T#7          |->  A#23,
           S#4          |->  A#24[(var X#20)]}

and instantiated rules:

                                  (letrec {X#19=A#23[A#24[(var X#20)]];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=A#23[(var X#2)];X#2=A#24[(var X#20)];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=A#23[A#24[(var X#20)]];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=A#23[A#24[(var X#20)]];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(var X#2)])]
       ;X#2= S#4
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#22[X#20,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[S#4])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#22[X#20,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#18,T#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),A#23[(app A#24[(var X#20)] T#25)]),
             (S#4,A#23[(app A#24[(var X#20)] T#25)]),
             ((letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(dummy3 )])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#23[(app A#24[(var X#20)] T#25[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[S#4])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           T#7          |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[S#4])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[S#4])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(var X#2)])];X#2=S#4;X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[S#4])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[S#4])];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#2)
       ;X#2= A#18[(var X#20)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#22[X#20,A#14[(var X#11)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= A#18[(var X#20)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#21[X#10,(var X#19)]
       ;EE#22[X#20,A#14[(\ X#9.S#13)]]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             (A#18[(var X#20)],[.]),
             ((letrec {X#19=(dummy3 );X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#18[(var X#20)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=A#18[(var X#20)];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|},
           T#7          |->  [.],
           S#4          |->  A#18[(var X#20)]}

and instantiated rules:

                                  (letrec {X#19=A#18[(var X#20)];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=(var X#2);X#2=A#18[(var X#20)];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=A#18[(var X#20)];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=A#18[(var X#20)];X#8=(\ X#9.S#13);E#12;EE#21[X#10,(var X#19)];EE#22[X#20,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(var X#2)]]
       ;X#2= (var X#11)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(\ X#9.S#13)]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#22,A#18,T#7,A#14,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#2),A#21[A#23[[.]]]),
             ((var X#11),A#21[A#23[[.]]]),
             ((letrec {X#19=A#21[A#23[(dummy3 )]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#11),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#21[A#23[[.]]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#23[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|},
           A#18         |->  A#21,
           T#7          |->  A#21[A#23[[.]]],
           A#14         |->  A#23,
           T#22         |->  A#23[[.]],
           T#24         |->  [.],
           S#4          |->  (var X#11)}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(var X#11)]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=A#21[A#23[(var X#2)]];X#2=(var X#11);X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(var X#11)]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(\ X#9.S#13)]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(var X#2)]]
       ;X#2= A#24[(var X#11)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= A#21[A#23[A#24[(\ X#9.S#13)]]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#22,A#18,T#7,A#14,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#2),A#21[A#23]),
             (A#24[(var X#11)],A#21[A#23]),
             ((letrec {X#19=A#21[A#23[(dummy3 )]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#24[(var X#11)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#21[A#23[[.]]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#23[A#24[[.]]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|},
           A#18         |->  A#21,
           T#7          |->  A#21[A#23],
           A#14         |->  A#23[A#24],
           T#22         |->  A#23,
           S#4          |->  A#24[(var X#11)]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[A#24[(var X#11)]]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=A#21[A#23[(var X#2)]];X#2=A#24[(var X#11)];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[A#24[(var X#11)]]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[A#24[(\ X#9.S#13)]]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(app A#24[(var X#11)] T#25[(var X#2)])]]
       ;X#2= S#4
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[(\ X#9.S#13)] T#25[S#4])]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#22,A#18,T#7,A#14,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),A#21[A#23[(app A#24[(var X#11)] T#25)]]),
             (S#4,A#21[A#23[(app A#24[(var X#11)] T#25)]]),
             ((letrec {X#19=A#21[A#23[(app A#24[(var X#11)] T#25[(dummy3 )])]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#21[A#23[(app A#24[(var X#11)] T#25[[.]])]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#23[(app A#24[[.]] T#25[S#4])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|},
           A#18         |->  A#21,
           T#7          |->  A#21[A#23[(app A#24[(var X#11)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#11)] T#25)],
           A#14         |->  A#23[(app A#24 T#25[S#4])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#11)] T#25[S#4])]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=A#21[A#23[(app A#24[(var X#11)] T#25[(var X#2)])]];X#2=S#4;X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#11)] T#25[S#4])]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(app A#24[(\ X#9.S#13)] T#25[S#4])]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(var X#2)]
       ;X#2= A#14[(var X#11)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= A#21[A#14[(\ X#9.S#13)]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#18,T#7,A#14,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),A#21[[.]]),
             (A#14[(var X#11)],A#21[[.]]),
             ((letrec {X#19=A#21[(dummy3 )];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#14[(var X#11)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#21[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|},
           A#18         |->  A#21,
           T#7          |->  A#21[[.]],
           T#22         |->  [.],
           S#4          |->  A#14[(var X#11)]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#14[(var X#11)]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=A#21[(var X#2)];X#2=A#14[(var X#11)];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=A#21[A#14[(var X#11)]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#14[(\ X#9.S#13)]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(var X#2)]
       ;X#2= A#22[A#14[(var X#11)]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= A#21[A#22[A#14[(\ X#9.S#13)]]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#18,T#7,A#14,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),A#21),
             (A#22[A#14[(var X#11)]],A#21),
             ((letrec {X#19=A#21[(dummy3 )];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#22[A#14[(var X#11)]],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#21[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=A#21[A#22[[.2]]];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|},
           A#18         |->  A#21[A#22],
           T#7          |->  A#21,
           S#4          |->  A#22[A#14[(var X#11)]]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#22[A#14[(var X#11)]]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=A#21[(var X#2)];X#2=A#22[A#14[(var X#11)]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=A#21[A#22[A#14[(var X#11)]]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#22[A#14[(\ X#9.S#13)]]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[A#14[(var X#11)]] T#23[(var X#2)])]
       ;X#2= S#4
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[A#14[(\ X#9.S#13)]] T#23[S#4])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#18,T#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),A#21[(app A#22[A#14[(var X#11)]] T#23)]),
             (S#4,A#21[(app A#22[A#14[(var X#11)]] T#23)]),
             ((letrec {X#19=A#21[(app A#22[A#14[(var X#11)]] T#23[(dummy3 )])];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#21[(app A#22[A#14[(var X#11)]] T#23[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[S#4])];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|},
           T#7          |->  A#21[(app A#22[A#14[(var X#11)]] T#23)],
           A#18         |->  A#21[(app A#22 T#23[S#4])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[A#14[(var X#11)]] T#23[S#4])];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=A#21[(app A#22[A#14[(var X#11)]] T#23[(var X#2)])];X#2=S#4;X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[A#14[(var X#11)]] T#23[S#4])];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[A#14[(\ X#9.S#13)]] T#23[S#4])];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(var X#2)]
       ;X#2= (var X#11)
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= A#21[(\ X#9.S#13)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#7,A#14,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),A#21[[.]]),
             ((var X#11),A#21[[.]]),
             ((letrec {X#19=A#21[(dummy3 )];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#11),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#21[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#21[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|},
           A#18         |->  [.],
           A#14         |->  A#21,
           T#7          |->  A#21[[.]],
           T#22         |->  [.],
           S#4          |->  (var X#11)}

and instantiated rules:

                                  (letrec {X#19=A#21[(var X#11)];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=A#21[(var X#2)];X#2=(var X#11);X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=A#21[(var X#11)];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(\ X#9.S#13)];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(var X#2)]
       ;X#2= A#22[(var X#11)]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= A#21[A#22[(\ X#9.S#13)]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#7,A#14,A#21}
   Delta2 = {}
   Delta3 = {((var X#2),A#21),
             (A#22[(var X#11)],A#21),
             ((letrec {X#19=A#21[(dummy3 )];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#22[(var X#11)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#21[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#21[A#22[[.]]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|},
           A#18         |->  [.],
           A#14         |->  A#21[A#22],
           T#7          |->  A#21,
           S#4          |->  A#22[(var X#11)]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#22[(var X#11)]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=A#21[(var X#2)];X#2=A#22[(var X#11)];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=A#21[A#22[(var X#11)]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#22[(\ X#9.S#13)]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(var X#11)] T#23[(var X#2)])]
       ;X#2= S#4
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(\ X#9.S#13)] T#23[S#4])]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {T#7,A#14}
   Delta2 = {}
   Delta3 = {((var X#2),A#21[(app A#22[(var X#11)] T#23)]),
             (S#4,A#21[(app A#22[(var X#11)] T#23)]),
             ((letrec {X#19=A#21[(app A#22[(var X#11)] T#23[(dummy3 )])];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),A#21[(app A#22[(var X#11)] T#23[[.]])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#21[(app A#22[[.]] T#23[S#4])]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|},
           A#18         |->  [.],
           T#7          |->  A#21[(app A#22[(var X#11)] T#23)],
           A#14         |->  A#21[(app A#22 T#23[S#4])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(var X#11)] T#23[S#4])];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=A#21[(app A#22[(var X#11)] T#23[(var X#2)])];X#2=S#4;X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(var X#11)] T#23[S#4])];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[(\ X#9.S#13)] T#23[S#4])];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (var X#2)
       ;X#2= A#18[A#14[(var X#11)]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
    ,
     (letrec
        X#19= A#18[A#14[(\ X#9.S#13)]]
       ;X#8= (\ X#9.S#13)
       ;E#12
       ;EE#20[X#10,(var X#19)]
       ;VV#17|X#11,(var X#8)|
     in
        A#15[(var X#10)]
     )
  )

where

   Delta1 = {A#14}
   Delta2 = {}
   Delta3 = {((var X#2),[.]),
             (A#18[A#14[(var X#11)]],[.]),
             ((letrec {X#19=(dummy3 );X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#18[A#14[(var X#11)]],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]]),
             ((var X#11),A#14[[.]]),
             ((var X#8),[.]),
             ((var X#10),A#15[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,cp-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(\ X#9.S#13)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    and constraints: A#14/= [.]

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(\ X#9.S#13);E#12;EE#16[X#10,A#14[(var X#11)]];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])}
      Delta1=  {A#14}
      Delta2=  {}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#2),T#7[[.]]),((var X#8),[.]),((var X#10),A#15[[.]]),((var X#11),A#14[[.]]),((var X#8),[.]),((var X#10),A#15[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#15[(var X#10)],
           EE#16[.1,.2] |-> {X#19=A#18[[.2]];EE#20[[.1],(var X#19)]},
           X#1          |->  X#19,
           E#3          |->  {X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|},
           T#7          |->  [.],
           S#4          |->  A#18[A#14[(var X#11)]]}

and instantiated rules:

                                  (letrec {X#19=A#18[A#14[(var X#11)]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -ucp2->                       (letrec {X#19=(var X#2);X#2=A#18[A#14[(var X#11)]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    ................................................................................
                                  (letrec {X#19=A#18[A#14[(var X#11)]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    -SR,cp-e2->                   (letrec {X#19=A#18[A#14[(\ X#9.S#13)]];X#8=(\ X#9.S#13);E#12;EE#20[X#10,(var X#19)];VV#17|X#11,(var X#8)|} in A#15[(var X#10)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        (letrec {E#9} in T#12[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])
     )
    ,
     (letrec {E#8;E#9} in T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)])
  )

where

   Delta1 = {T#11,T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             [{E#8},(letrec {E#9} in [.])],
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in (letrec {E#9} in S#10))
    -SR,llet-in1->                (letrec {E#8;E#9} in S#10)
    and constraints: E#8/= {}, E#9/= {}, ({E#8},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in (letrec {E#9} in S#10))}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),[{E#8},(letrec {E#9} in [.])],((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in (letrec {E#9} in T#12)),
           T#11  |->  (letrec {E#9} in T#12),
           S#10  |->  T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#8} in (letrec {E#9} in T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)]))
    -ucp2->                       (letrec {E#8} in (letrec {E#9} in T#12[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]))
    ................................................................................
                                  (letrec {E#8} in (letrec {E#9} in T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)]))
    -SR,llet-in1->                (letrec {E#8;E#9} in T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        (letrec
           X#13= T#12[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
          ;E#15
        in
           S#10
        )
     )
    ,
     (letrec {X#13=T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#15;E#8} in S#10)
  )

where

   Delta1 = {T#11,T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             [{E#8},(letrec {X#13=T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#15} in [.])],
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in (letrec {E#9} in S#10))
    -SR,llet-in1->                (letrec {E#8;E#9} in S#10)
    and constraints: E#8/= {}, E#9/= {}, ({E#8},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in (letrec {E#9} in S#10))}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),[{E#8},(letrec {E#9} in [.])],((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in (letrec {X#13=T#12;E#15} in S#10)),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#10),
           E#9   |->  {X#13=T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {E#8} in (letrec {X#13=T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#15} in S#10))
    -ucp2->                       (letrec {E#8} in (letrec {X#13=T#12[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#15} in S#10))
    ................................................................................
                                  (letrec {E#8} in (letrec {X#13=T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#15} in S#10))
    -SR,llet-in1->                (letrec {X#13=T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#15;E#8} in S#10)
    

================================================================================
Critical Pair:

  (
     (letrec {E#8} in (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#12} in S#10))
    ,
     (letrec {X#1=T#7[S#4];E#12;E#8} in S#10)
  )

where

   Delta1 = {T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#12} in S#10),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             [{E#8},(letrec {X#1=T#7[S#4];E#12} in [.])],
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in (letrec {E#9} in S#10))
    -SR,llet-in1->                (letrec {E#8;E#9} in S#10)
    and constraints: E#8/= {}, E#9/= {}, ({E#8},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in (letrec {E#9} in S#10))}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),[{E#8},(letrec {E#9} in [.])],((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in [.]),
           T#11  |->  [.],
           S#5   |->  S#10,
           E#9   |->  {X#1=T#7[S#4];E#12},
           E#3   |->  {E#12}}

and instantiated rules:

                                  (letrec {E#8} in (letrec {X#1=T#7[S#4];E#12} in S#10))
    -ucp2->                       (letrec {E#8} in (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#12} in S#10))
    ................................................................................
                                  (letrec {E#8} in (letrec {X#1=T#7[S#4];E#12} in S#10))
    -SR,llet-in1->                (letrec {X#1=T#7[S#4];E#12;E#8} in S#10)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#12= T#11[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
       ;E#14
     in
        (letrec {E#9} in S#10)
     )
    ,
     (letrec {X#12=T#11[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#14;E#9} in S#10)
  )

where

   Delta1 = {T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             [{X#12=T#11[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#14},(letrec {E#9} in [.])],
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in (letrec {E#9} in S#10))
    -SR,llet-in1->                (letrec {E#8;E#9} in S#10)
    and constraints: E#8/= {}, E#9/= {}, ({E#8},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in (letrec {E#9} in S#10))}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),[{E#8},(letrec {E#9} in [.])],((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#12=T#11;E#14} in (letrec {E#9} in S#10)),
           E#8   |->  {X#12=T#11[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#14},
           E#13  |->  {E#14}}

and instantiated rules:

                                  (letrec {X#12=T#11[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#14} in (letrec {E#9} in S#10))
    -ucp2->                       (letrec {X#12=T#11[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#14} in (letrec {E#9} in S#10))
    ................................................................................
                                  (letrec {X#12=T#11[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#14} in (letrec {E#9} in S#10))
    -SR,llet-in1->                (letrec {X#12=T#11[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#14;E#9} in S#10)
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#11} in (letrec {E#9} in S#10))
    ,
     (letrec {X#1=T#7[S#4];E#11;E#9} in S#10)
  )

where

   Delta1 = {}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#11} in (letrec {E#9} in S#10)),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             [{X#1=T#7[S#4];E#11},(letrec {E#9} in [.])],
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-in1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in (letrec {E#9} in S#10))
    -SR,llet-in1->                (letrec {E#8;E#9} in S#10)
    and constraints: E#8/= {}, E#9/= {}, ({E#8},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in (letrec {E#9} in S#10))}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),[{E#8},(letrec {E#9} in [.])],((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6  |->  [.],
           S#5  |->  (letrec {E#9} in S#10),
           E#8  |->  {X#1=T#7[S#4];E#11},
           E#3  |->  {E#11}}

and instantiated rules:

                                  (letrec {X#1=T#7[S#4];E#11} in (letrec {E#9} in S#10))
    -ucp2->                       (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#11} in (letrec {E#9} in S#10))
    ................................................................................
                                  (letrec {X#1=T#7[S#4];E#11} in (letrec {E#9} in S#10))
    -SR,llet-in1->                (letrec {X#1=T#7[S#4];E#11;E#9} in S#10)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {E#9} in S#11)
       ;E#10
     in
        A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
     )
    ,
     (letrec
        X#8= S#11
       ;E#10
       ;E#9
     in
        A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#13,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])],(letrec {E#9} in [.])),
             [{E#10},(letrec {E#9} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),A#14[(app A#15[[.]] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])]),
             ((var X#8),A#14[(app A#15[[.]] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),T#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#14[(app A#15[(var X#8)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#8)] T#16)],
           A#12  |->  A#14[(app A#15 T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -ucp2->                       (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#14[(app A#15[(var X#8)] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {E#9} in T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])
       ;E#10
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#8= T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)]
       ;E#10
       ;E#9
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#13,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{E#10},(letrec {E#9} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),T#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(letrec {E#9} in T#16);E#10} in A#12[(var X#8)]),
           X#14  |->  X#8,
           E#15  |->  {E#10},
           T#13  |->  (letrec {E#9} in T#16),
           S#11  |->  T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#9} in T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)]);E#10} in A#12[(var X#8)])
    -ucp2->                       (letrec {X#8=(letrec {E#9} in T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]);E#10} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)]);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#10;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec
                X#17= T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
               ;E#19
             in
                S#11
             )
       ;E#10
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#17= T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)]
       ;X#8= S#11
       ;E#10
       ;E#19
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#13,T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (A#12[(var X#8)],(letrec {X#17=T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#19} in [.])),
             [{E#10},(letrec {X#17=T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#19} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),T#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(letrec {X#17=T#16;E#19} in S#11);E#10} in A#12[(var X#8)]),
           X#14  |->  X#8,
           E#15  |->  {E#10},
           T#13  |->  (letrec {X#17=T#16;E#19} in S#11),
           E#9   |->  {X#17=T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#19},
           E#18  |->  {E#19}}

and instantiated rules:

                                  (letrec {X#8=(letrec {X#17=T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#19} in S#11);E#10} in A#12[(var X#8)])
    -ucp2->                       (letrec {X#8=(letrec {X#17=T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#19} in S#11);E#10} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(letrec {X#17=T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#19} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#17=T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=S#11;E#10;E#19} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#16} in S#11)
       ;E#10
     in
        A#12[(var X#8)]
     )
    ,
     (letrec {X#1=T#7[S#4];X#8=S#11;E#10;E#16} in A#12[(var X#8)])
  )

where

   Delta1 = {T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#16} in S#11),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (A#12[(var X#8)],(letrec {X#1=T#7[S#4];E#16} in [.])),
             [{E#10},(letrec {X#1=T#7[S#4];E#16} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),T#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=[.];E#10} in A#12[(var X#8)]),
           X#14  |->  X#8,
           E#15  |->  {E#10},
           T#13  |->  [.],
           S#5   |->  S#11,
           E#9   |->  {X#1=T#7[S#4];E#16},
           E#3   |->  {E#16}}

and instantiated rules:

                                  (letrec {X#8=(letrec {X#1=T#7[S#4];E#16} in S#11);E#10} in A#12[(var X#8)])
    -ucp2->                       (letrec {X#8=(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#16} in S#11);E#10} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(letrec {X#1=T#7[S#4];E#16} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#1=T#7[S#4];X#8=S#11;E#10;E#16} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
       ;X#8= (letrec {E#9} in S#11)
       ;E#16
     in
        A#12[(var X#8)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)]
       ;X#8= S#11
       ;E#16
       ;E#9
     in
        A#12[(var X#8)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16},(letrec {E#9} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),T#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#14=T#13;X#8=(letrec {E#9} in S#11);E#16} in A#12[(var X#8)]),
           E#10  |->  {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16},
           E#15  |->  {X#8=(letrec {E#9} in S#11);E#16}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(letrec {E#9} in S#11);E#16} in A#12[(var X#8)])
    -ucp2->                       (letrec {X#14=T#13[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];X#8=(letrec {E#9} in S#11);E#16} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(letrec {E#9} in S#11);E#16} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=S#11;E#16;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#2=S#4;X#8=(letrec {E#9} in T#13[(var X#2)]);E#10} in A#12[(var X#8)])
    ,
     (letrec {X#8=T#13[S#4];E#10;E#9} in A#12[(var X#8)])
  )

where

   Delta1 = {T#7}
   Delta2 = {E#9}
   Delta3 = {((var X#2),(letrec {E#9} in T#13)),
             (S#4,(letrec {E#9} in T#13)),
             ((letrec {X#8=(letrec {E#9} in T#13[(dummy3 )]);E#10} in A#12[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{E#10},(letrec {E#9} in [.])],
             ((var X#2),(letrec {E#9} in T#13[[.]])),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),T#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#8)],
           X#1   |->  X#8,
           E#3   |->  {E#10},
           T#7   |->  (letrec {E#9} in T#13),
           S#11  |->  T#13[S#4]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#9} in T#13[S#4]);E#10} in A#12[(var X#8)])
    -ucp2->                       (letrec {X#2=S#4;X#8=(letrec {E#9} in T#13[(var X#2)]);E#10} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in T#13[S#4]);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=T#13[S#4];E#10;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= (letrec {X#14=T#13[(var X#2)];E#16} in S#11)
       ;E#10
     in
        A#12[(var X#8)]
     )
    ,
     (letrec {X#14=T#13[S#4];X#8=S#11;E#10;E#16} in A#12[(var X#8)])
  )

where

   Delta1 = {T#7}
   Delta2 = {E#9}
   Delta3 = {((var X#2),(letrec {X#14=T#13;E#16} in S#11)),
             (S#4,(letrec {X#14=T#13;E#16} in S#11)),
             ((letrec {X#8=(letrec {X#14=T#13[(dummy3 )];E#16} in S#11);E#10} in A#12[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (A#12[(var X#8)],(letrec {X#14=T#13[S#4];E#16} in [.])),
             [{E#10},(letrec {X#14=T#13[S#4];E#16} in [.])],
             ((var X#2),(letrec {X#14=T#13[[.]];E#16} in S#11)),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),T#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#8)],
           X#1   |->  X#8,
           E#3   |->  {E#10},
           T#7   |->  (letrec {X#14=T#13;E#16} in S#11),
           E#9   |->  {X#14=T#13[S#4];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {X#8=(letrec {X#14=T#13[S#4];E#16} in S#11);E#10} in A#12[(var X#8)])
    -ucp2->                       (letrec {X#2=S#4;X#8=(letrec {X#14=T#13[(var X#2)];E#16} in S#11);E#10} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(letrec {X#14=T#13[S#4];E#16} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#14=T#13[S#4];X#8=S#11;E#10;E#16} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#2=(letrec {E#9} in S#11);X#8=(var X#2);E#10} in A#12[(var X#8)])
    ,
     (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#2),[.]),
             ((letrec {E#9} in S#11),[.]),
             ((letrec {X#8=(dummy3 );E#10} in A#12[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((letrec {E#9} in S#11),(letrec {X#2=(dummy3 )} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{E#10},(letrec {E#9} in [.])],
             ((var X#2),[.]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),T#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6  |->  [.],
           S#5  |->  A#12[(var X#8)],
           X#1  |->  X#8,
           E#3  |->  {E#10},
           T#7  |->  [.],
           S#4  |->  (letrec {E#9} in S#11)}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -ucp2->                       (letrec {X#2=(letrec {E#9} in S#11);X#8=(var X#2);E#10} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= T#7[(var X#2)]
       ;X#2= S#4
       ;X#8= (letrec {E#9} in S#11)
       ;E#13
     in
        A#12[(var X#8)]
     )
    ,
     (letrec {X#1=T#7[S#4];X#8=S#11;E#13;E#9} in A#12[(var X#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];X#8=(letrec {E#9} in S#11);E#13} in A#12[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (A#12[(var X#8)],(letrec {E#9} in [.])),
             [{X#1=T#7[S#4];E#13},(letrec {E#9} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),A#12[[.]]),
             ((var X#8),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#8=S#11;E#10;E#9} in A#12[(var X#8)])
    and constraints: E#9/= {}, (A#12[(var X#8)],(letrec {E#9} in [.])), ({E#10},(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#9} in S#11);E#10} in A#12[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(A#12[(var X#8)],(letrec {E#9} in [.])),[{E#10},(letrec {E#9} in [.])],((var X#2),T#7[[.]]),((var X#8),A#12[[.]]),((var X#8),A#12[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#12[(var X#8)],
           E#10  |->  {X#1=T#7[S#4];E#13},
           E#3   |->  {X#8=(letrec {E#9} in S#11);E#13}}

and instantiated rules:

                                  (letrec {X#1=T#7[S#4];X#8=(letrec {E#9} in S#11);E#13} in A#12[(var X#8)])
    -ucp2->                       (letrec {X#1=T#7[(var X#2)];X#2=S#4;X#8=(letrec {E#9} in S#11);E#13} in A#12[(var X#8)])
    ................................................................................
                                  (letrec {X#1=T#7[S#4];X#8=(letrec {E#9} in S#11);E#13} in A#12[(var X#8)])
    -SR,llet-e1->                 (letrec {X#1=T#7[S#4];X#8=S#11;E#13;E#9} in A#12[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#14[X#9,(var X#8)]
     in
        A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
     )
    ,
     (letrec
        X#8= S#12
       ;E#10
       ;E#11
       ;EE#14[X#9,(var X#8)]
     in
        A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#13,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),
             (A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])],(letrec {E#10} in [.])),
             [{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#16[(app A#17[[.]] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])]),
             ((var X#8),[.]),
             ((var X#9),A#16[(app A#17[[.]] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#16[(app A#17[(var X#9)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#9)] T#18)],
           A#13  |->  A#16[(app A#17 T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -ucp2->                       (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#16[(app A#17[(var X#9)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {E#10} in T#18[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])
       ;E#11
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#8= T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)]
       ;E#10
       ;E#11
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(letrec {E#10} in T#18);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)]),
           X#16  |->  X#8,
           E#17  |->  {E#11;EE#14[X#9,(var X#8)]},
           T#15  |->  (letrec {E#10} in T#18),
           S#12  |->  T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)]);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#8=(letrec {E#10} in T#18[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)]);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec
                X#19= T#18[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
               ;E#21
             in
                S#12
             )
       ;E#11
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)]
       ;X#8= S#12
       ;E#11
       ;E#21
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#19=T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#11;E#21;EE#14[X#9,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {X#19=T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#21} in [.])),
             [{E#11;EE#14[X#9,(var X#8)]},(letrec {X#19=T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#21} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=(letrec {X#19=T#18;E#21} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)]),
           X#16  |->  X#8,
           E#17  |->  {E#11;EE#14[X#9,(var X#8)]},
           T#15  |->  (letrec {X#19=T#18;E#21} in S#12),
           E#10  |->  {X#19=T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#21},
           E#20  |->  {E#21}}

and instantiated rules:

                                  (letrec {X#8=(letrec {X#19=T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#21} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#8=(letrec {X#19=T#18[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#21} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {X#19=T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#21} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#19=T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=S#12;E#11;E#21;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#18} in S#12)
       ;E#11
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= T#7[S#4]
       ;X#8= S#12
       ;E#11
       ;E#18
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#18} in S#12),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=T#7[S#4];E#11;E#18;EE#14[X#9,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {X#1=T#7[S#4];E#18} in [.])),
             [{E#11;EE#14[X#9,(var X#8)]},(letrec {X#1=T#7[S#4];E#18} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#8=[.];E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)]),
           X#16  |->  X#8,
           E#17  |->  {E#11;EE#14[X#9,(var X#8)]},
           T#15  |->  [.],
           S#5   |->  S#12,
           E#10  |->  {X#1=T#7[S#4];E#18},
           E#3   |->  {E#18}}

and instantiated rules:

                                  (letrec {X#8=(letrec {X#1=T#7[S#4];E#18} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#8=(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#18} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {X#1=T#7[S#4];E#18} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#1=T#7[S#4];X#8=S#12;E#11;E#18;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
       ;X#8= (letrec {E#10} in S#12)
       ;E#18
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)]
       ;X#8= S#12
       ;E#10
       ;E#18
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#10;E#18;EE#14[X#9,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#16=T#15;X#8=(letrec {E#10} in S#12);E#18;EE#14[X#9,(var X#8)]} in A#13[(var X#9)]),
           E#11  |->  {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18},
           E#17  |->  {X#8=(letrec {E#10} in S#12);E#18;EE#14[X#9,(var X#8)]}}

and instantiated rules:

                                  (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(letrec {E#10} in S#12);E#18;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#16=T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];X#8=(letrec {E#10} in S#12);E#18;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=(letrec {E#10} in S#12);E#18;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];X#8=S#12;E#10;E#18;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {E#10} in S#12)
       ;X#9= A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;E#11
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#8= S#12
       ;X#9= A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;E#10
       ;E#11
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#9=A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;E#11} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#9=A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#11},(letrec {E#10} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#19[(app A#20[(var X#8)] T#21)];E#11} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])]},
           X#16         |->  X#9,
           E#17         |->  {X#8=(letrec {E#10} in S#12);E#11},
           T#15         |->  A#19[(app A#20[(var X#8)] T#21)],
           A#18         |->  A#19[(app A#20 T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#11} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#8=(letrec {E#10} in S#12);X#9=A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];E#11} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#11} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;X#9=A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;E#11} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (letrec {E#10} in S#12)
       ;X#9= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;E#11
       ;EE#20[X#19,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#8= S#12
       ;X#9= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;E#10
       ;E#11
       ;EE#20[X#19,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;E#11;EE#20[X#19,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#11;EE#20[X#19,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#21[(app A#22[(var X#19)] T#23)];E#11;EE#20[X#19,(var X#8)]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];EE#20[X#19,[.2]]},
           X#16         |->  X#9,
           E#17         |->  {X#8=(letrec {E#10} in S#12);E#11;EE#20[X#19,(var X#8)]},
           T#15         |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#11;EE#20[X#19,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#8=(letrec {E#10} in S#12);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];E#11;EE#20[X#19,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#11;EE#20[X#19,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;X#9=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;E#11;EE#20[X#19,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#21[X#9,(var X#19)]
       ;EE#22[X#20,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#21[X#9,(var X#19)]
       ;EE#22[X#20,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];X#8=(letrec {E#10} in S#12);E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#8=(letrec {E#10} in S#12);E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]},
           T#15         |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(letrec {E#10} in S#12);E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];X#8=(letrec {E#10} in S#12);E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(letrec {E#10} in S#12);E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=S#12;E#10;E#11;EE#21[X#9,(var X#19)];EE#22[X#20,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#20[X#9,(var X#19)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#10;E#11;EE#20[X#9,(var X#19)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#11;EE#20[X#9,(var X#19)]},(letrec {E#10} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23)];X#8=(letrec {E#10} in S#12);E#11;EE#20[X#9,(var X#19)]} in A#13[(var X#9)]),
           EE#14[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#8=(letrec {E#10} in S#12);E#11;EE#20[X#9,(var X#19)]},
           T#15         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(letrec {E#10} in S#12);E#11;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];X#8=(letrec {E#10} in S#12);E#11;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=(letrec {E#10} in S#12);E#11;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];X#8=S#12;E#10;E#11;EE#20[X#9,(var X#19)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= (letrec {E#10} in T#15[(var X#2)])
       ;E#11
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec {X#8=T#15[S#4];E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
  )

where

   Delta1 = {T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(letrec {E#10} in T#15)),
             (S#4,(letrec {E#10} in T#15)),
             ((letrec {X#8=(letrec {E#10} in T#15[(dummy3 )]);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),(letrec {E#10} in T#15[[.]])),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#9)],
           X#1   |->  X#8,
           E#3   |->  {E#11;EE#14[X#9,(var X#8)]},
           T#7   |->  (letrec {E#10} in T#15),
           S#12  |->  T#15[S#4]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in T#15[S#4]);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#2=S#4;X#8=(letrec {E#10} in T#15[(var X#2)]);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in T#15[S#4]);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=T#15[S#4];E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= (letrec {X#16=T#15[(var X#2)];E#18} in S#12)
       ;E#11
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= T#15[S#4]
       ;X#8= S#12
       ;E#11
       ;E#18
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(letrec {X#16=T#15;E#18} in S#12)),
             (S#4,(letrec {X#16=T#15;E#18} in S#12)),
             ((letrec {X#8=(letrec {X#16=T#15[(dummy3 )];E#18} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#16=T#15[S#4];E#11;E#18;EE#14[X#9,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {X#16=T#15[S#4];E#18} in [.])),
             [{E#11;EE#14[X#9,(var X#8)]},(letrec {X#16=T#15[S#4];E#18} in [.])],
             ((var X#2),(letrec {X#16=T#15[[.]];E#18} in S#12)),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#9)],
           X#1   |->  X#8,
           E#3   |->  {E#11;EE#14[X#9,(var X#8)]},
           T#7   |->  (letrec {X#16=T#15;E#18} in S#12),
           E#10  |->  {X#16=T#15[S#4];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {X#8=(letrec {X#16=T#15[S#4];E#18} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#2=S#4;X#8=(letrec {X#16=T#15[(var X#2)];E#18} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {X#16=T#15[S#4];E#18} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=T#15[S#4];X#8=S#12;E#11;E#18;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (letrec {E#10} in S#12)
       ;X#8= (var X#2)
       ;E#11
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),[.]),
             ((letrec {E#10} in S#12),[.]),
             ((letrec {X#8=(dummy3 );E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             ((letrec {E#10} in S#12),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6  |->  [.],
           S#5  |->  A#13[(var X#9)],
           X#1  |->  X#8,
           E#3  |->  {E#11;EE#14[X#9,(var X#8)]},
           T#7  |->  [.],
           S#4  |->  (letrec {E#10} in S#12)}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#2=(letrec {E#10} in S#12);X#8=(var X#2);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= T#7[(var X#2)]
       ;X#2= S#4
       ;X#8= (letrec {E#10} in S#12)
       ;E#15
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#1= T#7[S#4]
       ;X#8= S#12
       ;E#10
       ;E#15
       ;EE#14[X#9,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];X#8=(letrec {E#10} in S#12);E#15;EE#14[X#9,(var X#8)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=T#7[S#4];E#10;E#15;EE#14[X#9,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#1=T#7[S#4];E#15;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),T#7[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  [.],
           S#5   |->  A#13[(var X#9)],
           E#11  |->  {X#1=T#7[S#4];E#15},
           E#3   |->  {X#8=(letrec {E#10} in S#12);E#15;EE#14[X#9,(var X#8)]}}

and instantiated rules:

                                  (letrec {X#1=T#7[S#4];X#8=(letrec {E#10} in S#12);E#15;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#1=T#7[(var X#2)];X#2=S#4;X#8=(letrec {E#10} in S#12);E#15;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#1=T#7[S#4];X#8=(letrec {E#10} in S#12);E#15;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#1=T#7[S#4];X#8=S#12;E#10;E#15;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#8)
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= A#16[(var X#2)]
       ;E#11
     in
        A#13[(var X#9)]
     )
    ,
     (letrec {X#8=S#12;X#9=A#16[(var X#8)];E#10;E#11} in A#13[(var X#9)])
  )

where

   Delta1 = {A#15,T#7,A#16}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#16[[.]]),
             ((var X#8),A#16[[.]]),
             ((letrec {X#8=(letrec {E#10} in S#12);X#9=A#16[(dummy3 )];E#11} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#9=A#16[(var X#8)];E#10;E#11} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#9=A#16[(var X#8)];E#11},(letrec {E#10} in [.])],
             ((var X#2),A#16[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#1          |->  X#9,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11},
           A#15         |->  A#16,
           T#7          |->  A#16[[.]],
           T#17         |->  [.],
           S#4          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#16[(var X#8)];E#11} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#2=(var X#8);X#8=(letrec {E#10} in S#12);X#9=A#16[(var X#2)];E#11} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#16[(var X#8)];E#11} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;X#9=A#16[(var X#8)];E#10;E#11} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= A#17[(var X#8)]
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= A#16[(var X#2)]
       ;E#11
     in
        A#13[(var X#9)]
     )
    ,
     (letrec {X#8=S#12;X#9=A#16[A#17[(var X#8)]];E#10;E#11} in A#13[(var X#9)])
  )

where

   Delta1 = {A#15,T#7,A#16}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#16),
             (A#17[(var X#8)],A#16),
             ((letrec {X#8=(letrec {E#10} in S#12);X#9=A#16[(dummy3 )];E#11} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#17[(var X#8)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#9=A#16[A#17[(var X#8)]];E#10;E#11} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#9=A#16[A#17[(var X#8)]];E#11},(letrec {E#10} in [.])],
             ((var X#2),A#16[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=A#16[A#17[[.2]]]},
           X#1          |->  X#9,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11},
           A#15         |->  A#16[A#17],
           T#7          |->  A#16,
           S#4          |->  A#17[(var X#8)]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#16[A#17[(var X#8)]];E#11} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#2=A#17[(var X#8)];X#8=(letrec {E#10} in S#12);X#9=A#16[(var X#2)];E#11} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#16[A#17[(var X#8)]];E#11} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;X#9=A#16[A#17[(var X#8)]];E#10;E#11} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= A#16[(app A#17[(var X#8)] T#18[(var X#2)])]
       ;E#11
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#8= S#12
       ;X#9= A#16[(app A#17[(var X#8)] T#18[S#4])]
       ;E#10
       ;E#11
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#15,T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#16[(app A#17[(var X#8)] T#18)]),
             (S#4,A#16[(app A#17[(var X#8)] T#18)]),
             ((letrec {X#8=(letrec {E#10} in S#12);X#9=A#16[(app A#17[(var X#8)] T#18[(dummy3 )])];E#11} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#9=A#16[(app A#17[(var X#8)] T#18[S#4])];E#10;E#11} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#9=A#16[(app A#17[(var X#8)] T#18[S#4])];E#11},(letrec {E#10} in [.])],
             ((var X#2),A#16[(app A#17[(var X#8)] T#18[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[S#4])]},
           X#1          |->  X#9,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11},
           T#7          |->  A#16[(app A#17[(var X#8)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[S#4])]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#16[(app A#17[(var X#8)] T#18[S#4])];E#11} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#2=S#4;X#8=(letrec {E#10} in S#12);X#9=A#16[(app A#17[(var X#8)] T#18[(var X#2)])];E#11} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#16[(app A#17[(var X#8)] T#18[S#4])];E#11} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;X#9=A#16[(app A#17[(var X#8)] T#18[S#4])];E#10;E#11} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= A#15[(var X#8)]
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= (var X#2)
       ;E#11
     in
        A#13[(var X#9)]
     )
    ,
     (letrec {X#8=S#12;X#9=A#15[(var X#8)];E#10;E#11} in A#13[(var X#9)])
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),[.]),
             (A#15[(var X#8)],[.]),
             ((letrec {X#8=(letrec {E#10} in S#12);X#9=(dummy3 );E#11} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#15[(var X#8)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#9=A#15[(var X#8)];E#10;E#11} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#9=A#15[(var X#8)];E#11},(letrec {E#10} in [.])],
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#1          |->  X#9,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11},
           T#7          |->  [.],
           S#4          |->  A#15[(var X#8)]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#15[(var X#8)];E#11} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#2=A#15[(var X#8)];X#8=(letrec {E#10} in S#12);X#9=(var X#2);E#11} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#15[(var X#8)];E#11} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;X#9=A#15[(var X#8)];E#10;E#11} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#16)
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= A#18[(var X#2)]
       ;E#11
       ;EE#17[X#16,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#8= S#12
       ;X#9= A#18[(var X#16)]
       ;E#10
       ;E#11
       ;EE#17[X#16,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#15,T#7,A#18}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18[[.]]),
             ((var X#16),A#18[[.]]),
             ((letrec {X#8=(letrec {E#10} in S#12);X#9=A#18[(dummy3 )];E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#16),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#9=A#18[(var X#16)];E#10;E#11;EE#17[X#16,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#9=A#18[(var X#16)];E#11;EE#17[X#16,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),A#18[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=A#18[(var X#16)];EE#17[X#16,[.2]]},
           X#1          |->  X#9,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#17[X#16,(var X#8)]},
           A#15         |->  A#18,
           T#7          |->  A#18[[.]],
           T#19         |->  [.],
           S#4          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#18[(var X#16)];E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#2=(var X#16);X#8=(letrec {E#10} in S#12);X#9=A#18[(var X#2)];E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#18[(var X#16)];E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;X#9=A#18[(var X#16)];E#10;E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= A#19[(var X#16)]
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= A#18[(var X#2)]
       ;E#11
       ;EE#17[X#16,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#8= S#12
       ;X#9= A#18[A#19[(var X#16)]]
       ;E#10
       ;E#11
       ;EE#17[X#16,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#15,T#7,A#18}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18),
             (A#19[(var X#16)],A#18),
             ((letrec {X#8=(letrec {E#10} in S#12);X#9=A#18[(dummy3 )];E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#19[(var X#16)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#9=A#18[A#19[(var X#16)]];E#10;E#11;EE#17[X#16,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#9=A#18[A#19[(var X#16)]];E#11;EE#17[X#16,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),A#18[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=A#18[A#19[(var X#16)]];EE#17[X#16,[.2]]},
           X#1          |->  X#9,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#17[X#16,(var X#8)]},
           A#15         |->  A#18[A#19],
           T#7          |->  A#18,
           S#4          |->  A#19[(var X#16)]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#18[A#19[(var X#16)]];E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#2=A#19[(var X#16)];X#8=(letrec {E#10} in S#12);X#9=A#18[(var X#2)];E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#18[A#19[(var X#16)]];E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;X#9=A#18[A#19[(var X#16)]];E#10;E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= A#18[(app A#19[(var X#16)] T#20[(var X#2)])]
       ;E#11
       ;EE#17[X#16,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#8= S#12
       ;X#9= A#18[(app A#19[(var X#16)] T#20[S#4])]
       ;E#10
       ;E#11
       ;EE#17[X#16,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#15,T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18[(app A#19[(var X#16)] T#20)]),
             (S#4,A#18[(app A#19[(var X#16)] T#20)]),
             ((letrec {X#8=(letrec {E#10} in S#12);X#9=A#18[(app A#19[(var X#16)] T#20[(dummy3 )])];E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#9=A#18[(app A#19[(var X#16)] T#20[S#4])];E#10;E#11;EE#17[X#16,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#9=A#18[(app A#19[(var X#16)] T#20[S#4])];E#11;EE#17[X#16,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),A#18[(app A#19[(var X#16)] T#20[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[S#4])];EE#17[X#16,[.2]]},
           X#1          |->  X#9,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#17[X#16,(var X#8)]},
           T#7          |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#4])]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#18[(app A#19[(var X#16)] T#20[S#4])];E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#2=S#4;X#8=(letrec {E#10} in S#12);X#9=A#18[(app A#19[(var X#16)] T#20[(var X#2)])];E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#18[(app A#19[(var X#16)] T#20[S#4])];E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;X#9=A#18[(app A#19[(var X#16)] T#20[S#4])];E#10;E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= A#15[(var X#16)]
       ;X#8= (letrec {E#10} in S#12)
       ;X#9= (var X#2)
       ;E#11
       ;EE#17[X#16,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#8= S#12
       ;X#9= A#15[(var X#16)]
       ;E#10
       ;E#11
       ;EE#17[X#16,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),[.]),
             (A#15[(var X#16)],[.]),
             ((letrec {X#8=(letrec {E#10} in S#12);X#9=(dummy3 );E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#15[(var X#16)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#9=A#15[(var X#16)];E#10;E#11;EE#17[X#16,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#9=A#15[(var X#16)];E#11;EE#17[X#16,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {[.1]=A#15[(var X#16)];EE#17[X#16,[.2]]},
           X#1          |->  X#9,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#17[X#16,(var X#8)]},
           T#7          |->  [.],
           S#4          |->  A#15[(var X#16)]}

and instantiated rules:

                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#15[(var X#16)];E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#2=A#15[(var X#16)];X#8=(letrec {E#10} in S#12);X#9=(var X#2);E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);X#9=A#15[(var X#16)];E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;X#9=A#15[(var X#16)];E#10;E#11;EE#17[X#16,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(var X#2)]
       ;X#2= (var X#17)
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#17,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#20[(var X#17)]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#17,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#15,T#7,A#20}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#20[[.]]),
             ((var X#17),A#20[[.]]),
             ((letrec {X#16=A#20[(dummy3 )];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#16=A#20[(var X#17)];E#10;E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=A#20[(var X#17)];E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),A#20[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#20[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#1          |->  X#16,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]},
           A#15         |->  A#20,
           T#7          |->  A#20[[.]],
           T#21         |->  [.],
           S#4          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#16=A#20[(var X#17)];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#16=A#20[(var X#2)];X#2=(var X#17);X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#20[(var X#17)];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=A#20[(var X#17)];X#8=S#12;E#10;E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(var X#2)]
       ;X#2= A#21[(var X#17)]
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#17,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#20[A#21[(var X#17)]]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#17,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#15,T#7,A#20}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#20),
             (A#21[(var X#17)],A#20),
             ((letrec {X#16=A#20[(dummy3 )];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#21[(var X#17)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#16=A#20[A#21[(var X#17)]];E#10;E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=A#20[A#21[(var X#17)]];E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),A#20[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#20[A#21[(var X#17)]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#1          |->  X#16,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]},
           A#15         |->  A#20[A#21],
           T#7          |->  A#20,
           S#4          |->  A#21[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#21[(var X#17)]];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#16=A#20[(var X#2)];X#2=A#21[(var X#17)];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#20[A#21[(var X#17)]];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=A#20[A#21[(var X#17)]];X#8=S#12;E#10;E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(var X#2)])]
       ;X#2= S#4
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#17,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[S#4])]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#17,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#15,T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#20[(app A#21[(var X#17)] T#22)]),
             (S#4,A#20[(app A#21[(var X#17)] T#22)]),
             ((letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(dummy3 )])];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#4])];E#10;E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=A#20[(app A#21[(var X#17)] T#22[S#4])];E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),A#20[(app A#21[(var X#17)] T#22[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[S#4])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#1          |->  X#16,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]},
           T#7          |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[S#4])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#4])];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(var X#2)])];X#2=S#4;X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#4])];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#4])];X#8=S#12;E#10;E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#2)
       ;X#2= A#15[(var X#17)]
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#17,(var X#8)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#15[(var X#17)]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#18[X#9,(var X#16)]
       ;EE#19[X#17,(var X#8)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),[.]),
             (A#15[(var X#17)],[.]),
             ((letrec {X#16=(dummy3 );X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#15[(var X#17)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#16=A#15[(var X#17)];E#10;E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=A#15[(var X#17)];E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]},(letrec {E#10} in [.])],
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#15[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#1          |->  X#16,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]},
           T#7          |->  [.],
           S#4          |->  A#15[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#15[(var X#17)];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#16=(var X#2);X#2=A#15[(var X#17)];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#15[(var X#17)];X#8=(letrec {E#10} in S#12);E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=A#15[(var X#17)];X#8=S#12;E#10;E#11;EE#18[X#9,(var X#16)];EE#19[X#17,(var X#8)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(var X#2)]
       ;X#2= (var X#8)
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#18[(var X#8)]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#15,T#7,A#18}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18[[.]]),
             ((var X#8),A#18[[.]]),
             ((letrec {X#16=A#18[(dummy3 )];X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#16=A#18[(var X#8)];E#10;E#11;EE#17[X#9,(var X#16)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=A#18[(var X#8)];E#11;EE#17[X#9,(var X#16)]},(letrec {E#10} in [.])],
             ((var X#2),A#18[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]},
           A#15         |->  A#18,
           T#7          |->  A#18[[.]],
           T#19         |->  [.],
           S#4          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#16=A#18[(var X#8)];X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#16=A#18[(var X#2)];X#2=(var X#8);X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#18[(var X#8)];X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=A#18[(var X#8)];X#8=S#12;E#10;E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(var X#2)]
       ;X#2= A#19[(var X#8)]
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#18[A#19[(var X#8)]]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#15,T#7,A#18}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18),
             (A#19[(var X#8)],A#18),
             ((letrec {X#16=A#18[(dummy3 )];X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#19[(var X#8)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#16=A#18[A#19[(var X#8)]];E#10;E#11;EE#17[X#9,(var X#16)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=A#18[A#19[(var X#8)]];E#11;EE#17[X#9,(var X#16)]},(letrec {E#10} in [.])],
             ((var X#2),A#18[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#18[A#19[[.2]]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]},
           A#15         |->  A#18[A#19],
           T#7          |->  A#18,
           S#4          |->  A#19[(var X#8)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#19[(var X#8)]];X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#16=A#18[(var X#2)];X#2=A#19[(var X#8)];X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#18[A#19[(var X#8)]];X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=A#18[A#19[(var X#8)]];X#8=S#12;E#10;E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(var X#8)] T#20[(var X#2)])]
       ;X#2= S#4
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(var X#8)] T#20[S#4])]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {A#15,T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18[(app A#19[(var X#8)] T#20)]),
             (S#4,A#18[(app A#19[(var X#8)] T#20)]),
             ((letrec {X#16=A#18[(app A#19[(var X#8)] T#20[(dummy3 )])];X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#16=A#18[(app A#19[(var X#8)] T#20[S#4])];E#10;E#11;EE#17[X#9,(var X#16)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=A#18[(app A#19[(var X#8)] T#20[S#4])];E#11;EE#17[X#9,(var X#16)]},(letrec {E#10} in [.])],
             ((var X#2),A#18[(app A#19[(var X#8)] T#20[[.]])]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[S#4])];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]},
           T#7          |->  A#18[(app A#19[(var X#8)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#4])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(var X#8)] T#20[S#4])];X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#16=A#18[(app A#19[(var X#8)] T#20[(var X#2)])];X#2=S#4;X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(var X#8)] T#20[S#4])];X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=A#18[(app A#19[(var X#8)] T#20[S#4])];X#8=S#12;E#10;E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#2)
       ;X#2= A#15[(var X#8)]
       ;X#8= (letrec {E#10} in S#12)
       ;E#11
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
    ,
     (letrec
        X#16= A#15[(var X#8)]
       ;X#8= S#12
       ;E#10
       ;E#11
       ;EE#17[X#9,(var X#16)]
     in
        A#13[(var X#9)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),[.]),
             (A#15[(var X#8)],[.]),
             ((letrec {X#16=(dummy3 );X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#15[(var X#8)],(letrec {X#2=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#16=A#15[(var X#8)];E#10;E#11;EE#17[X#9,(var X#16)]} in [.])),
             (A#13[(var X#9)],(letrec {E#10} in [.])),
             [{X#16=A#15[(var X#8)];E#11;EE#17[X#9,(var X#16)]},(letrec {E#10} in [.])],
             ((var X#2),[.]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]]),
             ((var X#8),[.]),
             ((var X#9),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,llet-e2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#8=S#12;E#10;E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])
    and constraints: E#10/= {}, ((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])), (A#13[(var X#9)],(letrec {E#10} in [.])), ({E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {X#8=(letrec {E#10} in S#12);E#11;EE#14[X#9,(var X#8)]} in A#13[(var X#9)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),((var X#8),(letrec {E#10;E#11;EE#14[X#9,(var X#8)]} in [.])),(A#13[(var X#9)],(letrec {E#10} in [.])),[{E#11;EE#14[X#9,(var X#8)]},(letrec {E#10} in [.])],((var X#2),T#7[[.]]),((var X#8),[.]),((var X#9),A#13[[.]]),((var X#8),[.]),((var X#9),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#9)],
           EE#14[.1,.2] |-> {X#16=A#15[[.2]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]},
           T#7          |->  [.],
           S#4          |->  A#15[(var X#8)]}

and instantiated rules:

                                  (letrec {X#16=A#15[(var X#8)];X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -ucp2->                       (letrec {X#16=(var X#2);X#2=A#15[(var X#8)];X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    ................................................................................
                                  (letrec {X#16=A#15[(var X#8)];X#8=(letrec {E#10} in S#12);E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    -SR,llet-e2->                 (letrec {X#16=A#15[(var X#8)];X#8=S#12;E#10;E#11;EE#17[X#9,(var X#16)]} in A#13[(var X#9)])
    

================================================================================
Critical Pair:

  (
     A#12[(app (letrec {E#8} in T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#9)]
    ,
     A#12[(letrec {E#8} in (app T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#9))]
  )

where

   Delta1 = {T#14,T#13,A#11,T#6,A#12}
   Delta2 = {E#8}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {A#11  |->  A#12,
           T#6   |->  A#12[(app (letrec {E#8} in T#15) S#9)],
           T#13  |->  (app (letrec {E#8} in T#15) S#9),
           T#14  |->  (letrec {E#8} in T#15),
           S#10  |->  T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  A#12[(app (letrec {E#8} in T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#9)]
    -ucp2->                       A#12[(app (letrec {E#8} in T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#9)]
    ................................................................................
                                  A#12[(app (letrec {E#8} in T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#9)]
    -SR,lapp1->                   A#12[(letrec {E#8} in (app T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#9))]
    

================================================================================
Critical Pair:

  (
     A#12[(app (letrec
                   X#16= T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
                  ;E#18
                in
                   S#10
                ) S#9)]
    ,
     A#12[(letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18} in (app S#10 S#9))]
  )

where

   Delta1 = {T#14,T#13,A#11,T#6,A#12}
   Delta2 = {E#8}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#9,(letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {A#11  |->  A#12,
           T#6   |->  A#12[(app (letrec {X#16=T#15;E#18} in S#10) S#9)],
           T#13  |->  (app (letrec {X#16=T#15;E#18} in S#10) S#9),
           T#14  |->  (letrec {X#16=T#15;E#18} in S#10),
           E#8   |->  {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  A#12[(app (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18} in S#10) S#9)]
    -ucp2->                       A#12[(app (letrec {X#16=T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#18} in S#10) S#9)]
    ................................................................................
                                  A#12[(app (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18} in S#10) S#9)]
    -SR,lapp1->                   A#12[(letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18} in (app S#10 S#9))]
    

================================================================================
Critical Pair:

  (
     A#12[(app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#15} in S#10) S#9)]
    ,
     A#12[(letrec {X#1=T#7[S#4];E#15} in (app S#10 S#9))]
  )

where

   Delta1 = {T#13,A#11,T#6,A#12}
   Delta2 = {E#8}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#15} in S#10),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#9,(letrec {X#1=T#7[S#4];E#15} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {A#11  |->  A#12,
           T#6   |->  A#12[(app [.] S#9)],
           T#13  |->  (app [.] S#9),
           T#14  |->  [.],
           S#5   |->  S#10,
           E#8   |->  {X#1=T#7[S#4];E#15},
           E#3   |->  {E#15}}

and instantiated rules:

                                  A#12[(app (letrec {X#1=T#7[S#4];E#15} in S#10) S#9)]
    -ucp2->                       A#12[(app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#15} in S#10) S#9)]
    ................................................................................
                                  A#12[(app (letrec {X#1=T#7[S#4];E#15} in S#10) S#9)]
    -SR,lapp1->                   A#12[(letrec {X#1=T#7[S#4];E#15} in (app S#10 S#9))]
    

================================================================================
Critical Pair:

  (
     A#12[(app (letrec {E#8} in S#10) T#14[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
    ,
     A#12[(letrec {E#8} in (app S#10 T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)]))]
  )

where

   Delta1 = {T#13,A#11,T#6,A#12}
   Delta2 = {E#8}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {E#8} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {A#11  |->  A#12,
           T#6   |->  A#12[(app (letrec {E#8} in S#10) T#14)],
           T#13  |->  (app (letrec {E#8} in S#10) T#14),
           S#9   |->  T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  A#12[(app (letrec {E#8} in S#10) T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
    -ucp2->                       A#12[(app (letrec {E#8} in S#10) T#14[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
    ................................................................................
                                  A#12[(app (letrec {E#8} in S#10) T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
    -SR,lapp1->                   A#12[(letrec {E#8} in (app S#10 T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)]))]
    

================================================================================
Critical Pair:

  (
     A#12[(app A#13[(app (letrec {E#8} in S#10) S#9)] T#14[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
    ,
     A#12[(app A#13[(letrec {E#8} in (app S#10 S#9))] T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
  )

where

   Delta1 = {A#11,T#6}
   Delta2 = {E#8}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  A#12[(app A#13[(app (letrec {E#8} in S#10) S#9)] T#14)],
           A#11  |->  A#12[(app A#13 T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  A#12[(app A#13[(app (letrec {E#8} in S#10) S#9)] T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
    -ucp2->                       A#12[(app A#13[(app (letrec {E#8} in S#10) S#9)] T#14[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
    ................................................................................
                                  A#12[(app A#13[(app (letrec {E#8} in S#10) S#9)] T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
    -SR,lapp1->                   A#12[(app A#13[(letrec {E#8} in (app S#10 S#9))] T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#8} in T#13[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#9)
    ,
     (letrec {E#8} in (app T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#9))
  )

where

   Delta1 = {T#12,T#6}
   Delta2 = {E#8}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#9,(letrec {E#8} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {A#11  |->  [.],
           T#6   |->  (app (letrec {E#8} in T#13) S#9),
           T#12  |->  (letrec {E#8} in T#13),
           S#10  |->  T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (app (letrec {E#8} in T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#9)
    -ucp2->                       (app (letrec {E#8} in T#13[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#9)
    ................................................................................
                                  (app (letrec {E#8} in T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#9)
    -SR,lapp1->                   (letrec {E#8} in (app T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#9))
    

================================================================================
Critical Pair:

  (
     (app (letrec
             X#14= T#13[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
            ;E#16
          in
             S#10
          ) S#9)
    ,
     (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16} in (app S#10 S#9))
  )

where

   Delta1 = {T#12,T#6}
   Delta2 = {E#8}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#9,(letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {A#11  |->  [.],
           T#6   |->  (app (letrec {X#14=T#13;E#16} in S#10) S#9),
           T#12  |->  (letrec {X#14=T#13;E#16} in S#10),
           E#8   |->  {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (app (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16} in S#10) S#9)
    -ucp2->                       (app (letrec {X#14=T#13[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#16} in S#10) S#9)
    ................................................................................
                                  (app (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16} in S#10) S#9)
    -SR,lapp1->                   (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16} in (app S#10 S#9))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#13} in S#10) S#9)
    ,
     (letrec {X#1=T#7[S#4];E#13} in (app S#10 S#9))
  )

where

   Delta1 = {T#6}
   Delta2 = {E#8}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#13} in S#10),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#9,(letrec {X#1=T#7[S#4];E#13} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {A#11  |->  [.],
           T#6   |->  (app [.] S#9),
           T#12  |->  [.],
           S#5   |->  S#10,
           E#8   |->  {X#1=T#7[S#4];E#13},
           E#3   |->  {E#13}}

and instantiated rules:

                                  (app (letrec {X#1=T#7[S#4];E#13} in S#10) S#9)
    -ucp2->                       (app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#13} in S#10) S#9)
    ................................................................................
                                  (app (letrec {X#1=T#7[S#4];E#13} in S#10) S#9)
    -SR,lapp1->                   (letrec {X#1=T#7[S#4];E#13} in (app S#10 S#9))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#8} in S#10) T#12[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])
    ,
     (letrec {E#8} in (app S#10 T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)]))
  )

where

   Delta1 = {T#6}
   Delta2 = {E#8}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {E#8} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp1-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  A#11[(app (letrec {E#8} in S#10) S#9)]
    -SR,lapp1->                   A#11[(letrec {E#8} in (app S#10 S#9))]
    and constraints: E#8/= {}, (S#9,(letrec {E#8} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        A#11[(app (letrec {E#8} in S#10) S#9)]}
      Delta1=  {}
      Delta2=  {E#8}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#9,(letrec {E#8} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {A#11  |->  [.],
           T#6   |->  (app (letrec {E#8} in S#10) T#12),
           S#9   |->  T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (app (letrec {E#8} in S#10) T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)])
    -ucp2->                       (app (letrec {E#8} in S#10) T#12[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])
    ................................................................................
                                  (app (letrec {E#8} in S#10) T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)])
    -SR,lapp1->                   (letrec {E#8} in (app S#10 T#12[(letrec {X#1=T#7[S#4];E#3} in S#5)]))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#14[(app (letrec {E#9} in T#17[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#10)]
     )
    ,
     (letrec
        E#8
     in
        A#14[(letrec {E#9} in (app T#17[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#10))]
     )
  )

where

   Delta1 = {T#16,T#15,A#12,T#13,T#6,A#14}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#10,(letrec {E#9} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(letrec {E#9} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in A#14[(app (letrec {E#9} in T#17) S#10)]),
           A#12  |->  A#14,
           T#13  |->  A#14[(app (letrec {E#9} in T#17) S#10)],
           T#15  |->  (app (letrec {E#9} in T#17) S#10),
           T#16  |->  (letrec {E#9} in T#17),
           S#11  |->  T#17[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#8} in A#14[(app (letrec {E#9} in T#17[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#10)])
    -ucp2->                       (letrec {E#8} in A#14[(app (letrec {E#9} in T#17[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#10)])
    ................................................................................
                                  (letrec {E#8} in A#14[(app (letrec {E#9} in T#17[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#14[(letrec {E#9} in (app T#17[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#10))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#14[(app (letrec
                      X#18= T#17[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
                     ;E#20
                   in
                      S#11
                   ) S#10)]
     )
    ,
     (letrec
        E#8
     in
        A#14[(letrec {X#18=T#17[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#20} in (app S#11 S#10))]
     )
  )

where

   Delta1 = {T#16,T#15,A#12,T#13,T#6,A#14}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#10,(letrec {X#18=T#17[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#20} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(letrec {E#9} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in A#14[(app (letrec {X#18=T#17;E#20} in S#11) S#10)]),
           A#12  |->  A#14,
           T#13  |->  A#14[(app (letrec {X#18=T#17;E#20} in S#11) S#10)],
           T#15  |->  (app (letrec {X#18=T#17;E#20} in S#11) S#10),
           T#16  |->  (letrec {X#18=T#17;E#20} in S#11),
           E#9   |->  {X#18=T#17[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#20},
           E#19  |->  {E#20}}

and instantiated rules:

                                  (letrec {E#8} in A#14[(app (letrec {X#18=T#17[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#20} in S#11) S#10)])
    -ucp2->                       (letrec {E#8} in A#14[(app (letrec {X#18=T#17[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#20} in S#11) S#10)])
    ................................................................................
                                  (letrec {E#8} in A#14[(app (letrec {X#18=T#17[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#20} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#14[(letrec {X#18=T#17[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#20} in (app S#11 S#10))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#14[(app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#17} in S#11) S#10)]
     )
    ,
     (letrec {E#8} in A#14[(letrec {X#1=T#7[S#4];E#17} in (app S#11 S#10))])
  )

where

   Delta1 = {T#15,A#12,T#13,T#6,A#14}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#17} in S#11),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#10,(letrec {X#1=T#7[S#4];E#17} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(letrec {E#9} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in A#14[(app [.] S#10)]),
           A#12  |->  A#14,
           T#13  |->  A#14[(app [.] S#10)],
           T#15  |->  (app [.] S#10),
           T#16  |->  [.],
           S#5   |->  S#11,
           E#9   |->  {X#1=T#7[S#4];E#17},
           E#3   |->  {E#17}}

and instantiated rules:

                                  (letrec {E#8} in A#14[(app (letrec {X#1=T#7[S#4];E#17} in S#11) S#10)])
    -ucp2->                       (letrec {E#8} in A#14[(app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#17} in S#11) S#10)])
    ................................................................................
                                  (letrec {E#8} in A#14[(app (letrec {X#1=T#7[S#4];E#17} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#14[(letrec {X#1=T#7[S#4];E#17} in (app S#11 S#10))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#14[(app (letrec {E#9} in S#11) T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
     )
    ,
     (letrec
        E#8
     in
        A#14[(letrec {E#9} in (app S#11 T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)]))]
     )
  )

where

   Delta1 = {T#15,A#12,T#13,T#6,A#14}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {E#9} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(letrec {E#9} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in A#14[(app (letrec {E#9} in S#11) T#16)]),
           A#12  |->  A#14,
           T#13  |->  A#14[(app (letrec {E#9} in S#11) T#16)],
           T#15  |->  (app (letrec {E#9} in S#11) T#16),
           S#10  |->  T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#8} in A#14[(app (letrec {E#9} in S#11) T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -ucp2->                       (letrec {E#8} in A#14[(app (letrec {E#9} in S#11) T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#8} in A#14[(app (letrec {E#9} in S#11) T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -SR,lapp2->                   (letrec {E#8} in A#14[(letrec {E#9} in (app S#11 T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        A#14[(app A#15[(app (letrec {E#9} in S#11) S#10)] T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
     )
    ,
     (letrec
        E#8
     in
        A#14[(app A#15[(letrec {E#9} in (app S#11 S#10))] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#12,T#13,T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#10,(letrec {E#9} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(letrec {E#9} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in A#14[(app A#15[(app (letrec {E#9} in S#11) S#10)] T#16)]),
           T#13  |->  A#14[(app A#15[(app (letrec {E#9} in S#11) S#10)] T#16)],
           A#12  |->  A#14[(app A#15 T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {E#8} in A#14[(app A#15[(app (letrec {E#9} in S#11) S#10)] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -ucp2->                       (letrec {E#8} in A#14[(app A#15[(app (letrec {E#9} in S#11) S#10)] T#16[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#8} in A#14[(app A#15[(app (letrec {E#9} in S#11) S#10)] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -SR,lapp2->                   (letrec {E#8} in A#14[(app A#15[(letrec {E#9} in (app S#11 S#10))] T#16[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        (app (letrec {E#9} in T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#10)
     )
    ,
     (letrec
        E#8
     in
        (letrec {E#9} in (app T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#10))
     )
  )

where

   Delta1 = {T#14,T#13,T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#10,(letrec {E#9} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(letrec {E#9} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in (app (letrec {E#9} in T#15) S#10)),
           A#12  |->  [.],
           T#13  |->  (app (letrec {E#9} in T#15) S#10),
           T#14  |->  (letrec {E#9} in T#15),
           S#11  |->  T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#8} in (app (letrec {E#9} in T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#10))
    -ucp2->                       (letrec {E#8} in (app (letrec {E#9} in T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#10))
    ................................................................................
                                  (letrec {E#8} in (app (letrec {E#9} in T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#10))
    -SR,lapp2->                   (letrec {E#8} in (letrec {E#9} in (app T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#10)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        (app (letrec
                X#16= T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
               ;E#18
             in
                S#11
             ) S#10)
     )
    ,
     (letrec
        E#8
     in
        (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18} in (app S#11 S#10))
     )
  )

where

   Delta1 = {T#14,T#13,T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#10,(letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(letrec {E#9} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in (app (letrec {X#16=T#15;E#18} in S#11) S#10)),
           A#12  |->  [.],
           T#13  |->  (app (letrec {X#16=T#15;E#18} in S#11) S#10),
           T#14  |->  (letrec {X#16=T#15;E#18} in S#11),
           E#9   |->  {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {E#8} in (app (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18} in S#11) S#10))
    -ucp2->                       (letrec {E#8} in (app (letrec {X#16=T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#18} in S#11) S#10))
    ................................................................................
                                  (letrec {E#8} in (app (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18} in S#11) S#10))
    -SR,lapp2->                   (letrec {E#8} in (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18} in (app S#11 S#10)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#8} in (app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#15} in S#11) S#10))
    ,
     (letrec {E#8} in (letrec {X#1=T#7[S#4];E#15} in (app S#11 S#10)))
  )

where

   Delta1 = {T#13,T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#15} in S#11),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#10,(letrec {X#1=T#7[S#4];E#15} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(letrec {E#9} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in (app [.] S#10)),
           A#12  |->  [.],
           T#13  |->  (app [.] S#10),
           T#14  |->  [.],
           S#5   |->  S#11,
           E#9   |->  {X#1=T#7[S#4];E#15},
           E#3   |->  {E#15}}

and instantiated rules:

                                  (letrec {E#8} in (app (letrec {X#1=T#7[S#4];E#15} in S#11) S#10))
    -ucp2->                       (letrec {E#8} in (app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#15} in S#11) S#10))
    ................................................................................
                                  (letrec {E#8} in (app (letrec {X#1=T#7[S#4];E#15} in S#11) S#10))
    -SR,lapp2->                   (letrec {E#8} in (letrec {X#1=T#7[S#4];E#15} in (app S#11 S#10)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#8
     in
        (app (letrec {E#9} in S#11) T#14[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])
     )
    ,
     (letrec
        E#8
     in
        (letrec {E#9} in (app S#11 T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)]))
     )
  )

where

   Delta1 = {T#13,T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {E#9} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(letrec {E#9} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#8} in (app (letrec {E#9} in S#11) T#14)),
           A#12  |->  [.],
           T#13  |->  (app (letrec {E#9} in S#11) T#14),
           S#10  |->  T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {E#8} in (app (letrec {E#9} in S#11) T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)]))
    -ucp2->                       (letrec {E#8} in (app (letrec {E#9} in S#11) T#14[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]))
    ................................................................................
                                  (letrec {E#8} in (app (letrec {E#9} in S#11) T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)]))
    -SR,lapp2->                   (letrec {E#8} in (letrec {E#9} in (app S#11 T#14[(letrec {X#1=T#7[S#4];E#3} in S#5)])))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
       ;E#16
     in
        A#12[(app (letrec {E#9} in S#11) S#10)]
     )
    ,
     (letrec
        X#14= T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)]
       ;E#16
     in
        A#12[(letrec {E#9} in (app S#11 S#10))]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#10,(letrec {E#9} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(letrec {E#9} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#14=T#13;E#16} in A#12[(app (letrec {E#9} in S#11) S#10)]),
           E#8   |->  {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -ucp2->                       (letrec {X#14=T#13[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#16} in A#12[(app (letrec {E#9} in S#11) S#10)])
    ................................................................................
                                  (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {X#14=T#13[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#16} in A#12[(letrec {E#9} in (app S#11 S#10))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= T#7[(var X#2)]
       ;X#2= S#4
       ;E#13
     in
        A#12[(app (letrec {E#9} in S#11) S#10)]
     )
    ,
     (letrec {X#1=T#7[S#4];E#13} in A#12[(letrec {E#9} in (app S#11 S#10))])
  )

where

   Delta1 = {}
   Delta2 = {E#8,E#9}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#13} in A#12[(app (letrec {E#9} in S#11) S#10)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#10,(letrec {E#9} in [.])),
             ((var X#2),T#7[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp2-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {E#8} in A#12[(letrec {E#9} in (app S#11 S#10))])
    and constraints: E#8/= {}, E#9/= {}, (S#10,(letrec {E#9} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#8} in A#12[(app (letrec {E#9} in S#11) S#10)])}
      Delta1=  {}
      Delta2=  {E#8,E#9}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#10,(letrec {E#9} in [.])),((var X#2),T#7[[.]])}


and found solution:

    Sol = {T#6  |->  [.],
           S#5  |->  A#12[(app (letrec {E#9} in S#11) S#10)],
           E#8  |->  {X#1=T#7[S#4];E#13},
           E#3  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#1=T#7[S#4];E#13} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -ucp2->                       (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#13} in A#12[(app (letrec {E#9} in S#11) S#10)])
    ................................................................................
                                  (letrec {X#1=T#7[S#4];E#13} in A#12[(app (letrec {E#9} in S#11) S#10)])
    -SR,lapp2->                   (letrec {X#1=T#7[S#4];E#13} in A#12[(letrec {E#9} in (app S#11 S#10))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#9
       ;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]
     in
        A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
     )
    ,
     (letrec
        E#9
       ;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]
     in
        A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
     )
  )

where

   Delta1 = {A#13,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#16[(app A#17[[.]] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])]),
             ((var X#8),A#16[(app A#17[[.]] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#8)] T#18)],
           A#13  |->  A#16[(app A#17 T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -ucp2->                       (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])])
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#16[(app A#17[(var X#8)] T#18[(letrec {X#1=T#7[S#4];E#3} in S#5)])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
       ;E#18
       ;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)]
       ;E#18
       ;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6   |->  (letrec {X#16=T#15;E#18;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)]),
           E#9   |->  {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18},
           E#17  |->  {E#18;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]}}

and instantiated rules:

                                  (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=T#15[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#18;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=T#15[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#18;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#19[(app (letrec {E#10} in T#22[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#11)]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#19[(letrec {E#10} in (app T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#11))]
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#21,T#20,A#18,T#15,T#6,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#19[(app (letrec {E#10} in T#22) S#11)];E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  A#19,
           T#15         |->  A#19[(app (letrec {E#10} in T#22) S#11)],
           T#20         |->  (app (letrec {E#10} in T#22) S#11),
           T#21         |->  (letrec {E#10} in T#22),
           S#12         |->  T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=A#19[(app (letrec {E#10} in T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#11)];E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#8=A#19[(app (letrec {E#10} in T#22[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#11)];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#19[(app (letrec {E#10} in T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#11)];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#19[(letrec {E#10} in (app T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#11))];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#19[(app (letrec
                           X#23= T#22[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
                          ;E#25
                        in
                           S#12
                        ) S#11)]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#19[(letrec {X#23=T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#25} in (app S#12 S#11))]
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#21,T#20,A#18,T#15,T#6,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {X#23=T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#25} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#19[(app (letrec {X#23=T#22;E#25} in S#12) S#11)];E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  A#19,
           T#15         |->  A#19[(app (letrec {X#23=T#22;E#25} in S#12) S#11)],
           T#20         |->  (app (letrec {X#23=T#22;E#25} in S#12) S#11),
           T#21         |->  (letrec {X#23=T#22;E#25} in S#12),
           E#10         |->  {X#23=T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#25},
           E#24         |->  {E#25}}

and instantiated rules:

                                  (letrec {X#8=A#19[(app (letrec {X#23=T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#25} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#8=A#19[(app (letrec {X#23=T#22[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#25} in S#12) S#11)];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#19[(app (letrec {X#23=T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#25} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#19[(letrec {X#23=T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#25} in (app S#12 S#11))];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#19[(app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#22} in S#12) S#11)]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#19[(letrec {X#1=T#7[S#4];E#22} in (app S#12 S#11))]
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#6,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#22} in S#12),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {X#1=T#7[S#4];E#22} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#19[(app [.] S#11)];E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  A#19,
           T#15         |->  A#19[(app [.] S#11)],
           T#20         |->  (app [.] S#11),
           T#21         |->  [.],
           S#5          |->  S#12,
           E#10         |->  {X#1=T#7[S#4];E#22},
           E#3          |->  {E#22}}

and instantiated rules:

                                  (letrec {X#8=A#19[(app (letrec {X#1=T#7[S#4];E#22} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#8=A#19[(app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#22} in S#12) S#11)];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#19[(app (letrec {X#1=T#7[S#4];E#22} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#19[(letrec {X#1=T#7[S#4];E#22} in (app S#12 S#11))];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#19[(app (letrec {E#10} in S#12) T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#19[(letrec {E#10} in (app S#12 T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]))]
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#6,A#19}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {E#10} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#19[(app (letrec {E#10} in S#12) T#21)];E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  A#19,
           T#15         |->  A#19[(app (letrec {E#10} in S#12) T#21)],
           T#20         |->  (app (letrec {E#10} in S#12) T#21),
           S#11         |->  T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=A#19[(app (letrec {E#10} in S#12) T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#8=A#19[(app (letrec {E#10} in S#12) T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#19[(app (letrec {E#10} in S#12) T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#19[(letrec {E#10} in (app S#12 T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]))];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#19[(app A#20[(letrec {E#10} in (app S#12 S#11))] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] T#21)];E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           T#15         |->  A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] T#21)],
           A#18         |->  A#19[(app A#20 T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#8=A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#19[(app A#20[(app (letrec {E#10} in S#12) S#11)] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#19[(app A#20[(letrec {E#10} in (app S#12 S#11))] T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (app (letrec {E#10} in T#20[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#11)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= (letrec {E#10} in (app T#20[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#11))
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#19,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=(app (letrec {E#10} in T#20) S#11);E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  [.],
           T#15         |->  (app (letrec {E#10} in T#20) S#11),
           T#19         |->  (letrec {E#10} in T#20),
           S#12         |->  T#20[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=(app (letrec {E#10} in T#20[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#11);E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#8=(app (letrec {E#10} in T#20[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#11);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (letrec {E#10} in T#20[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#11);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=(letrec {E#10} in (app T#20[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#11));E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (app (letrec
                     X#21= T#20[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
                    ;E#23
                  in
                     S#12
                  ) S#11)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= (letrec {X#21=T#20[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#23} in (app S#12 S#11))
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#19,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {X#21=T#20[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#23} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=(app (letrec {X#21=T#20;E#23} in S#12) S#11);E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  [.],
           T#15         |->  (app (letrec {X#21=T#20;E#23} in S#12) S#11),
           T#19         |->  (letrec {X#21=T#20;E#23} in S#12),
           E#10         |->  {X#21=T#20[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#23},
           E#22         |->  {E#23}}

and instantiated rules:

                                  (letrec {X#8=(app (letrec {X#21=T#20[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#23} in S#12) S#11);E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#8=(app (letrec {X#21=T#20[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#23} in S#12) S#11);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (letrec {X#21=T#20[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#23} in S#12) S#11);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=(letrec {X#21=T#20[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#23} in (app S#12 S#11));E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#20} in S#12) S#11)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= (letrec {X#1=T#7[S#4];E#20} in (app S#12 S#11))
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#20} in S#12),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {X#1=T#7[S#4];E#20} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=(app [.] S#11);E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  [.],
           T#15         |->  (app [.] S#11),
           T#19         |->  [.],
           S#5          |->  S#12,
           E#10         |->  {X#1=T#7[S#4];E#20},
           E#3          |->  {E#20}}

and instantiated rules:

                                  (letrec {X#8=(app (letrec {X#1=T#7[S#4];E#20} in S#12) S#11);E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#8=(app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#20} in S#12) S#11);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (letrec {X#1=T#7[S#4];E#20} in S#12) S#11);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=(letrec {X#1=T#7[S#4];E#20} in (app S#12 S#11));E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= (app (letrec {E#10} in S#12) T#19[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= (letrec {E#10} in (app S#12 T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)]))
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {E#10} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=(app (letrec {E#10} in S#12) T#19);E#9} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#8,
           E#17         |->  {E#9},
           A#18         |->  [.],
           T#15         |->  (app (letrec {E#10} in S#12) T#19),
           S#11         |->  T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#8=(app (letrec {E#10} in S#12) T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)]);E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#8=(app (letrec {E#10} in S#12) T#19[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (letrec {E#10} in S#12) T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)]);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=(letrec {E#10} in (app S#12 T#19[(letrec {X#1=T#7[S#4];E#3} in S#5)]));E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#8= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;E#9
       ;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;E#9
       ;EE#20[X#19,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#8=A#21[(app A#22[(var X#19)] T#23)];E#9;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];EE#20[X#19,[.2]]},
           X#16         |->  X#8,
           E#17         |->  {E#9;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]},
           T#15         |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];E#9;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9;EE#20[X#19,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9;EE#20[X#19,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;E#9
       ;EE#21[X#8,(var X#19)]
       ;EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;E#9
       ;EE#21[X#8,(var X#19)]
       ;EE#22[X#20,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];E#9;EE#21[X#8,(var X#19)];EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#21[X#8,(var X#19)];EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]},
           T#15         |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9;EE#21[X#8,(var X#19)];EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];E#9;EE#21[X#8,(var X#19)];EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9;EE#21[X#8,(var X#19)];EE#22[X#20,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9;EE#21[X#8,(var X#19)];EE#22[X#20,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app (letrec {E#10} in T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#11)]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(letrec {E#10} in (app T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#11))]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#23,T#22,A#18,T#15,T#6,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app (letrec {E#10} in T#24) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  A#21,
           T#15         |->  A#21[(app (letrec {E#10} in T#24) S#11)],
           T#22         |->  (app (letrec {E#10} in T#24) S#11),
           T#23         |->  (letrec {E#10} in T#24),
           S#12         |->  T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app (letrec {E#10} in T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#19=A#21[(app (letrec {E#10} in T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app (letrec {E#10} in T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#21[(letrec {E#10} in (app T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#11))];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app (letrec
                            X#25= T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
                           ;E#27
                         in
                            S#12
                         ) S#11)]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(letrec {X#25=T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#27} in (app S#12 S#11))]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#23,T#22,A#18,T#15,T#6,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {X#25=T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#27} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app (letrec {X#25=T#24;E#27} in S#12) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  A#21,
           T#15         |->  A#21[(app (letrec {X#25=T#24;E#27} in S#12) S#11)],
           T#22         |->  (app (letrec {X#25=T#24;E#27} in S#12) S#11),
           T#23         |->  (letrec {X#25=T#24;E#27} in S#12),
           E#10         |->  {X#25=T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#27},
           E#26         |->  {E#27}}

and instantiated rules:

                                  (letrec {X#19=A#21[(app (letrec {X#25=T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#27} in S#12) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#19=A#21[(app (letrec {X#25=T#24[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#27} in S#12) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app (letrec {X#25=T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#27} in S#12) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#21[(letrec {X#25=T#24[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#27} in (app S#12 S#11))];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#24} in S#12) S#11)]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(letrec {X#1=T#7[S#4];E#24} in (app S#12 S#11))]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#6,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#24} in S#12),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {X#1=T#7[S#4];E#24} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app [.] S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  A#21,
           T#15         |->  A#21[(app [.] S#11)],
           T#22         |->  (app [.] S#11),
           T#23         |->  [.],
           S#5          |->  S#12,
           E#10         |->  {X#1=T#7[S#4];E#24},
           E#3          |->  {E#24}}

and instantiated rules:

                                  (letrec {X#19=A#21[(app (letrec {X#1=T#7[S#4];E#24} in S#12) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#19=A#21[(app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#24} in S#12) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app (letrec {X#1=T#7[S#4];E#24} in S#12) S#11)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#21[(letrec {X#1=T#7[S#4];E#24} in (app S#12 S#11))];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app (letrec {E#10} in S#12) T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(letrec {E#10} in (app S#12 T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)]))]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#6,A#21}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {E#10} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app (letrec {E#10} in S#12) T#23)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  A#21,
           T#15         |->  A#21[(app (letrec {E#10} in S#12) T#23)],
           T#22         |->  (app (letrec {E#10} in S#12) T#23),
           S#11         |->  T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app (letrec {E#10} in S#12) T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#19=A#21[(app (letrec {E#10} in S#12) T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app (letrec {E#10} in S#12) T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#21[(letrec {E#10} in (app S#12 T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)]))];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(letrec {E#10} in (app S#12 S#11))] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])]
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#18,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] T#23)];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           T#15         |->  A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#19=A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] T#23[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(app (letrec {E#10} in S#12) S#11)] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=A#21[(app A#22[(letrec {E#10} in (app S#12 S#11))] T#23[(letrec {X#1=T#7[S#4];E#3} in S#5)])];E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (app (letrec {E#10} in T#22[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#11)
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= (letrec {E#10} in (app T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#11))
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#21,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=(app (letrec {E#10} in T#22) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  [.],
           T#15         |->  (app (letrec {E#10} in T#22) S#11),
           T#21         |->  (letrec {E#10} in T#22),
           S#12         |->  T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#19=(app (letrec {E#10} in T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#19=(app (letrec {E#10} in T#22[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=(app (letrec {E#10} in T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)]) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=(letrec {E#10} in (app T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)] S#11));E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (app (letrec
                      X#23= T#22[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
                     ;E#25
                   in
                      S#12
                   ) S#11)
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= (letrec {X#23=T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#25} in (app S#12 S#11))
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#21,T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {X#23=T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#25} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=(app (letrec {X#23=T#22;E#25} in S#12) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  [.],
           T#15         |->  (app (letrec {X#23=T#22;E#25} in S#12) S#11),
           T#21         |->  (letrec {X#23=T#22;E#25} in S#12),
           E#10         |->  {X#23=T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#25},
           E#24         |->  {E#25}}

and instantiated rules:

                                  (letrec {X#19=(app (letrec {X#23=T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#25} in S#12) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#19=(app (letrec {X#23=T#22[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)];E#25} in S#12) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=(app (letrec {X#23=T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#25} in S#12) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=(letrec {X#23=T#22[(letrec {X#1=T#7[S#4];E#3} in S#5)];E#25} in (app S#12 S#11));E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#22} in S#12) S#11)
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= (letrec {X#1=T#7[S#4];E#22} in (app S#12 S#11))
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#22} in S#12),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {X#1=T#7[S#4];E#22} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=(app [.] S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  [.],
           T#15         |->  (app [.] S#11),
           T#21         |->  [.],
           S#5          |->  S#12,
           E#10         |->  {X#1=T#7[S#4];E#22},
           E#3          |->  {E#22}}

and instantiated rules:

                                  (letrec {X#19=(app (letrec {X#1=T#7[S#4];E#22} in S#12) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#19=(app (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#22} in S#12) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=(app (letrec {X#1=T#7[S#4];E#22} in S#12) S#11);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=(letrec {X#1=T#7[S#4];E#22} in (app S#12 S#11));E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (app (letrec {E#10} in S#12) T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)])
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#19= (letrec {E#10} in (app S#12 T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]))
       ;E#9
       ;EE#20[X#8,(var X#19)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#15,T#6}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)],(letrec {E#10} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  (letrec {X#19=(app (letrec {E#10} in S#12) T#21);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)]),
           EE#14[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {E#9;EE#20[X#8,(var X#19)]},
           A#18         |->  [.],
           T#15         |->  (app (letrec {E#10} in S#12) T#21),
           S#11         |->  T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]}

and instantiated rules:

                                  (letrec {X#19=(app (letrec {E#10} in S#12) T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#19=(app (letrec {E#10} in S#12) T#21[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#19=(app (letrec {E#10} in S#12) T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]);E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#19=(letrec {E#10} in (app S#12 T#21[(letrec {X#1=T#7[S#4];E#3} in S#5)]));E#9;EE#20[X#8,(var X#19)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= T#7[(var X#2)]
       ;X#2= S#4
       ;E#15
       ;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#1= T#7[S#4]
       ;E#15
       ;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),T#7),
             (S#4,T#7),
             ((letrec {X#1=T#7[(dummy3 )];E#15;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),T#7[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6  |->  [.],
           S#5  |->  A#13[(var X#8)],
           E#9  |->  {X#1=T#7[S#4];E#15},
           E#3  |->  {E#15;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]}}

and instantiated rules:

                                  (letrec {X#1=T#7[S#4];E#15;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#1=T#7[(var X#2)];X#2=S#4;E#15;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#1=T#7[S#4];E#15;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#1=T#7[S#4];E#15;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= A#16[(app (letrec {E#10} in T#19[(var X#2)]) S#11)]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#16[(letrec {E#10} in (app T#19[S#4] S#11))]
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#7,A#16}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#16[(app (letrec {E#10} in T#19) S#11)]),
             (S#4,A#16[(app (letrec {E#10} in T#19) S#11)]),
             ((letrec {X#8=A#16[(app (letrec {E#10} in T#19[(dummy3 )]) S#11)];E#9} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#16[(app (letrec {E#10} in T#19[[.]]) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#9},
           A#15         |->  A#16,
           T#7          |->  A#16[(app (letrec {E#10} in T#19) S#11)],
           T#17         |->  (app (letrec {E#10} in T#19) S#11),
           T#18         |->  (letrec {E#10} in T#19),
           S#12         |->  T#19[S#4]}

and instantiated rules:

                                  (letrec {X#8=A#16[(app (letrec {E#10} in T#19[S#4]) S#11)];E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=S#4;X#8=A#16[(app (letrec {E#10} in T#19[(var X#2)]) S#11)];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#16[(app (letrec {E#10} in T#19[S#4]) S#11)];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#16[(letrec {E#10} in (app T#19[S#4] S#11))];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= A#16[(app (letrec {X#20=T#19[(var X#2)];E#22} in S#12) S#11)]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#16[(letrec {X#20=T#19[S#4];E#22} in (app S#12 S#11))]
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#7,A#16}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#16[(app (letrec {X#20=T#19;E#22} in S#12) S#11)]),
             (S#4,A#16[(app (letrec {X#20=T#19;E#22} in S#12) S#11)]),
             ((letrec {X#8=A#16[(app (letrec {X#20=T#19[(dummy3 )];E#22} in S#12) S#11)];E#9} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {X#20=T#19[S#4];E#22} in [.])),
             ((var X#2),A#16[(app (letrec {X#20=T#19[[.]];E#22} in S#12) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#9},
           A#15         |->  A#16,
           T#7          |->  A#16[(app (letrec {X#20=T#19;E#22} in S#12) S#11)],
           T#17         |->  (app (letrec {X#20=T#19;E#22} in S#12) S#11),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#12),
           E#10         |->  {X#20=T#19[S#4];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#8=A#16[(app (letrec {X#20=T#19[S#4];E#22} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=S#4;X#8=A#16[(app (letrec {X#20=T#19[(var X#2)];E#22} in S#12) S#11)];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#16[(app (letrec {X#20=T#19[S#4];E#22} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#16[(letrec {X#20=T#19[S#4];E#22} in (app S#12 S#11))];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (letrec {E#10} in S#12)
       ;X#8= A#16[(app (var X#2) S#11)]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec {X#8=A#16[(letrec {E#10} in (app S#12 S#11))];E#9} in A#13[(var X#8)])
  )

where

   Delta1 = {T#17,A#15,T#7,A#16}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#16[(app [.] S#11)]),
             ((letrec {E#10} in S#12),A#16[(app [.] S#11)]),
             ((letrec {X#8=A#16[(app (dummy3 ) S#11)];E#9} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((letrec {E#10} in S#12),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#16[(app [.] S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#9},
           A#15         |->  A#16,
           T#7          |->  A#16[(app [.] S#11)],
           T#17         |->  (app [.] S#11),
           T#18         |->  [.],
           S#4          |->  (letrec {E#10} in S#12)}

and instantiated rules:

                                  (letrec {X#8=A#16[(app (letrec {E#10} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=(letrec {E#10} in S#12);X#8=A#16[(app (var X#2) S#11)];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#16[(app (letrec {E#10} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#16[(letrec {E#10} in (app S#12 S#11))];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= A#16[(app (letrec {E#10} in S#12) T#18[(var X#2)])]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#16[(letrec {E#10} in (app S#12 T#18[S#4]))]
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#17,A#15,T#7,A#16}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#16[(app (letrec {E#10} in S#12) T#18)]),
             (S#4,A#16[(app (letrec {E#10} in S#12) T#18)]),
             ((letrec {X#8=A#16[(app (letrec {E#10} in S#12) T#18[(dummy3 )])];E#9} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#18[S#4],(letrec {E#10} in [.])),
             ((var X#2),A#16[(app (letrec {E#10} in S#12) T#18[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#9},
           A#15         |->  A#16,
           T#7          |->  A#16[(app (letrec {E#10} in S#12) T#18)],
           T#17         |->  (app (letrec {E#10} in S#12) T#18),
           S#11         |->  T#18[S#4]}

and instantiated rules:

                                  (letrec {X#8=A#16[(app (letrec {E#10} in S#12) T#18[S#4])];E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=S#4;X#8=A#16[(app (letrec {E#10} in S#12) T#18[(var X#2)])];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#16[(app (letrec {E#10} in S#12) T#18[S#4])];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#16[(letrec {E#10} in (app S#12 T#18[S#4]))];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (app (letrec {E#10} in S#12) S#11)
       ;X#8= A#16[(var X#2)]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec {X#8=A#16[(letrec {E#10} in (app S#12 S#11))];E#9} in A#13[(var X#8)])
  )

where

   Delta1 = {A#15,T#7,A#16}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#16[[.]]),
             ((app (letrec {E#10} in S#12) S#11),A#16[[.]]),
             ((letrec {X#8=A#16[(dummy3 )];E#9} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((app (letrec {E#10} in S#12) S#11),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#16[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#9},
           A#15         |->  A#16,
           T#7          |->  A#16[[.]],
           T#17         |->  [.],
           S#4          |->  (app (letrec {E#10} in S#12) S#11)}

and instantiated rules:

                                  (letrec {X#8=A#16[(app (letrec {E#10} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=(app (letrec {E#10} in S#12) S#11);X#8=A#16[(var X#2)];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#16[(app (letrec {E#10} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#16[(letrec {E#10} in (app S#12 S#11))];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= A#17[(app (letrec {E#10} in S#12) S#11)]
       ;X#8= A#16[(var X#2)]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#16[A#17[(letrec {E#10} in (app S#12 S#11))]]
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7,A#16}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#16),
             (A#17[(app (letrec {E#10} in S#12) S#11)],A#16),
             ((letrec {X#8=A#16[(dummy3 )];E#9} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#17[(app (letrec {E#10} in S#12) S#11)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#16[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#16[A#17[[.2]]]},
           X#1          |->  X#8,
           E#3          |->  {E#9},
           A#15         |->  A#16[A#17],
           T#7          |->  A#16,
           S#4          |->  A#17[(app (letrec {E#10} in S#12) S#11)]}

and instantiated rules:

                                  (letrec {X#8=A#16[A#17[(app (letrec {E#10} in S#12) S#11)]];E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=A#17[(app (letrec {E#10} in S#12) S#11)];X#8=A#16[(var X#2)];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#16[A#17[(app (letrec {E#10} in S#12) S#11)]];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#16[A#17[(letrec {E#10} in (app S#12 S#11))]];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= A#16[(app A#17[(app (letrec {E#10} in S#12) S#11)] T#18[(var X#2)])]
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#16[(app A#17[(letrec {E#10} in (app S#12 S#11))] T#18[S#4])]
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#16[(app A#17[(app (letrec {E#10} in S#12) S#11)] T#18)]),
             (S#4,A#16[(app A#17[(app (letrec {E#10} in S#12) S#11)] T#18)]),
             ((letrec {X#8=A#16[(app A#17[(app (letrec {E#10} in S#12) S#11)] T#18[(dummy3 )])];E#9} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#16[(app A#17[(app (letrec {E#10} in S#12) S#11)] T#18[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[S#4])]},
           X#1          |->  X#8,
           E#3          |->  {E#9},
           T#7          |->  A#16[(app A#17[(app (letrec {E#10} in S#12) S#11)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[S#4])]}

and instantiated rules:

                                  (letrec {X#8=A#16[(app A#17[(app (letrec {E#10} in S#12) S#11)] T#18[S#4])];E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=S#4;X#8=A#16[(app A#17[(app (letrec {E#10} in S#12) S#11)] T#18[(var X#2)])];E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#16[(app A#17[(app (letrec {E#10} in S#12) S#11)] T#18[S#4])];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#16[(app A#17[(letrec {E#10} in (app S#12 S#11))] T#18[S#4])];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= (app (letrec {E#10} in T#17[(var X#2)]) S#11)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec {X#8=(letrec {E#10} in (app T#17[S#4] S#11));E#9} in A#13[(var X#8)])
  )

where

   Delta1 = {T#16,T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(app (letrec {E#10} in T#17) S#11)),
             (S#4,(app (letrec {E#10} in T#17) S#11)),
             ((letrec {X#8=(app (letrec {E#10} in T#17[(dummy3 )]) S#11);E#9} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),(app (letrec {E#10} in T#17[[.]]) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#8,
           E#3          |->  {E#9},
           A#15         |->  [.],
           T#7          |->  (app (letrec {E#10} in T#17) S#11),
           T#16         |->  (letrec {E#10} in T#17),
           S#12         |->  T#17[S#4]}

and instantiated rules:

                                  (letrec {X#8=(app (letrec {E#10} in T#17[S#4]) S#11);E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=S#4;X#8=(app (letrec {E#10} in T#17[(var X#2)]) S#11);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (letrec {E#10} in T#17[S#4]) S#11);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=(letrec {E#10} in (app T#17[S#4] S#11));E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= (app (letrec {X#18=T#17[(var X#2)];E#20} in S#12) S#11)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= (letrec {X#18=T#17[S#4];E#20} in (app S#12 S#11))
       ;E#9
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#16,T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(app (letrec {X#18=T#17;E#20} in S#12) S#11)),
             (S#4,(app (letrec {X#18=T#17;E#20} in S#12) S#11)),
             ((letrec {X#8=(app (letrec {X#18=T#17[(dummy3 )];E#20} in S#12) S#11);E#9} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {X#18=T#17[S#4];E#20} in [.])),
             ((var X#2),(app (letrec {X#18=T#17[[.]];E#20} in S#12) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#8,
           E#3          |->  {E#9},
           A#15         |->  [.],
           T#7          |->  (app (letrec {X#18=T#17;E#20} in S#12) S#11),
           T#16         |->  (letrec {X#18=T#17;E#20} in S#12),
           E#10         |->  {X#18=T#17[S#4];E#20},
           E#19         |->  {E#20}}

and instantiated rules:

                                  (letrec {X#8=(app (letrec {X#18=T#17[S#4];E#20} in S#12) S#11);E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=S#4;X#8=(app (letrec {X#18=T#17[(var X#2)];E#20} in S#12) S#11);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (letrec {X#18=T#17[S#4];E#20} in S#12) S#11);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=(letrec {X#18=T#17[S#4];E#20} in (app S#12 S#11));E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (letrec {E#10} in S#12)
       ;X#8= (app (var X#2) S#11)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec {X#8=(letrec {E#10} in (app S#12 S#11));E#9} in A#13[(var X#8)])
  )

where

   Delta1 = {T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(app [.] S#11)),
             ((letrec {E#10} in S#12),(app [.] S#11)),
             ((letrec {X#8=(app (dummy3 ) S#11);E#9} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((letrec {E#10} in S#12),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),(app [.] S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#8,
           E#3          |->  {E#9},
           A#15         |->  [.],
           T#7          |->  (app [.] S#11),
           T#16         |->  [.],
           S#4          |->  (letrec {E#10} in S#12)}

and instantiated rules:

                                  (letrec {X#8=(app (letrec {E#10} in S#12) S#11);E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=(letrec {E#10} in S#12);X#8=(app (var X#2) S#11);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (letrec {E#10} in S#12) S#11);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=(letrec {E#10} in (app S#12 S#11));E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= (app (letrec {E#10} in S#12) T#16[(var X#2)])
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec {X#8=(letrec {E#10} in (app S#12 T#16[S#4]));E#9} in A#13[(var X#8)])
  )

where

   Delta1 = {T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(app (letrec {E#10} in S#12) T#16)),
             (S#4,(app (letrec {E#10} in S#12) T#16)),
             ((letrec {X#8=(app (letrec {E#10} in S#12) T#16[(dummy3 )]);E#9} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#16[S#4],(letrec {E#10} in [.])),
             ((var X#2),(app (letrec {E#10} in S#12) T#16[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=[.2]},
           X#1          |->  X#8,
           E#3          |->  {E#9},
           A#15         |->  [.],
           T#7          |->  (app (letrec {E#10} in S#12) T#16),
           S#11         |->  T#16[S#4]}

and instantiated rules:

                                  (letrec {X#8=(app (letrec {E#10} in S#12) T#16[S#4]);E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=S#4;X#8=(app (letrec {E#10} in S#12) T#16[(var X#2)]);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=(app (letrec {E#10} in S#12) T#16[S#4]);E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=(letrec {E#10} in (app S#12 T#16[S#4]));E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= A#15[(app (letrec {E#10} in S#12) S#11)]
       ;X#8= (var X#2)
       ;E#9
     in
        A#13[(var X#8)]
     )
    ,
     (letrec {X#8=A#15[(letrec {E#10} in (app S#12 S#11))];E#9} in A#13[(var X#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),[.]),
             (A#15[(app (letrec {E#10} in S#12) S#11)],[.]),
             ((letrec {X#8=(dummy3 );E#9} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#15[(app (letrec {E#10} in S#12) S#11)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#9},
           T#7          |->  [.],
           S#4          |->  A#15[(app (letrec {E#10} in S#12) S#11)]}

and instantiated rules:

                                  (letrec {X#8=A#15[(app (letrec {E#10} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=A#15[(app (letrec {E#10} in S#12) S#11)];X#8=(var X#2);E#9} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#15[(app (letrec {E#10} in S#12) S#11)];E#9} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#15[(letrec {E#10} in (app S#12 S#11))];E#9} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= (var X#16)
       ;X#8= A#18[(var X#2)]
       ;E#9
       ;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#18[(var X#16)]
       ;E#9
       ;EE#17[X#16,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7,A#18}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18[[.]]),
             ((var X#16),A#18[[.]]),
             ((letrec {X#8=A#18[(dummy3 )];E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#16),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#18[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#18[(var X#16)];EE#17[X#16,[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]},
           A#15         |->  A#18,
           T#7          |->  A#18[[.]],
           T#19         |->  [.],
           S#4          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#8=A#18[(var X#16)];E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=(var X#16);X#8=A#18[(var X#2)];E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#18[(var X#16)];E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#18[(var X#16)];E#9;EE#17[X#16,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= A#19[(var X#16)]
       ;X#8= A#18[(var X#2)]
       ;E#9
       ;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#18[A#19[(var X#16)]]
       ;E#9
       ;EE#17[X#16,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7,A#18}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18),
             (A#19[(var X#16)],A#18),
             ((letrec {X#8=A#18[(dummy3 )];E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#19[(var X#16)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#18[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#18[A#19[(var X#16)]];EE#17[X#16,[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]},
           A#15         |->  A#18[A#19],
           T#7          |->  A#18,
           S#4          |->  A#19[(var X#16)]}

and instantiated rules:

                                  (letrec {X#8=A#18[A#19[(var X#16)]];E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=A#19[(var X#16)];X#8=A#18[(var X#2)];E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#18[A#19[(var X#16)]];E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#18[A#19[(var X#16)]];E#9;EE#17[X#16,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= S#4
       ;X#8= A#18[(app A#19[(var X#16)] T#20[(var X#2)])]
       ;E#9
       ;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#18[(app A#19[(var X#16)] T#20[S#4])]
       ;E#9
       ;EE#17[X#16,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18[(app A#19[(var X#16)] T#20)]),
             (S#4,A#18[(app A#19[(var X#16)] T#20)]),
             ((letrec {X#8=A#18[(app A#19[(var X#16)] T#20[(dummy3 )])];E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#18[(app A#19[(var X#16)] T#20[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[S#4])];EE#17[X#16,[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]},
           T#7          |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#4])]}

and instantiated rules:

                                  (letrec {X#8=A#18[(app A#19[(var X#16)] T#20[S#4])];E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=S#4;X#8=A#18[(app A#19[(var X#16)] T#20[(var X#2)])];E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#18[(app A#19[(var X#16)] T#20[S#4])];E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#18[(app A#19[(var X#16)] T#20[S#4])];E#9;EE#17[X#16,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#2= A#15[(var X#16)]
       ;X#8= (var X#2)
       ;E#9
       ;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#8= A#15[(var X#16)]
       ;E#9
       ;EE#17[X#16,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),[.]),
             (A#15[(var X#16)],[.]),
             ((letrec {X#8=(dummy3 );E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#15[(var X#16)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {[.1]=A#15[(var X#16)];EE#17[X#16,[.2]]},
           X#1          |->  X#8,
           E#3          |->  {E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]},
           T#7          |->  [.],
           S#4          |->  A#15[(var X#16)]}

and instantiated rules:

                                  (letrec {X#8=A#15[(var X#16)];E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#2=A#15[(var X#16)];X#8=(var X#2);E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#8=A#15[(var X#16)];E#9;EE#17[X#16,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#8=A#15[(var X#16)];E#9;EE#17[X#16,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(var X#2)]
       ;X#2= (var X#17)
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#20[(var X#17)]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7,A#20}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#20[[.]]),
             ((var X#17),A#20[[.]]),
             ((letrec {X#16=A#20[(dummy3 )];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#20[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#20[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]},
           A#15         |->  A#20,
           T#7          |->  A#20[[.]],
           T#21         |->  [.],
           S#4          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#16=A#20[(var X#17)];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#20[(var X#2)];X#2=(var X#17);E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#20[(var X#17)];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=A#20[(var X#17)];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(var X#2)]
       ;X#2= A#21[(var X#17)]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#20[A#21[(var X#17)]]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7,A#20}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#20),
             (A#21[(var X#17)],A#20),
             ((letrec {X#16=A#20[(dummy3 )];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#21[(var X#17)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#20[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#20[A#21[(var X#17)]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]},
           A#15         |->  A#20[A#21],
           T#7          |->  A#20,
           S#4          |->  A#21[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#21[(var X#17)]];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#20[(var X#2)];X#2=A#21[(var X#17)];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#20[A#21[(var X#17)]];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=A#20[A#21[(var X#17)]];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(var X#2)])]
       ;X#2= S#4
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[S#4])]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#20[(app A#21[(var X#17)] T#22)]),
             (S#4,A#20[(app A#21[(var X#17)] T#22)]),
             ((letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(dummy3 )])];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#20[(app A#21[(var X#17)] T#22[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[S#4])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]},
           T#7          |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[S#4])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#4])];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(var X#2)])];X#2=S#4;E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#4])];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#4])];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#2)
       ;X#2= A#15[(var X#17)]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#15[(var X#17)]
       ;E#9
       ;EE#18[X#8,(var X#16)]
       ;EE#19[X#17,(letrec {E#10} in (app S#12 S#11))]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),[.]),
             (A#15[(var X#17)],[.]),
             ((letrec {X#16=(dummy3 );E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#15[(var X#17)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#15[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]},
           T#7          |->  [.],
           S#4          |->  A#15[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#15[(var X#17)];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=(var X#2);X#2=A#15[(var X#17)];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#15[(var X#17)];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=A#15[(var X#17)];E#9;EE#18[X#8,(var X#16)];EE#19[X#17,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {E#10} in T#21[(var X#2)]) S#11)]
       ;X#2= S#4
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#10} in (app T#21[S#4] S#11))]
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#7,A#18}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18[(app (letrec {E#10} in T#21) S#11)]),
             (S#4,A#18[(app (letrec {E#10} in T#21) S#11)]),
             ((letrec {X#16=A#18[(app (letrec {E#10} in T#21[(dummy3 )]) S#11)];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#18[(app (letrec {E#10} in T#21[[.]]) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#17[X#8,(var X#16)]},
           A#15         |->  A#18,
           T#7          |->  A#18[(app (letrec {E#10} in T#21) S#11)],
           T#19         |->  (app (letrec {E#10} in T#21) S#11),
           T#20         |->  (letrec {E#10} in T#21),
           S#12         |->  T#21[S#4]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#10} in T#21[S#4]) S#11)];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#18[(app (letrec {E#10} in T#21[(var X#2)]) S#11)];X#2=S#4;E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#10} in T#21[S#4]) S#11)];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#10} in (app T#21[S#4] S#11))];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {X#22=T#21[(var X#2)];E#24} in S#12) S#11)]
       ;X#2= S#4
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#22=T#21[S#4];E#24} in (app S#12 S#11))]
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#7,A#18}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18[(app (letrec {X#22=T#21;E#24} in S#12) S#11)]),
             (S#4,A#18[(app (letrec {X#22=T#21;E#24} in S#12) S#11)]),
             ((letrec {X#16=A#18[(app (letrec {X#22=T#21[(dummy3 )];E#24} in S#12) S#11)];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {X#22=T#21[S#4];E#24} in [.])),
             ((var X#2),A#18[(app (letrec {X#22=T#21[[.]];E#24} in S#12) S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#17[X#8,(var X#16)]},
           A#15         |->  A#18,
           T#7          |->  A#18[(app (letrec {X#22=T#21;E#24} in S#12) S#11)],
           T#19         |->  (app (letrec {X#22=T#21;E#24} in S#12) S#11),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#12),
           E#10         |->  {X#22=T#21[S#4];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[S#4];E#24} in S#12) S#11)];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#18[(app (letrec {X#22=T#21[(var X#2)];E#24} in S#12) S#11)];X#2=S#4;E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[S#4];E#24} in S#12) S#11)];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {X#22=T#21[S#4];E#24} in (app S#12 S#11))];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (var X#2) S#11)]
       ;X#2= (letrec {E#10} in S#12)
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#10} in (app S#12 S#11))]
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#19,A#15,T#7,A#18}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18[(app [.] S#11)]),
             ((letrec {E#10} in S#12),A#18[(app [.] S#11)]),
             ((letrec {X#16=A#18[(app (dummy3 ) S#11)];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((letrec {E#10} in S#12),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#18[(app [.] S#11)]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#17[X#8,(var X#16)]},
           A#15         |->  A#18,
           T#7          |->  A#18[(app [.] S#11)],
           T#19         |->  (app [.] S#11),
           T#20         |->  [.],
           S#4          |->  (letrec {E#10} in S#12)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#10} in S#12) S#11)];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#18[(app (var X#2) S#11)];X#2=(letrec {E#10} in S#12);E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#10} in S#12) S#11)];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#10} in (app S#12 S#11))];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {E#10} in S#12) T#20[(var X#2)])]
       ;X#2= S#4
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#10} in (app S#12 T#20[S#4]))]
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#19,A#15,T#7,A#18}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18[(app (letrec {E#10} in S#12) T#20)]),
             (S#4,A#18[(app (letrec {E#10} in S#12) T#20)]),
             ((letrec {X#16=A#18[(app (letrec {E#10} in S#12) T#20[(dummy3 )])];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#20[S#4],(letrec {E#10} in [.])),
             ((var X#2),A#18[(app (letrec {E#10} in S#12) T#20[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#17[X#8,(var X#16)]},
           A#15         |->  A#18,
           T#7          |->  A#18[(app (letrec {E#10} in S#12) T#20)],
           T#19         |->  (app (letrec {E#10} in S#12) T#20),
           S#11         |->  T#20[S#4]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#10} in S#12) T#20[S#4])];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#18[(app (letrec {E#10} in S#12) T#20[(var X#2)])];X#2=S#4;E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#10} in S#12) T#20[S#4])];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#10} in (app S#12 T#20[S#4]))];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(var X#2)]
       ;X#2= (app (letrec {E#10} in S#12) S#11)
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#10} in (app S#12 S#11))]
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7,A#18}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18[[.]]),
             ((app (letrec {E#10} in S#12) S#11),A#18[[.]]),
             ((letrec {X#16=A#18[(dummy3 )];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((app (letrec {E#10} in S#12) S#11),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#18[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#17[X#8,(var X#16)]},
           A#15         |->  A#18,
           T#7          |->  A#18[[.]],
           T#19         |->  [.],
           S#4          |->  (app (letrec {E#10} in S#12) S#11)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#10} in S#12) S#11)];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#18[(var X#2)];X#2=(app (letrec {E#10} in S#12) S#11);E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#10} in S#12) S#11)];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#10} in (app S#12 S#11))];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(var X#2)]
       ;X#2= A#19[(app (letrec {E#10} in S#12) S#11)]
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#18[A#19[(letrec {E#10} in (app S#12 S#11))]]
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7,A#18}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18),
             (A#19[(app (letrec {E#10} in S#12) S#11)],A#18),
             ((letrec {X#16=A#18[(dummy3 )];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#19[(app (letrec {E#10} in S#12) S#11)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#18[[.]]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#18[A#19[[.2]]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#17[X#8,(var X#16)]},
           A#15         |->  A#18[A#19],
           T#7          |->  A#18,
           S#4          |->  A#19[(app (letrec {E#10} in S#12) S#11)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#19[(app (letrec {E#10} in S#12) S#11)]];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#18[(var X#2)];X#2=A#19[(app (letrec {E#10} in S#12) S#11)];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#18[A#19[(app (letrec {E#10} in S#12) S#11)]];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=A#18[A#19[(letrec {E#10} in (app S#12 S#11))]];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(app (letrec {E#10} in S#12) S#11)] T#20[(var X#2)])]
       ;X#2= S#4
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {E#10} in (app S#12 S#11))] T#20[S#4])]
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {A#15,T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),A#18[(app A#19[(app (letrec {E#10} in S#12) S#11)] T#20)]),
             (S#4,A#18[(app A#19[(app (letrec {E#10} in S#12) S#11)] T#20)]),
             ((letrec {X#16=A#18[(app A#19[(app (letrec {E#10} in S#12) S#11)] T#20[(dummy3 )])];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),A#18[(app A#19[(app (letrec {E#10} in S#12) S#11)] T#20[[.]])]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[S#4])];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#17[X#8,(var X#16)]},
           T#7          |->  A#18[(app A#19[(app (letrec {E#10} in S#12) S#11)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#4])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#10} in S#12) S#11)] T#20[S#4])];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=A#18[(app A#19[(app (letrec {E#10} in S#12) S#11)] T#20[(var X#2)])];X#2=S#4;E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#10} in S#12) S#11)] T#20[S#4])];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=A#18[(app A#19[(letrec {E#10} in (app S#12 S#11))] T#20[S#4])];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {E#10} in T#19[(var X#2)]) S#11)
       ;X#2= S#4
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (letrec {E#10} in (app T#19[S#4] S#11))
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#18,T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(app (letrec {E#10} in T#19) S#11)),
             (S#4,(app (letrec {E#10} in T#19) S#11)),
             ((letrec {X#16=(app (letrec {E#10} in T#19[(dummy3 )]) S#11);E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),(app (letrec {E#10} in T#19[[.]]) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#17[X#8,(var X#16)]},
           A#15         |->  [.],
           T#7          |->  (app (letrec {E#10} in T#19) S#11),
           T#18         |->  (letrec {E#10} in T#19),
           S#12         |->  T#19[S#4]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#10} in T#19[S#4]) S#11);E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=(app (letrec {E#10} in T#19[(var X#2)]) S#11);X#2=S#4;E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#10} in T#19[S#4]) S#11);E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#10} in (app T#19[S#4] S#11));E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {X#20=T#19[(var X#2)];E#22} in S#12) S#11)
       ;X#2= S#4
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (letrec {X#20=T#19[S#4];E#22} in (app S#12 S#11))
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#18,T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(app (letrec {X#20=T#19;E#22} in S#12) S#11)),
             (S#4,(app (letrec {X#20=T#19;E#22} in S#12) S#11)),
             ((letrec {X#16=(app (letrec {X#20=T#19[(dummy3 )];E#22} in S#12) S#11);E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {X#20=T#19[S#4];E#22} in [.])),
             ((var X#2),(app (letrec {X#20=T#19[[.]];E#22} in S#12) S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#17[X#8,(var X#16)]},
           A#15         |->  [.],
           T#7          |->  (app (letrec {X#20=T#19;E#22} in S#12) S#11),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#12),
           E#10         |->  {X#20=T#19[S#4];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {X#20=T#19[S#4];E#22} in S#12) S#11);E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=(app (letrec {X#20=T#19[(var X#2)];E#22} in S#12) S#11);X#2=S#4;E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {X#20=T#19[S#4];E#22} in S#12) S#11);E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(letrec {X#20=T#19[S#4];E#22} in (app S#12 S#11));E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (var X#2) S#11)
       ;X#2= (letrec {E#10} in S#12)
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (letrec {E#10} in (app S#12 S#11))
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(app [.] S#11)),
             ((letrec {E#10} in S#12),(app [.] S#11)),
             ((letrec {X#16=(app (dummy3 ) S#11);E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             ((letrec {E#10} in S#12),(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),(app [.] S#11)),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#17[X#8,(var X#16)]},
           A#15         |->  [.],
           T#7          |->  (app [.] S#11),
           T#18         |->  [.],
           S#4          |->  (letrec {E#10} in S#12)}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#10} in S#12) S#11);E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=(app (var X#2) S#11);X#2=(letrec {E#10} in S#12);E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#10} in S#12) S#11);E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#10} in (app S#12 S#11));E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {E#10} in S#12) T#18[(var X#2)])
       ;X#2= S#4
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= (letrec {E#10} in (app S#12 T#18[S#4]))
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {T#7}
   Delta2 = {E#10}
   Delta3 = {((var X#2),(app (letrec {E#10} in S#12) T#18)),
             (S#4,(app (letrec {E#10} in S#12) T#18)),
             ((letrec {X#16=(app (letrec {E#10} in S#12) T#18[(dummy3 )]);E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (S#4,(letrec {X#2=(dummy3 )} in [.])),
             (T#18[S#4],(letrec {E#10} in [.])),
             ((var X#2),(app (letrec {E#10} in S#12) T#18[[.]])),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#17[X#8,(var X#16)]},
           A#15         |->  [.],
           T#7          |->  (app (letrec {E#10} in S#12) T#18),
           S#11         |->  T#18[S#4]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#10} in S#12) T#18[S#4]);E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=(app (letrec {E#10} in S#12) T#18[(var X#2)]);X#2=S#4;E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#10} in S#12) T#18[S#4]);E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#10} in (app S#12 T#18[S#4]));E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (var X#2)
       ;X#2= A#15[(app (letrec {E#10} in S#12) S#11)]
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
    ,
     (letrec
        X#16= A#15[(letrec {E#10} in (app S#12 S#11))]
       ;E#9
       ;EE#17[X#8,(var X#16)]
     in
        A#13[(var X#8)]
     )
  )

where

   Delta1 = {}
   Delta2 = {E#10}
   Delta3 = {((var X#2),[.]),
             (A#15[(app (letrec {E#10} in S#12) S#11)],[.]),
             ((letrec {X#16=(dummy3 );E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)]),(letrec {X#2=(dummy3 )} in [.])),
             (A#15[(app (letrec {E#10} in S#12) S#11)],(letrec {X#2=(dummy3 )} in [.])),
             (S#11,(letrec {E#10} in [.])),
             ((var X#2),[.]),
             ((var X#8),A#13[[.]]),
             ((var X#8),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp2-> . -SR,lapp3-> with input rules:

                                  T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
    -ucp2->                       T#6[(letrec {X#1=T#7[(var X#2)];X#2=S#4;E#3} in S#5)]
    and constraints: ((var X#2),T#7), (S#4,T#7), ((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])), (S#4,(letrec {X#2=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {E#9;EE#14[X#8,(letrec {E#10} in (app S#12 S#11))]} in A#13[(var X#8)])
    and constraints: E#10/= {}, (S#11,(letrec {E#10} in [.]))

and letrec unification problem:

      Gamma ={
        T#6[(letrec {X#1=T#7[S#4];E#3} in S#5)]
        =?=
        (letrec {E#9;EE#14[X#8,(app (letrec {E#10} in S#12) S#11)]} in A#13[(var X#8)])}
      Delta1=  {}
      Delta2=  {E#10}
      Delta3=  {((var X#2),T#7),(S#4,T#7),((letrec {X#1=T#7[(dummy3 )];E#3} in S#5),(letrec {X#2=(dummy3 )} in [.])),(S#4,(letrec {X#2=(dummy3 )} in [.])),(S#11,(letrec {E#10} in [.])),((var X#2),T#7[[.]]),((var X#8),A#13[[.]]),((var X#8),A#13[[.]])}


and found solution:

    Sol = {T#6          |->  [.],
           S#5          |->  A#13[(var X#8)],
           EE#14[.1,.2] |-> {X#16=A#15[[.2]];EE#17[[.1],(var X#16)]},
           X#1          |->  X#16,
           E#3          |->  {E#9;EE#17[X#8,(var X#16)]},
           T#7          |->  [.],
           S#4          |->  A#15[(app (letrec {E#10} in S#12) S#11)]}

and instantiated rules:

                                  (letrec {X#16=A#15[(app (letrec {E#10} in S#12) S#11)];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -ucp2->                       (letrec {X#16=(var X#2);X#2=A#15[(app (letrec {E#10} in S#12) S#11)];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    ................................................................................
                                  (letrec {X#16=A#15[(app (letrec {E#10} in S#12) S#11)];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    -SR,lapp3->                   (letrec {X#16=A#15[(letrec {E#10} in (app S#12 S#11))];E#9;EE#17[X#8,(var X#16)]} in A#13[(var X#8)])
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {X#1=(\ X#5.S#7)} in (var X#1)) S#6)]
    ,
     A#9[(letrec {X#5=S#6} in S#7)]
  )

where

   Delta1 = {T#10,A#8,T#3,A#9}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((\ X#5.S#7),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[(app [.] S#6)],
           T#10  |->  (app [.] S#6),
           T#11  |->  [.],
           T#4   |->  [.],
           S#2   |->  (\ X#5.S#7)}

and instantiated rules:

                                  A#9[(app (\ X#5.S#7) S#6)]
    -ucp3->                       A#9[(app (letrec {X#1=(\ X#5.S#7)} in (var X#1)) S#6)]
    ................................................................................
                                  A#9[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#9[(letrec {X#5=S#6} in S#7)]
    

================================================================================
Critical Pair:

  (
     A#9[(app (\ X#5.S#7) T#11[(letrec {X#1=S#2} in T#4[(var X#1)])])]
    ,
     A#9[(letrec {X#5=T#11[T#4[S#2]]} in S#7)]
  )

where

   Delta1 = {T#10,A#8,T#3,A#9}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[T#4[S#2]],(\ X#5.[.])),
             (T#11[T#4[S#2]],(letrec {X#5=[.]} in S#7)),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[(app (\ X#5.S#7) T#11)],
           T#10  |->  (app (\ X#5.S#7) T#11),
           S#6   |->  T#11[T#4[S#2]]}

and instantiated rules:

                                  A#9[(app (\ X#5.S#7) T#11[T#4[S#2]])]
    -ucp3->                       A#9[(app (\ X#5.S#7) T#11[(letrec {X#1=S#2} in T#4[(var X#1)])])]
    ................................................................................
                                  A#9[(app (\ X#5.S#7) T#11[T#4[S#2]])]
    -SR,lbeta1->                  A#9[(letrec {X#5=T#11[T#4[S#2]]} in S#7)]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=(\ X#5.S#7)} in (app (var X#1) S#6))]
    ,
     A#9[(letrec {X#5=S#6} in S#7)]
  )

where

   Delta1 = {T#4,A#8,T#3,A#9}
   Delta2 = {}
   Delta3 = {((var X#1),(app [.] S#6)),
             ((\ X#5.S#7),(app [.] S#6)),
             ((app (dummy3 ) S#6),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),(app [.] S#6))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[[.]],
           T#10  |->  [.],
           T#4   |->  (app [.] S#6),
           T#11  |->  [.],
           S#2   |->  (\ X#5.S#7)}

and instantiated rules:

                                  A#9[(app (\ X#5.S#7) S#6)]
    -ucp3->                       A#9[(letrec {X#1=(\ X#5.S#7)} in (app (var X#1) S#6))]
    ................................................................................
                                  A#9[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#9[(letrec {X#5=S#6} in S#7)]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=S#2} in (app (\ X#5.S#7) T#11[(var X#1)]))]
    ,
     A#9[(letrec {X#5=T#11[S#2]} in S#7)]
  )

where

   Delta1 = {T#4,A#8,T#3,A#9}
   Delta2 = {}
   Delta3 = {((var X#1),(app (\ X#5.S#7) T#11)),
             (S#2,(app (\ X#5.S#7) T#11)),
             ((app (\ X#5.S#7) T#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[S#2],(\ X#5.[.])),
             (T#11[S#2],(letrec {X#5=[.]} in S#7)),
             ((var X#1),(app (\ X#5.S#7) T#11[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[[.]],
           T#10  |->  [.],
           T#4   |->  (app (\ X#5.S#7) T#11),
           S#6   |->  T#11[S#2]}

and instantiated rules:

                                  A#9[(app (\ X#5.S#7) T#11[S#2])]
    -ucp3->                       A#9[(letrec {X#1=S#2} in (app (\ X#5.S#7) T#11[(var X#1)]))]
    ................................................................................
                                  A#9[(app (\ X#5.S#7) T#11[S#2])]
    -SR,lbeta1->                  A#9[(letrec {X#5=T#11[S#2]} in S#7)]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=(app (\ X#5.S#7) S#6)} in (var X#1))]
    ,
     A#9[(letrec {X#5=S#6} in S#7)]
  )

where

   Delta1 = {A#8,T#3,A#9}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((app (\ X#5.S#7) S#6),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#5.S#7) S#6),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[[.]],
           T#10  |->  [.],
           T#4   |->  [.],
           S#2   |->  (app (\ X#5.S#7) S#6)}

and instantiated rules:

                                  A#9[(app (\ X#5.S#7) S#6)]
    -ucp3->                       A#9[(letrec {X#1=(app (\ X#5.S#7) S#6)} in (var X#1))]
    ................................................................................
                                  A#9[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#9[(letrec {X#5=S#6} in S#7)]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=(\ X#5.S#7)} in A#11[(app (var X#1) S#6)])]
    ,
     A#9[A#11[(letrec {X#5=S#6} in S#7)]]
  )

where

   Delta1 = {T#12,A#10,T#4,A#8,T#3,A#9,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),A#11[(app [.] S#6)]),
             ((\ X#5.S#7),A#11[(app [.] S#6)]),
             (A#11[(app (dummy3 ) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),A#11[(app [.] S#6)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[A#11],
           T#3   |->  A#9,
           A#10  |->  A#11,
           T#4   |->  A#11[(app [.] S#6)],
           T#12  |->  (app [.] S#6),
           T#13  |->  [.],
           S#2   |->  (\ X#5.S#7)}

and instantiated rules:

                                  A#9[A#11[(app (\ X#5.S#7) S#6)]]
    -ucp3->                       A#9[(letrec {X#1=(\ X#5.S#7)} in A#11[(app (var X#1) S#6)])]
    ................................................................................
                                  A#9[A#11[(app (\ X#5.S#7) S#6)]]
    -SR,lbeta1->                  A#9[A#11[(letrec {X#5=S#6} in S#7)]]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=S#2} in A#11[(app (\ X#5.S#7) T#13[(var X#1)])])]
    ,
     A#9[A#11[(letrec {X#5=T#13[S#2]} in S#7)]]
  )

where

   Delta1 = {T#12,A#10,T#4,A#8,T#3,A#9,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),A#11[(app (\ X#5.S#7) T#13)]),
             (S#2,A#11[(app (\ X#5.S#7) T#13)]),
             (A#11[(app (\ X#5.S#7) T#13[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#13[S#2],(\ X#5.[.])),
             (T#13[S#2],(letrec {X#5=[.]} in S#7)),
             ((var X#1),A#11[(app (\ X#5.S#7) T#13[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[A#11],
           T#3   |->  A#9,
           A#10  |->  A#11,
           T#4   |->  A#11[(app (\ X#5.S#7) T#13)],
           T#12  |->  (app (\ X#5.S#7) T#13),
           S#6   |->  T#13[S#2]}

and instantiated rules:

                                  A#9[A#11[(app (\ X#5.S#7) T#13[S#2])]]
    -ucp3->                       A#9[(letrec {X#1=S#2} in A#11[(app (\ X#5.S#7) T#13[(var X#1)])])]
    ................................................................................
                                  A#9[A#11[(app (\ X#5.S#7) T#13[S#2])]]
    -SR,lbeta1->                  A#9[A#11[(letrec {X#5=T#13[S#2]} in S#7)]]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=(app (\ X#5.S#7) S#6)} in A#11[(var X#1)])]
    ,
     A#9[A#11[(letrec {X#5=S#6} in S#7)]]
  )

where

   Delta1 = {A#10,T#4,A#8,T#3,A#9,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),A#11[[.]]),
             ((app (\ X#5.S#7) S#6),A#11[[.]]),
             (A#11[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#5.S#7) S#6),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[A#11],
           T#3   |->  A#9,
           A#10  |->  A#11,
           T#4   |->  A#11[[.]],
           T#12  |->  [.],
           S#2   |->  (app (\ X#5.S#7) S#6)}

and instantiated rules:

                                  A#9[A#11[(app (\ X#5.S#7) S#6)]]
    -ucp3->                       A#9[(letrec {X#1=(app (\ X#5.S#7) S#6)} in A#11[(var X#1)])]
    ................................................................................
                                  A#9[A#11[(app (\ X#5.S#7) S#6)]]
    -SR,lbeta1->                  A#9[A#11[(letrec {X#5=S#6} in S#7)]]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=A#12[(app (\ X#5.S#7) S#6)]} in A#11[(var X#1)])]
    ,
     A#9[A#11[A#12[(letrec {X#5=S#6} in S#7)]]]
  )

where

   Delta1 = {A#10,T#4,A#8,T#3,A#9,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),A#11),
             (A#12[(app (\ X#5.S#7) S#6)],A#11),
             (A#11[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(app (\ X#5.S#7) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[A#11[A#12]],
           T#3   |->  A#9,
           A#10  |->  A#11[A#12],
           T#4   |->  A#11,
           S#2   |->  A#12[(app (\ X#5.S#7) S#6)]}

and instantiated rules:

                                  A#9[A#11[A#12[(app (\ X#5.S#7) S#6)]]]
    -ucp3->                       A#9[(letrec {X#1=A#12[(app (\ X#5.S#7) S#6)]} in A#11[(var X#1)])]
    ................................................................................
                                  A#9[A#11[A#12[(app (\ X#5.S#7) S#6)]]]
    -SR,lbeta1->                  A#9[A#11[A#12[(letrec {X#5=S#6} in S#7)]]]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=S#2} in A#11[(app A#12[(app (\ X#5.S#7) S#6)] T#13[(var X#1)])])]
    ,
     A#9[A#11[(app A#12[(letrec {X#5=S#6} in S#7)] T#13[S#2])]]
  )

where

   Delta1 = {A#10,T#4,A#8,T#3,A#9}
   Delta2 = {}
   Delta3 = {((var X#1),A#11[(app A#12[(app (\ X#5.S#7) S#6)] T#13)]),
             (S#2,A#11[(app A#12[(app (\ X#5.S#7) S#6)] T#13)]),
             (A#11[(app A#12[(app (\ X#5.S#7) S#6)] T#13[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),A#11[(app A#12[(app (\ X#5.S#7) S#6)] T#13[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[A#11[(app A#12 T#13[S#2])]],
           T#3   |->  A#9,
           T#4   |->  A#11[(app A#12[(app (\ X#5.S#7) S#6)] T#13)],
           A#10  |->  A#11[(app A#12 T#13[S#2])]}

and instantiated rules:

                                  A#9[A#11[(app A#12[(app (\ X#5.S#7) S#6)] T#13[S#2])]]
    -ucp3->                       A#9[(letrec {X#1=S#2} in A#11[(app A#12[(app (\ X#5.S#7) S#6)] T#13[(var X#1)])])]
    ................................................................................
                                  A#9[A#11[(app A#12[(app (\ X#5.S#7) S#6)] T#13[S#2])]]
    -SR,lbeta1->                  A#9[A#11[(app A#12[(letrec {X#5=S#6} in S#7)] T#13[S#2])]]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=(\ X#5.S#7)} in (app (var X#1) S#6))]
    ,
     A#9[(letrec {X#5=S#6} in S#7)]
  )

where

   Delta1 = {T#4,A#8,T#3,A#9}
   Delta2 = {}
   Delta3 = {((var X#1),(app [.] S#6)),
             ((\ X#5.S#7),(app [.] S#6)),
             ((app (dummy3 ) S#6),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),(app [.] S#6))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[[.]],
           T#3   |->  A#9,
           A#10  |->  [.],
           T#4   |->  (app [.] S#6),
           T#11  |->  [.],
           S#2   |->  (\ X#5.S#7)}

and instantiated rules:

                                  A#9[(app (\ X#5.S#7) S#6)]
    -ucp3->                       A#9[(letrec {X#1=(\ X#5.S#7)} in (app (var X#1) S#6))]
    ................................................................................
                                  A#9[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#9[(letrec {X#5=S#6} in S#7)]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=S#2} in (app (\ X#5.S#7) T#11[(var X#1)]))]
    ,
     A#9[(letrec {X#5=T#11[S#2]} in S#7)]
  )

where

   Delta1 = {T#4,A#8,T#3,A#9}
   Delta2 = {}
   Delta3 = {((var X#1),(app (\ X#5.S#7) T#11)),
             (S#2,(app (\ X#5.S#7) T#11)),
             ((app (\ X#5.S#7) T#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[S#2],(\ X#5.[.])),
             (T#11[S#2],(letrec {X#5=[.]} in S#7)),
             ((var X#1),(app (\ X#5.S#7) T#11[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[[.]],
           T#3   |->  A#9,
           A#10  |->  [.],
           T#4   |->  (app (\ X#5.S#7) T#11),
           S#6   |->  T#11[S#2]}

and instantiated rules:

                                  A#9[(app (\ X#5.S#7) T#11[S#2])]
    -ucp3->                       A#9[(letrec {X#1=S#2} in (app (\ X#5.S#7) T#11[(var X#1)]))]
    ................................................................................
                                  A#9[(app (\ X#5.S#7) T#11[S#2])]
    -SR,lbeta1->                  A#9[(letrec {X#5=T#11[S#2]} in S#7)]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=A#10[(app (\ X#5.S#7) S#6)]} in (var X#1))]
    ,
     A#9[A#10[(letrec {X#5=S#6} in S#7)]]
  )

where

   Delta1 = {A#8,T#3,A#9}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#10[(app (\ X#5.S#7) S#6)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(app (\ X#5.S#7) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8  |->  A#9[A#10],
           T#3  |->  A#9,
           T#4  |->  [.],
           S#2  |->  A#10[(app (\ X#5.S#7) S#6)]}

and instantiated rules:

                                  A#9[A#10[(app (\ X#5.S#7) S#6)]]
    -ucp3->                       A#9[(letrec {X#1=A#10[(app (\ X#5.S#7) S#6)]} in (var X#1))]
    ................................................................................
                                  A#9[A#10[(app (\ X#5.S#7) S#6)]]
    -SR,lbeta1->                  A#9[A#10[(letrec {X#5=S#6} in S#7)]]
    

================================================================================
Critical Pair:

  (
     A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(letrec {X#1=S#2} in T#4[(var X#1)])])]
    ,
     A#9[(app A#10[(letrec {X#5=S#6} in S#7)] T#11[T#4[S#2]])]
  )

where

   Delta1 = {A#8,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11)],
           A#8  |->  A#9[(app A#10 T#11[T#4[S#2]])]}

and instantiated rules:

                                  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[T#4[S#2]])]
    -ucp3->                       A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(letrec {X#1=S#2} in T#4[(var X#1)])])]
    ................................................................................
                                  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[T#4[S#2]])]
    -SR,lbeta1->                  A#9[(app A#10[(letrec {X#5=S#6} in S#7)] T#11[T#4[S#2]])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#1=(\ X#5.S#7)} in (var X#1)) S#6)
    ,
     (letrec {X#5=S#6} in S#7)
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((\ X#5.S#7),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8  |->  [.],
           T#3  |->  (app [.] S#6),
           T#9  |->  [.],
           T#4  |->  [.],
           S#2  |->  (\ X#5.S#7)}

and instantiated rules:

                                  (app (\ X#5.S#7) S#6)
    -ucp3->                       (app (letrec {X#1=(\ X#5.S#7)} in (var X#1)) S#6)
    ................................................................................
                                  (app (\ X#5.S#7) S#6)
    -SR,lbeta1->                  (letrec {X#5=S#6} in S#7)
    

================================================================================
Critical Pair:

  (
     (app (\ X#5.S#7) T#9[(letrec {X#1=S#2} in T#4[(var X#1)])])
    ,
     (letrec {X#5=T#9[T#4[S#2]]} in S#7)
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#9[T#4[S#2]],(\ X#5.[.])),
             (T#9[T#4[S#2]],(letrec {X#5=[.]} in S#7)),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8  |->  [.],
           T#3  |->  (app (\ X#5.S#7) T#9),
           S#6  |->  T#9[T#4[S#2]]}

and instantiated rules:

                                  (app (\ X#5.S#7) T#9[T#4[S#2]])
    -ucp3->                       (app (\ X#5.S#7) T#9[(letrec {X#1=S#2} in T#4[(var X#1)])])
    ................................................................................
                                  (app (\ X#5.S#7) T#9[T#4[S#2]])
    -SR,lbeta1->                  (letrec {X#5=T#9[T#4[S#2]]} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#5.S#7)} in A#9[(app (var X#1) S#6)])
    ,
     A#9[(letrec {X#5=S#6} in S#7)]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {}
   Delta3 = {((var X#1),A#9[(app [.] S#6)]),
             ((\ X#5.S#7),A#9[(app [.] S#6)]),
             (A#9[(app (dummy3 ) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),A#9[(app [.] S#6)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           A#8   |->  A#9,
           T#4   |->  A#9[(app [.] S#6)],
           T#10  |->  (app [.] S#6),
           T#11  |->  [.],
           S#2   |->  (\ X#5.S#7)}

and instantiated rules:

                                  A#9[(app (\ X#5.S#7) S#6)]
    -ucp3->                       (letrec {X#1=(\ X#5.S#7)} in A#9[(app (var X#1) S#6)])
    ................................................................................
                                  A#9[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#9[(letrec {X#5=S#6} in S#7)]
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#2} in A#9[(app (\ X#5.S#7) T#11[(var X#1)])])
    ,
     A#9[(letrec {X#5=T#11[S#2]} in S#7)]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {}
   Delta3 = {((var X#1),A#9[(app (\ X#5.S#7) T#11)]),
             (S#2,A#9[(app (\ X#5.S#7) T#11)]),
             (A#9[(app (\ X#5.S#7) T#11[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[S#2],(\ X#5.[.])),
             (T#11[S#2],(letrec {X#5=[.]} in S#7)),
             ((var X#1),A#9[(app (\ X#5.S#7) T#11[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           A#8   |->  A#9,
           T#4   |->  A#9[(app (\ X#5.S#7) T#11)],
           T#10  |->  (app (\ X#5.S#7) T#11),
           S#6   |->  T#11[S#2]}

and instantiated rules:

                                  A#9[(app (\ X#5.S#7) T#11[S#2])]
    -ucp3->                       (letrec {X#1=S#2} in A#9[(app (\ X#5.S#7) T#11[(var X#1)])])
    ................................................................................
                                  A#9[(app (\ X#5.S#7) T#11[S#2])]
    -SR,lbeta1->                  A#9[(letrec {X#5=T#11[S#2]} in S#7)]
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(app (\ X#5.S#7) S#6)} in A#9[(var X#1)])
    ,
     A#9[(letrec {X#5=S#6} in S#7)]
  )

where

   Delta1 = {A#8,T#4,A#9}
   Delta2 = {}
   Delta3 = {((var X#1),A#9[[.]]),
             ((app (\ X#5.S#7) S#6),A#9[[.]]),
             (A#9[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#5.S#7) S#6),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           A#8   |->  A#9,
           T#4   |->  A#9[[.]],
           T#10  |->  [.],
           S#2   |->  (app (\ X#5.S#7) S#6)}

and instantiated rules:

                                  A#9[(app (\ X#5.S#7) S#6)]
    -ucp3->                       (letrec {X#1=(app (\ X#5.S#7) S#6)} in A#9[(var X#1)])
    ................................................................................
                                  A#9[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#9[(letrec {X#5=S#6} in S#7)]
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=A#10[(app (\ X#5.S#7) S#6)]} in A#9[(var X#1)])
    ,
     A#9[A#10[(letrec {X#5=S#6} in S#7)]]
  )

where

   Delta1 = {A#8,T#4,A#9}
   Delta2 = {}
   Delta3 = {((var X#1),A#9),
             (A#10[(app (\ X#5.S#7) S#6)],A#9),
             (A#9[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(app (\ X#5.S#7) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           A#8  |->  A#9[A#10],
           T#4  |->  A#9,
           S#2  |->  A#10[(app (\ X#5.S#7) S#6)]}

and instantiated rules:

                                  A#9[A#10[(app (\ X#5.S#7) S#6)]]
    -ucp3->                       (letrec {X#1=A#10[(app (\ X#5.S#7) S#6)]} in A#9[(var X#1)])
    ................................................................................
                                  A#9[A#10[(app (\ X#5.S#7) S#6)]]
    -SR,lbeta1->                  A#9[A#10[(letrec {X#5=S#6} in S#7)]]
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#2} in A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(var X#1)])])
    ,
     A#9[(app A#10[(letrec {X#5=S#6} in S#7)] T#11[S#2])]
  )

where

   Delta1 = {A#8,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11)]),
             (S#2,A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11)]),
             (A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11)],
           A#8  |->  A#9[(app A#10 T#11[S#2])]}

and instantiated rules:

                                  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[S#2])]
    -ucp3->                       (letrec {X#1=S#2} in A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[(var X#1)])])
    ................................................................................
                                  A#9[(app A#10[(app (\ X#5.S#7) S#6)] T#11[S#2])]
    -SR,lbeta1->                  A#9[(app A#10[(letrec {X#5=S#6} in S#7)] T#11[S#2])]
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#5.S#7)} in (app (var X#1) S#6))
    ,
     (letrec {X#5=S#6} in S#7)
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(app [.] S#6)),
             ((\ X#5.S#7),(app [.] S#6)),
             ((app (dummy3 ) S#6),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),(app [.] S#6))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           A#8  |->  [.],
           T#4  |->  (app [.] S#6),
           T#9  |->  [.],
           S#2  |->  (\ X#5.S#7)}

and instantiated rules:

                                  (app (\ X#5.S#7) S#6)
    -ucp3->                       (letrec {X#1=(\ X#5.S#7)} in (app (var X#1) S#6))
    ................................................................................
                                  (app (\ X#5.S#7) S#6)
    -SR,lbeta1->                  (letrec {X#5=S#6} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#2} in (app (\ X#5.S#7) T#9[(var X#1)]))
    ,
     (letrec {X#5=T#9[S#2]} in S#7)
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(app (\ X#5.S#7) T#9)),
             (S#2,(app (\ X#5.S#7) T#9)),
             ((app (\ X#5.S#7) T#9[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#9[S#2],(\ X#5.[.])),
             (T#9[S#2],(letrec {X#5=[.]} in S#7)),
             ((var X#1),(app (\ X#5.S#7) T#9[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           A#8  |->  [.],
           T#4  |->  (app (\ X#5.S#7) T#9),
           S#6  |->  T#9[S#2]}

and instantiated rules:

                                  (app (\ X#5.S#7) T#9[S#2])
    -ucp3->                       (letrec {X#1=S#2} in (app (\ X#5.S#7) T#9[(var X#1)]))
    ................................................................................
                                  (app (\ X#5.S#7) T#9[S#2])
    -SR,lbeta1->                  (letrec {X#5=T#9[S#2]} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=A#8[(app (\ X#5.S#7) S#6)]} in (var X#1))
    ,
     A#8[(letrec {X#5=S#6} in S#7)]
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#8[(app (\ X#5.S#7) S#6)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#8[(app (\ X#5.S#7) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(\ X#5.[.])),
             (S#6,(letrec {X#5=[.]} in S#7)),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    and constraints: (S#6,(\ X#5.[.])), (S#6,(letrec {X#5=[.]} in S#7))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (\ X#5.S#7) S#6)]}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(\ X#5.[.])),(S#6,(letrec {X#5=[.]} in S#7)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  [.],
           S#2  |->  A#8[(app (\ X#5.S#7) S#6)]}

and instantiated rules:

                                  A#8[(app (\ X#5.S#7) S#6)]
    -ucp3->                       (letrec {X#1=A#8[(app (\ X#5.S#7) S#6)]} in (var X#1))
    ................................................................................
                                  A#8[(app (\ X#5.S#7) S#6)]
    -SR,lbeta1->                  A#8[(letrec {X#5=S#6} in S#7)]
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in A#11[(app (letrec {X#1=(\ X#5.S#8)} in (var X#1)) S#7)])
    ,
     (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {T#12,A#9,T#10,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),[.]),
             ((\ X#5.S#8),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in A#11[(app [.] S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app [.] S#7)],
           T#12  |->  (app [.] S#7),
           T#13  |->  [.],
           T#4   |->  [.],
           S#2   |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -ucp3->                       (letrec {E#6} in A#11[(app (letrec {X#1=(\ X#5.S#8)} in (var X#1)) S#7)])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#11[(app (\ X#5.S#8) T#13[(letrec {X#1=S#2} in T#4[(var X#1)])])]
     )
    ,
     (letrec {E#6} in A#11[(letrec {X#5=T#13[T#4[S#2]]} in S#8)])
  )

where

   Delta1 = {T#12,A#9,T#10,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#13[T#4[S#2]],(\ X#5.[.])),
             (T#13[T#4[S#2]],(letrec {X#5=[.]} in S#8)),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (\ X#5.S#8) T#13)],
           T#12  |->  (app (\ X#5.S#8) T#13),
           S#7   |->  T#13[T#4[S#2]]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[T#4[S#2]])])
    -ucp3->                       (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(letrec {X#1=S#2} in T#4[(var X#1)])])])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[T#4[S#2]])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=T#13[T#4[S#2]]} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in A#11[(letrec {X#1=(\ X#5.S#8)} in (app (var X#1) S#7))])
    ,
     (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {T#4,A#9,T#10,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(app [.] S#7)),
             ((\ X#5.S#8),(app [.] S#7)),
             ((app (dummy3 ) S#7),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),(app [.] S#7))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in A#11[[.]]),
           A#9   |->  A#11,
           T#10  |->  A#11[[.]],
           T#12  |->  [.],
           T#4   |->  (app [.] S#7),
           T#13  |->  [.],
           S#2   |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -ucp3->                       (letrec {E#6} in A#11[(letrec {X#1=(\ X#5.S#8)} in (app (var X#1) S#7))])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in A#11[(letrec {X#1=S#2} in (app (\ X#5.S#8) T#13[(var X#1)]))])
    ,
     (letrec {E#6} in A#11[(letrec {X#5=T#13[S#2]} in S#8)])
  )

where

   Delta1 = {T#4,A#9,T#10,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(app (\ X#5.S#8) T#13)),
             (S#2,(app (\ X#5.S#8) T#13)),
             ((app (\ X#5.S#8) T#13[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#13[S#2],(\ X#5.[.])),
             (T#13[S#2],(letrec {X#5=[.]} in S#8)),
             ((var X#1),(app (\ X#5.S#8) T#13[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in A#11[[.]]),
           A#9   |->  A#11,
           T#10  |->  A#11[[.]],
           T#12  |->  [.],
           T#4   |->  (app (\ X#5.S#8) T#13),
           S#7   |->  T#13[S#2]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[S#2])])
    -ucp3->                       (letrec {E#6} in A#11[(letrec {X#1=S#2} in (app (\ X#5.S#8) T#13[(var X#1)]))])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[S#2])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=T#13[S#2]} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in A#11[(letrec {X#1=(app (\ X#5.S#8) S#7)} in (var X#1))])
    ,
     (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {A#9,T#10,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),[.]),
             ((app (\ X#5.S#8) S#7),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#5.S#8) S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in A#11[[.]]),
           A#9   |->  A#11,
           T#10  |->  A#11[[.]],
           T#12  |->  [.],
           T#4   |->  [.],
           S#2   |->  (app (\ X#5.S#8) S#7)}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -ucp3->                       (letrec {E#6} in A#11[(letrec {X#1=(app (\ X#5.S#8) S#7)} in (var X#1))])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in A#11[(letrec {X#1=(\ X#5.S#8)} in A#13[(app (var X#1) S#7)])])
    ,
     (letrec {E#6} in A#11[A#13[(letrec {X#5=S#7} in S#8)]])
  )

where

   Delta1 = {T#14,A#12,T#4,A#9,T#10,T#3,A#11,A#13}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#13[(app [.] S#7)]),
             ((\ X#5.S#8),A#13[(app [.] S#7)]),
             (A#13[(app (dummy3 ) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),A#13[(app [.] S#7)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in A#11),
           A#9   |->  A#11[A#13],
           T#10  |->  A#11,
           A#12  |->  A#13,
           T#4   |->  A#13[(app [.] S#7)],
           T#14  |->  (app [.] S#7),
           T#15  |->  [.],
           S#2   |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {E#6} in A#11[A#13[(app (\ X#5.S#8) S#7)]])
    -ucp3->                       (letrec {E#6} in A#11[(letrec {X#1=(\ X#5.S#8)} in A#13[(app (var X#1) S#7)])])
    ................................................................................
                                  (letrec {E#6} in A#11[A#13[(app (\ X#5.S#8) S#7)]])
    -SR,lbeta2->                  (letrec {E#6} in A#11[A#13[(letrec {X#5=S#7} in S#8)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#11[(letrec {X#1=S#2} in A#13[(app (\ X#5.S#8) T#15[(var X#1)])])]
     )
    ,
     (letrec {E#6} in A#11[A#13[(letrec {X#5=T#15[S#2]} in S#8)]])
  )

where

   Delta1 = {T#14,A#12,T#4,A#9,T#10,T#3,A#11,A#13}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#13[(app (\ X#5.S#8) T#15)]),
             (S#2,A#13[(app (\ X#5.S#8) T#15)]),
             (A#13[(app (\ X#5.S#8) T#15[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#15[S#2],(\ X#5.[.])),
             (T#15[S#2],(letrec {X#5=[.]} in S#8)),
             ((var X#1),A#13[(app (\ X#5.S#8) T#15[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in A#11),
           A#9   |->  A#11[A#13],
           T#10  |->  A#11,
           A#12  |->  A#13,
           T#4   |->  A#13[(app (\ X#5.S#8) T#15)],
           T#14  |->  (app (\ X#5.S#8) T#15),
           S#7   |->  T#15[S#2]}

and instantiated rules:

                                  (letrec {E#6} in A#11[A#13[(app (\ X#5.S#8) T#15[S#2])]])
    -ucp3->                       (letrec {E#6} in A#11[(letrec {X#1=S#2} in A#13[(app (\ X#5.S#8) T#15[(var X#1)])])])
    ................................................................................
                                  (letrec {E#6} in A#11[A#13[(app (\ X#5.S#8) T#15[S#2])]])
    -SR,lbeta2->                  (letrec {E#6} in A#11[A#13[(letrec {X#5=T#15[S#2]} in S#8)]])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in A#11[(letrec {X#1=(app (\ X#5.S#8) S#7)} in A#13[(var X#1)])])
    ,
     (letrec {E#6} in A#11[A#13[(letrec {X#5=S#7} in S#8)]])
  )

where

   Delta1 = {A#12,T#4,A#9,T#10,T#3,A#11,A#13}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#13[[.]]),
             ((app (\ X#5.S#8) S#7),A#13[[.]]),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#5.S#8) S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in A#11),
           A#9   |->  A#11[A#13],
           T#10  |->  A#11,
           A#12  |->  A#13,
           T#4   |->  A#13[[.]],
           T#14  |->  [.],
           S#2   |->  (app (\ X#5.S#8) S#7)}

and instantiated rules:

                                  (letrec {E#6} in A#11[A#13[(app (\ X#5.S#8) S#7)]])
    -ucp3->                       (letrec {E#6} in A#11[(letrec {X#1=(app (\ X#5.S#8) S#7)} in A#13[(var X#1)])])
    ................................................................................
                                  (letrec {E#6} in A#11[A#13[(app (\ X#5.S#8) S#7)]])
    -SR,lbeta2->                  (letrec {E#6} in A#11[A#13[(letrec {X#5=S#7} in S#8)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#11[(letrec {X#1=A#14[(app (\ X#5.S#8) S#7)]} in A#13[(var X#1)])]
     )
    ,
     (letrec {E#6} in A#11[A#13[A#14[(letrec {X#5=S#7} in S#8)]]])
  )

where

   Delta1 = {A#12,T#4,A#9,T#10,T#3,A#11,A#13}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#13),
             (A#14[(app (\ X#5.S#8) S#7)],A#13),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(app (\ X#5.S#8) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in A#11),
           A#9   |->  A#11[A#13[A#14]],
           T#10  |->  A#11,
           A#12  |->  A#13[A#14],
           T#4   |->  A#13,
           S#2   |->  A#14[(app (\ X#5.S#8) S#7)]}

and instantiated rules:

                                  (letrec {E#6} in A#11[A#13[A#14[(app (\ X#5.S#8) S#7)]]])
    -ucp3->                       (letrec {E#6} in A#11[(letrec {X#1=A#14[(app (\ X#5.S#8) S#7)]} in A#13[(var X#1)])])
    ................................................................................
                                  (letrec {E#6} in A#11[A#13[A#14[(app (\ X#5.S#8) S#7)]]])
    -SR,lbeta2->                  (letrec {E#6} in A#11[A#13[A#14[(letrec {X#5=S#7} in S#8)]]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#11[(letrec {X#1=S#2} in A#13[(app A#14[(app (\ X#5.S#8) S#7)] T#15[(var X#1)])])]
     )
    ,
     (letrec {E#6} in A#11[A#13[(app A#14[(letrec {X#5=S#7} in S#8)] T#15[S#2])]])
  )

where

   Delta1 = {A#12,T#4,A#9,T#10,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#13[(app A#14[(app (\ X#5.S#8) S#7)] T#15)]),
             (S#2,A#13[(app A#14[(app (\ X#5.S#8) S#7)] T#15)]),
             (A#13[(app A#14[(app (\ X#5.S#8) S#7)] T#15[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),A#13[(app A#14[(app (\ X#5.S#8) S#7)] T#15[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in A#11),
           A#9   |->  A#11[A#13[(app A#14 T#15[S#2])]],
           T#10  |->  A#11,
           T#4   |->  A#13[(app A#14[(app (\ X#5.S#8) S#7)] T#15)],
           A#12  |->  A#13[(app A#14 T#15[S#2])]}

and instantiated rules:

                                  (letrec {E#6} in A#11[A#13[(app A#14[(app (\ X#5.S#8) S#7)] T#15[S#2])]])
    -ucp3->                       (letrec {E#6} in A#11[(letrec {X#1=S#2} in A#13[(app A#14[(app (\ X#5.S#8) S#7)] T#15[(var X#1)])])])
    ................................................................................
                                  (letrec {E#6} in A#11[A#13[(app A#14[(app (\ X#5.S#8) S#7)] T#15[S#2])]])
    -SR,lbeta2->                  (letrec {E#6} in A#11[A#13[(app A#14[(letrec {X#5=S#7} in S#8)] T#15[S#2])]])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in A#11[(letrec {X#1=(\ X#5.S#8)} in (app (var X#1) S#7))])
    ,
     (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {T#4,A#9,T#10,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(app [.] S#7)),
             ((\ X#5.S#8),(app [.] S#7)),
             ((app (dummy3 ) S#7),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),(app [.] S#7))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in A#11),
           A#9   |->  A#11[[.]],
           T#10  |->  A#11,
           A#12  |->  [.],
           T#4   |->  (app [.] S#7),
           T#13  |->  [.],
           S#2   |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -ucp3->                       (letrec {E#6} in A#11[(letrec {X#1=(\ X#5.S#8)} in (app (var X#1) S#7))])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in A#11[(letrec {X#1=S#2} in (app (\ X#5.S#8) T#13[(var X#1)]))])
    ,
     (letrec {E#6} in A#11[(letrec {X#5=T#13[S#2]} in S#8)])
  )

where

   Delta1 = {T#4,A#9,T#10,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(app (\ X#5.S#8) T#13)),
             (S#2,(app (\ X#5.S#8) T#13)),
             ((app (\ X#5.S#8) T#13[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#13[S#2],(\ X#5.[.])),
             (T#13[S#2],(letrec {X#5=[.]} in S#8)),
             ((var X#1),(app (\ X#5.S#8) T#13[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in A#11),
           A#9   |->  A#11[[.]],
           T#10  |->  A#11,
           A#12  |->  [.],
           T#4   |->  (app (\ X#5.S#8) T#13),
           S#7   |->  T#13[S#2]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[S#2])])
    -ucp3->                       (letrec {E#6} in A#11[(letrec {X#1=S#2} in (app (\ X#5.S#8) T#13[(var X#1)]))])
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[S#2])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=T#13[S#2]} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in A#11[(letrec {X#1=A#12[(app (\ X#5.S#8) S#7)]} in (var X#1))])
    ,
     (letrec {E#6} in A#11[A#12[(letrec {X#5=S#7} in S#8)]])
  )

where

   Delta1 = {A#9,T#10,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),[.]),
             (A#12[(app (\ X#5.S#8) S#7)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(app (\ X#5.S#8) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in A#11),
           A#9   |->  A#11[A#12],
           T#10  |->  A#11,
           T#4   |->  [.],
           S#2   |->  A#12[(app (\ X#5.S#8) S#7)]}

and instantiated rules:

                                  (letrec {E#6} in A#11[A#12[(app (\ X#5.S#8) S#7)]])
    -ucp3->                       (letrec {E#6} in A#11[(letrec {X#1=A#12[(app (\ X#5.S#8) S#7)]} in (var X#1))])
    ................................................................................
                                  (letrec {E#6} in A#11[A#12[(app (\ X#5.S#8) S#7)]])
    -SR,lbeta2->                  (letrec {E#6} in A#11[A#12[(letrec {X#5=S#7} in S#8)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(letrec {X#1=S#2} in T#4[(var X#1)])])]
     )
    ,
     (letrec {E#6} in A#11[(app A#12[(letrec {X#5=S#7} in S#8)] T#13[T#4[S#2]])])
  )

where

   Delta1 = {A#9,T#10,T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)]),
           T#10  |->  A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[T#4[S#2]])])
    -ucp3->                       (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(letrec {X#1=S#2} in T#4[(var X#1)])])])
    ................................................................................
                                  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[T#4[S#2]])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(app A#12[(letrec {X#5=S#7} in S#8)] T#13[T#4[S#2]])])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (app (letrec {X#1=(\ X#5.S#8)} in (var X#1)) S#7))
    ,
     (letrec {E#6} in (letrec {X#5=S#7} in S#8))
  )

where

   Delta1 = {T#10,T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),[.]),
             ((\ X#5.S#8),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in (app [.] S#7)),
           A#9   |->  [.],
           T#10  |->  (app [.] S#7),
           T#11  |->  [.],
           T#4   |->  [.],
           S#2   |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {E#6} in (app (\ X#5.S#8) S#7))
    -ucp3->                       (letrec {E#6} in (app (letrec {X#1=(\ X#5.S#8)} in (var X#1)) S#7))
    ................................................................................
                                  (letrec {E#6} in (app (\ X#5.S#8) S#7))
    -SR,lbeta2->                  (letrec {E#6} in (letrec {X#5=S#7} in S#8))
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (app (\ X#5.S#8) T#11[(letrec {X#1=S#2} in T#4[(var X#1)])]))
    ,
     (letrec {E#6} in (letrec {X#5=T#11[T#4[S#2]]} in S#8))
  )

where

   Delta1 = {T#10,T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[T#4[S#2]],(\ X#5.[.])),
             (T#11[T#4[S#2]],(letrec {X#5=[.]} in S#8)),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in (app (\ X#5.S#8) T#11)),
           A#9   |->  [.],
           T#10  |->  (app (\ X#5.S#8) T#11),
           S#7   |->  T#11[T#4[S#2]]}

and instantiated rules:

                                  (letrec {E#6} in (app (\ X#5.S#8) T#11[T#4[S#2]]))
    -ucp3->                       (letrec {E#6} in (app (\ X#5.S#8) T#11[(letrec {X#1=S#2} in T#4[(var X#1)])]))
    ................................................................................
                                  (letrec {E#6} in (app (\ X#5.S#8) T#11[T#4[S#2]]))
    -SR,lbeta2->                  (letrec {E#6} in (letrec {X#5=T#11[T#4[S#2]]} in S#8))
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (letrec {X#1=(\ X#5.S#8)} in A#11[(app (var X#1) S#7)]))
    ,
     (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {T#12,A#9,T#4,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#11[(app [.] S#7)]),
             ((\ X#5.S#8),A#11[(app [.] S#7)]),
             (A#11[(app (dummy3 ) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),A#11[(app [.] S#7)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in [.]),
           T#10  |->  [.],
           A#9   |->  A#11,
           T#4   |->  A#11[(app [.] S#7)],
           T#12  |->  (app [.] S#7),
           T#13  |->  [.],
           S#2   |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -ucp3->                       (letrec {E#6} in (letrec {X#1=(\ X#5.S#8)} in A#11[(app (var X#1) S#7)]))
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (letrec {X#1=S#2} in A#11[(app (\ X#5.S#8) T#13[(var X#1)])]))
    ,
     (letrec {E#6} in A#11[(letrec {X#5=T#13[S#2]} in S#8)])
  )

where

   Delta1 = {T#12,A#9,T#4,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#11[(app (\ X#5.S#8) T#13)]),
             (S#2,A#11[(app (\ X#5.S#8) T#13)]),
             (A#11[(app (\ X#5.S#8) T#13[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#13[S#2],(\ X#5.[.])),
             (T#13[S#2],(letrec {X#5=[.]} in S#8)),
             ((var X#1),A#11[(app (\ X#5.S#8) T#13[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in [.]),
           T#10  |->  [.],
           A#9   |->  A#11,
           T#4   |->  A#11[(app (\ X#5.S#8) T#13)],
           T#12  |->  (app (\ X#5.S#8) T#13),
           S#7   |->  T#13[S#2]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[S#2])])
    -ucp3->                       (letrec {E#6} in (letrec {X#1=S#2} in A#11[(app (\ X#5.S#8) T#13[(var X#1)])]))
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[S#2])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=T#13[S#2]} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (letrec {X#1=(app (\ X#5.S#8) S#7)} in A#11[(var X#1)]))
    ,
     (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {A#9,T#4,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#11[[.]]),
             ((app (\ X#5.S#8) S#7),A#11[[.]]),
             (A#11[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#5.S#8) S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in [.]),
           T#10  |->  [.],
           A#9   |->  A#11,
           T#4   |->  A#11[[.]],
           T#12  |->  [.],
           S#2   |->  (app (\ X#5.S#8) S#7)}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -ucp3->                       (letrec {E#6} in (letrec {X#1=(app (\ X#5.S#8) S#7)} in A#11[(var X#1)]))
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (letrec {X#1=A#12[(app (\ X#5.S#8) S#7)]} in A#11[(var X#1)]))
    ,
     (letrec {E#6} in A#11[A#12[(letrec {X#5=S#7} in S#8)]])
  )

where

   Delta1 = {A#9,T#4,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#11),
             (A#12[(app (\ X#5.S#8) S#7)],A#11),
             (A#11[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(app (\ X#5.S#8) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in [.]),
           T#10  |->  [.],
           A#9   |->  A#11[A#12],
           T#4   |->  A#11,
           S#2   |->  A#12[(app (\ X#5.S#8) S#7)]}

and instantiated rules:

                                  (letrec {E#6} in A#11[A#12[(app (\ X#5.S#8) S#7)]])
    -ucp3->                       (letrec {E#6} in (letrec {X#1=A#12[(app (\ X#5.S#8) S#7)]} in A#11[(var X#1)]))
    ................................................................................
                                  (letrec {E#6} in A#11[A#12[(app (\ X#5.S#8) S#7)]])
    -SR,lbeta2->                  (letrec {E#6} in A#11[A#12[(letrec {X#5=S#7} in S#8)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
     in
        (letrec {X#1=S#2} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(var X#1)])])
     )
    ,
     (letrec {E#6} in A#11[(app A#12[(letrec {X#5=S#7} in S#8)] T#13[S#2])])
  )

where

   Delta1 = {A#9,T#4,T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)]),
             (S#2,A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)]),
             (A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in [.]),
           T#10  |->  [.],
           T#4   |->  A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[S#2])]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[S#2])])
    -ucp3->                       (letrec {E#6} in (letrec {X#1=S#2} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(var X#1)])]))
    ................................................................................
                                  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[S#2])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(app A#12[(letrec {X#5=S#7} in S#8)] T#13[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (letrec {X#1=(\ X#5.S#8)} in (app (var X#1) S#7)))
    ,
     (letrec {E#6} in (letrec {X#5=S#7} in S#8))
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(app [.] S#7)),
             ((\ X#5.S#8),(app [.] S#7)),
             ((app (dummy3 ) S#7),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),(app [.] S#7))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in [.]),
           T#10  |->  [.],
           A#9   |->  [.],
           T#4   |->  (app [.] S#7),
           T#11  |->  [.],
           S#2   |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {E#6} in (app (\ X#5.S#8) S#7))
    -ucp3->                       (letrec {E#6} in (letrec {X#1=(\ X#5.S#8)} in (app (var X#1) S#7)))
    ................................................................................
                                  (letrec {E#6} in (app (\ X#5.S#8) S#7))
    -SR,lbeta2->                  (letrec {E#6} in (letrec {X#5=S#7} in S#8))
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (letrec {X#1=S#2} in (app (\ X#5.S#8) T#11[(var X#1)])))
    ,
     (letrec {E#6} in (letrec {X#5=T#11[S#2]} in S#8))
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(app (\ X#5.S#8) T#11)),
             (S#2,(app (\ X#5.S#8) T#11)),
             ((app (\ X#5.S#8) T#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[S#2],(\ X#5.[.])),
             (T#11[S#2],(letrec {X#5=[.]} in S#8)),
             ((var X#1),(app (\ X#5.S#8) T#11[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in [.]),
           T#10  |->  [.],
           A#9   |->  [.],
           T#4   |->  (app (\ X#5.S#8) T#11),
           S#7   |->  T#11[S#2]}

and instantiated rules:

                                  (letrec {E#6} in (app (\ X#5.S#8) T#11[S#2]))
    -ucp3->                       (letrec {E#6} in (letrec {X#1=S#2} in (app (\ X#5.S#8) T#11[(var X#1)])))
    ................................................................................
                                  (letrec {E#6} in (app (\ X#5.S#8) T#11[S#2]))
    -SR,lbeta2->                  (letrec {E#6} in (letrec {X#5=T#11[S#2]} in S#8))
    

================================================================================
Critical Pair:

  (
     (letrec {E#6} in (letrec {X#1=A#9[(app (\ X#5.S#8) S#7)]} in (var X#1)))
    ,
     (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),[.]),
             (A#9[(app (\ X#5.S#8) S#7)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(app (\ X#5.S#8) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6} in [.]),
           T#10  |->  [.],
           T#4   |->  [.],
           S#2   |->  A#9[(app (\ X#5.S#8) S#7)]}

and instantiated rules:

                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -ucp3->                       (letrec {E#6} in (letrec {X#1=A#9[(app (\ X#5.S#8) S#7)]} in (var X#1)))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(letrec {X#1=S#2} in T#4[(var X#1)])]
       ;E#13
     in
        A#9[(app (\ X#5.S#8) S#7)]
     )
    ,
     (letrec {X#11=T#10[T#4[S#2]];E#13} in A#9[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#11=T#10;E#13} in A#9[(app (\ X#5.S#8) S#7)]),
           E#6   |->  {X#11=T#10[T#4[S#2]];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[T#4[S#2]];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    -ucp3->                       (letrec {X#11=T#10[(letrec {X#1=S#2} in T#4[(var X#1)])];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    ................................................................................
                                  (letrec {X#11=T#10[T#4[S#2]];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {X#11=T#10[T#4[S#2]];E#13} in A#9[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#5.S#8)} in (letrec {E#6} in A#11[(app (var X#1) S#7)]))
    ,
     (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {E#6} in A#11[(app [.] S#7)])),
             ((\ X#5.S#8),(letrec {E#6} in A#11[(app [.] S#7)])),
             ((letrec {E#6} in A#11[(app (dummy3 ) S#7)]),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),(letrec {E#6} in A#11[(app [.] S#7)]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#6} in A#11[(app [.] S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app [.] S#7)],
           T#12  |->  (app [.] S#7),
           T#13  |->  [.],
           S#2   |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -ucp3->                       (letrec {X#1=(\ X#5.S#8)} in (letrec {E#6} in A#11[(app (var X#1) S#7)]))
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#2} in (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(var X#1)])]))
    ,
     (letrec {E#6} in A#11[(letrec {X#5=T#13[S#2]} in S#8)])
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {E#6} in A#11[(app (\ X#5.S#8) T#13)])),
             (S#2,(letrec {E#6} in A#11[(app (\ X#5.S#8) T#13)])),
             ((letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#13[S#2],(\ X#5.[.])),
             (T#13[S#2],(letrec {X#5=[.]} in S#8)),
             ((var X#1),(letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[[.]])]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (\ X#5.S#8) T#13)],
           T#12  |->  (app (\ X#5.S#8) T#13),
           S#7   |->  T#13[S#2]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[S#2])])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[(var X#1)])]))
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) T#13[S#2])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=T#13[S#2]} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(app (\ X#5.S#8) S#7)} in (letrec {E#6} in A#11[(var X#1)]))
    ,
     (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {A#9,T#10,T#4,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {E#6} in A#11[[.]])),
             ((app (\ X#5.S#8) S#7),(letrec {E#6} in A#11[[.]])),
             ((letrec {E#6} in A#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#5.S#8) S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),(letrec {E#6} in A#11[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#6} in A#11[[.]]),
           A#9   |->  A#11,
           T#10  |->  A#11[[.]],
           T#12  |->  [.],
           S#2   |->  (app (\ X#5.S#8) S#7)}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -ucp3->                       (letrec {X#1=(app (\ X#5.S#8) S#7)} in (letrec {E#6} in A#11[(var X#1)]))
    ................................................................................
                                  (letrec {E#6} in A#11[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=A#12[(app (\ X#5.S#8) S#7)]} in (letrec {E#6} in A#11[(var X#1)]))
    ,
     (letrec {E#6} in A#11[A#12[(letrec {X#5=S#7} in S#8)]])
  )

where

   Delta1 = {A#9,T#10,T#4,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {E#6} in A#11)),
             (A#12[(app (\ X#5.S#8) S#7)],(letrec {E#6} in A#11)),
             ((letrec {E#6} in A#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(app (\ X#5.S#8) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),(letrec {E#6} in A#11[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#6} in A#11),
           A#9   |->  A#11[A#12],
           T#10  |->  A#11,
           S#2   |->  A#12[(app (\ X#5.S#8) S#7)]}

and instantiated rules:

                                  (letrec {E#6} in A#11[A#12[(app (\ X#5.S#8) S#7)]])
    -ucp3->                       (letrec {X#1=A#12[(app (\ X#5.S#8) S#7)]} in (letrec {E#6} in A#11[(var X#1)]))
    ................................................................................
                                  (letrec {E#6} in A#11[A#12[(app (\ X#5.S#8) S#7)]])
    -SR,lbeta2->                  (letrec {E#6} in A#11[A#12[(letrec {X#5=S#7} in S#8)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(var X#1)])])
     )
    ,
     (letrec {E#6} in A#11[(app A#12[(letrec {X#5=S#7} in S#8)] T#13[S#2])])
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)])),
             (S#2,(letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)])),
             ((letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),(letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[[.]])]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)]),
           T#10  |->  A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[S#2])]}

and instantiated rules:

                                  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[S#2])])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[(var X#1)])]))
    ................................................................................
                                  (letrec {E#6} in A#11[(app A#12[(app (\ X#5.S#8) S#7)] T#13[S#2])])
    -SR,lbeta2->                  (letrec {E#6} in A#11[(app A#12[(letrec {X#5=S#7} in S#8)] T#13[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#5.S#8)} in (letrec {E#6} in (app (var X#1) S#7)))
    ,
     (letrec {E#6} in (letrec {X#5=S#7} in S#8))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {E#6} in (app [.] S#7))),
             ((\ X#5.S#8),(letrec {E#6} in (app [.] S#7))),
             ((letrec {E#6} in (app (dummy3 ) S#7)),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#5.S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),(letrec {E#6} in (app [.] S#7)))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#6} in (app [.] S#7)),
           A#9   |->  [.],
           T#10  |->  (app [.] S#7),
           T#11  |->  [.],
           S#2   |->  (\ X#5.S#8)}

and instantiated rules:

                                  (letrec {E#6} in (app (\ X#5.S#8) S#7))
    -ucp3->                       (letrec {X#1=(\ X#5.S#8)} in (letrec {E#6} in (app (var X#1) S#7)))
    ................................................................................
                                  (letrec {E#6} in (app (\ X#5.S#8) S#7))
    -SR,lbeta2->                  (letrec {E#6} in (letrec {X#5=S#7} in S#8))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#2} in (letrec {E#6} in (app (\ X#5.S#8) T#11[(var X#1)])))
    ,
     (letrec {E#6} in (letrec {X#5=T#11[S#2]} in S#8))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {E#6} in (app (\ X#5.S#8) T#11))),
             (S#2,(letrec {E#6} in (app (\ X#5.S#8) T#11))),
             ((letrec {E#6} in (app (\ X#5.S#8) T#11[(dummy3 )])),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[S#2],(\ X#5.[.])),
             (T#11[S#2],(letrec {X#5=[.]} in S#8)),
             ((var X#1),(letrec {E#6} in (app (\ X#5.S#8) T#11[[.]])))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#6} in (app (\ X#5.S#8) T#11)),
           A#9   |->  [.],
           T#10  |->  (app (\ X#5.S#8) T#11),
           S#7   |->  T#11[S#2]}

and instantiated rules:

                                  (letrec {E#6} in (app (\ X#5.S#8) T#11[S#2]))
    -ucp3->                       (letrec {X#1=S#2} in (letrec {E#6} in (app (\ X#5.S#8) T#11[(var X#1)])))
    ................................................................................
                                  (letrec {E#6} in (app (\ X#5.S#8) T#11[S#2]))
    -SR,lbeta2->                  (letrec {E#6} in (letrec {X#5=T#11[S#2]} in S#8))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=A#9[(app (\ X#5.S#8) S#7)]} in (letrec {E#6} in (var X#1)))
    ,
     (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {E#6} in [.])),
             (A#9[(app (\ X#5.S#8) S#7)],(letrec {E#6} in [.])),
             ((letrec {E#6} in (dummy3 )),(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(app (\ X#5.S#8) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),(letrec {E#6} in [.]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#6} in [.]),
           T#10  |->  [.],
           S#2   |->  A#9[(app (\ X#5.S#8) S#7)]}

and instantiated rules:

                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -ucp3->                       (letrec {X#1=A#9[(app (\ X#5.S#8) S#7)]} in (letrec {E#6} in (var X#1)))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {X#11=T#10[(var X#1)];E#13} in A#9[(app (\ X#5.S#8) S#7)])
     )
    ,
     (letrec {X#11=T#10[S#2];E#13} in A#9[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {X#11=T#10;E#13} in A#9[(app (\ X#5.S#8) S#7)])),
             (S#2,(letrec {X#11=T#10;E#13} in A#9[(app (\ X#5.S#8) S#7)])),
             ((letrec {X#11=T#10[(dummy3 )];E#13} in A#9[(app (\ X#5.S#8) S#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),(letrec {X#11=T#10[[.]];E#13} in A#9[(app (\ X#5.S#8) S#7)]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#11=T#10;E#13} in A#9[(app (\ X#5.S#8) S#7)]),
           E#6   |->  {X#11=T#10[S#2];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[S#2];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#11=T#10[(var X#1)];E#13} in A#9[(app (\ X#5.S#8) S#7)]))
    ................................................................................
                                  (letrec {X#11=T#10[S#2];E#13} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {X#11=T#10[S#2];E#13} in A#9[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])} in (var X#1))
    ,
     (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
  )

where

   Delta1 = {}
   Delta2 = {E#6}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)]),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(\ X#5.[.])),
             (S#7,(letrec {X#5=[.]} in S#8)),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    and constraints: E#6/= {}, (S#7,(\ X#5.[.])), (S#7,(letrec {X#5=[.]} in S#8))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(\ X#5.[.])),(S#7,(letrec {X#5=[.]} in S#8)),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  [.],
           S#2  |->  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])}

and instantiated rules:

                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -ucp3->                       (letrec {X#1=(letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])} in (var X#1))
    ................................................................................
                                  (letrec {E#6} in A#9[(app (\ X#5.S#8) S#7)])
    -SR,lbeta2->                  (letrec {E#6} in A#9[(letrec {X#5=S#7} in S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        A#13[(letrec {X#1=(var X#5)} in (var X#1))]
     )
    ,
     (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[(var X#5)])
  )

where

   Delta1 = {A#10,T#12,T#3,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#5),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#13[[.]]),
             ((var X#5),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[[.]]),
           A#10  |->  A#13,
           T#12  |->  A#13[[.]],
           T#14  |->  [.],
           T#4   |->  [.],
           S#2   |->  (var X#5)}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(var X#5)])
    -ucp3->                       (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(letrec {X#1=(var X#5)} in (var X#1))])
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        A#13[(letrec {X#1=(var X#5)} in A#15[(var X#1)])]
     )
    ,
     (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[A#15[(var X#5)]])
  )

where

   Delta1 = {A#14,T#4,A#10,T#12,T#3,A#13,A#15}
   Delta2 = {}
   Delta3 = {((var X#1),A#15[[.]]),
             ((var X#5),A#15[[.]]),
             (A#15[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#15[[.]]),
             ((var X#5),A#13[A#15[[.]]]),
             ((var X#5),A#13[A#15[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13),
           A#10  |->  A#13[A#15],
           T#12  |->  A#13,
           A#14  |->  A#15,
           T#4   |->  A#15[[.]],
           T#16  |->  [.],
           S#2   |->  (var X#5)}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[A#15[(var X#5)]])
    -ucp3->                       (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(letrec {X#1=(var X#5)} in A#15[(var X#1)])])
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[A#15[(var X#5)]])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[A#15[(var X#5)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        A#13[(letrec {X#1=A#16[(var X#5)]} in A#15[(var X#1)])]
     )
    ,
     (letrec
        E#7
       ;EE#11[X#5,(letrec {X#6=S#8} in S#9)]
     in
        A#13[A#15[A#16[(var X#5)]]]
     )
  )

where

   Delta1 = {A#14,T#4,A#10,T#12,T#3,A#13,A#15}
   Delta2 = {}
   Delta3 = {((var X#1),A#15),
             (A#16[(var X#5)],A#15),
             (A#15[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#16[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#15[[.]]),
             ((var X#5),A#13[A#15[A#16[[.]]]]),
             ((var X#5),A#13[A#15[A#16[[.]]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13),
           A#10  |->  A#13[A#15[A#16]],
           T#12  |->  A#13,
           A#14  |->  A#15[A#16],
           T#4   |->  A#15,
           S#2   |->  A#16[(var X#5)]}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[A#15[A#16[(var X#5)]]])
    -ucp3->                       (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(letrec {X#1=A#16[(var X#5)]} in A#15[(var X#1)])])
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[A#15[A#16[(var X#5)]]])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[A#15[A#16[(var X#5)]]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        A#13[(letrec {X#1=S#2} in A#15[(app A#16[(var X#5)] T#17[(var X#1)])])]
     )
    ,
     (letrec
        E#7
       ;EE#11[X#5,(letrec {X#6=S#8} in S#9)]
     in
        A#13[A#15[(app A#16[(var X#5)] T#17[S#2])]]
     )
  )

where

   Delta1 = {A#14,T#4,A#10,T#12,T#3,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),A#15[(app A#16[(var X#5)] T#17)]),
             (S#2,A#15[(app A#16[(var X#5)] T#17)]),
             (A#15[(app A#16[(var X#5)] T#17[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#15[(app A#16[(var X#5)] T#17[[.]])]),
             ((var X#5),A#13[A#15[(app A#16[[.]] T#17[S#2])]]),
             ((var X#5),A#13[A#15[(app A#16[[.]] T#17[S#2])]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13),
           A#10  |->  A#13[A#15[(app A#16 T#17[S#2])]],
           T#12  |->  A#13,
           T#4   |->  A#15[(app A#16[(var X#5)] T#17)],
           A#14  |->  A#15[(app A#16 T#17[S#2])]}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[A#15[(app A#16[(var X#5)] T#17[S#2])]])
    -ucp3->                       (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(letrec {X#1=S#2} in A#15[(app A#16[(var X#5)] T#17[(var X#1)])])])
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[A#15[(app A#16[(var X#5)] T#17[S#2])]])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[A#15[(app A#16[(var X#5)] T#17[S#2])]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        A#13[(letrec {X#1=A#14[(var X#5)]} in (var X#1))]
     )
    ,
     (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[A#14[(var X#5)]])
  )

where

   Delta1 = {A#10,T#12,T#3,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#14[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#13[A#14[[.]]]),
             ((var X#5),A#13[A#14[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13),
           A#10  |->  A#13[A#14],
           T#12  |->  A#13,
           T#4   |->  [.],
           S#2   |->  A#14[(var X#5)]}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[A#14[(var X#5)]])
    -ucp3->                       (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(letrec {X#1=A#14[(var X#5)]} in (var X#1))])
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[A#14[(var X#5)]])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[A#14[(var X#5)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        A#13[(app A#14[(var X#5)] T#15[(letrec {X#1=S#2} in T#4[(var X#1)])])]
     )
    ,
     (letrec
        E#7
       ;EE#11[X#5,(letrec {X#6=S#8} in S#9)]
     in
        A#13[(app A#14[(var X#5)] T#15[T#4[S#2]])]
     )
  )

where

   Delta1 = {A#10,T#12,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#13[(app A#14[[.]] T#15[T#4[S#2]])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[T#4[S#2]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#5)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[T#4[S#2]])])
    -ucp3->                       (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {X#1=S#2} in T#4[(var X#1)])])])
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[T#4[S#2]])])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[(app A#14[(var X#5)] T#15[T#4[S#2]])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        (letrec {X#1=(var X#5)} in A#13[(var X#1)])
     )
    ,
     (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[(var X#5)])
  )

where

   Delta1 = {A#10,T#4,T#3,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),A#13[[.]]),
             ((var X#5),A#13[[.]]),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#13[[.]]),
             ((var X#5),A#13[[.]]),
             ((var X#5),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in [.]),
           T#12  |->  [.],
           A#10  |->  A#13,
           T#4   |->  A#13[[.]],
           T#14  |->  [.],
           S#2   |->  (var X#5)}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(var X#5)])
    -ucp3->                       (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in (letrec {X#1=(var X#5)} in A#13[(var X#1)]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        (letrec {X#1=A#14[(var X#5)]} in A#13[(var X#1)])
     )
    ,
     (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[A#14[(var X#5)]])
  )

where

   Delta1 = {A#10,T#4,T#3,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),A#13),
             (A#14[(var X#5)],A#13),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#13[[.]]),
             ((var X#5),A#13[A#14[[.]]]),
             ((var X#5),A#13[A#14[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in [.]),
           T#12  |->  [.],
           A#10  |->  A#13[A#14],
           T#4   |->  A#13,
           S#2   |->  A#14[(var X#5)]}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[A#14[(var X#5)]])
    -ucp3->                       (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in (letrec {X#1=A#14[(var X#5)]} in A#13[(var X#1)]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[A#14[(var X#5)]])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[A#14[(var X#5)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        (letrec {X#1=S#2} in A#13[(app A#14[(var X#5)] T#15[(var X#1)])])
     )
    ,
     (letrec
        E#7
       ;EE#11[X#5,(letrec {X#6=S#8} in S#9)]
     in
        A#13[(app A#14[(var X#5)] T#15[S#2])]
     )
  )

where

   Delta1 = {A#10,T#4,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),A#13[(app A#14[(var X#5)] T#15)]),
             (S#2,A#13[(app A#14[(var X#5)] T#15)]),
             (A#13[(app A#14[(var X#5)] T#15[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#13[(app A#14[(var X#5)] T#15[[.]])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[S#2])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[S#2])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in [.]),
           T#12  |->  [.],
           T#4   |->  A#13[(app A#14[(var X#5)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[S#2])]}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[S#2])])
    -ucp3->                       (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in (letrec {X#1=S#2} in A#13[(app A#14[(var X#5)] T#15[(var X#1)])]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[S#2])])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[(app A#14[(var X#5)] T#15[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#7
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        (letrec {X#1=A#10[(var X#5)]} in (var X#1))
     )
    ,
     (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#10[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in [.]),
           T#12  |->  [.],
           T#4   |->  [.],
           S#2   |->  A#10[(var X#5)]}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in (letrec {X#1=A#10[(var X#5)]} in (var X#1)))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=S#2} in T#4[(var X#1)])]
       ;E#15
       ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#13= T#12[T#4[S#2]]
       ;E#15
       ;EE#11[X#5,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#13=T#12;E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           E#7   |->  {X#13=T#12[T#4[S#2]];E#15},
           E#14  |->  {E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[T#4[S#2]];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#13=T#12[(letrec {X#1=S#2} in T#4[(var X#1)])];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#13=T#12[T#4[S#2]];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#13=T#12[T#4[S#2]];E#15;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {X#1=(\ X#6.S#9)} in (var X#1)) S#8)]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#17,A#15,T#12,T#3,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((\ X#6.S#9),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[(app [.] S#8)];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[(app [.] S#8)],
           T#17         |->  (app [.] S#8),
           T#18         |->  [.],
           T#4          |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(app (letrec {X#1=(\ X#6.S#9)} in (var X#1)) S#8)];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (\ X#6.S#9) T#18[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {X#6=T#18[T#4[S#2]]} in S#9)];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#17,A#15,T#12,T#3,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[T#4[S#2]],(\ X#6.[.])),
             (T#18[T#4[S#2]],(letrec {X#6=[.]} in S#9)),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18)];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (\ X#6.S#9) T#18)],
           T#17         |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[T#4[S#2]]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[T#4[S#2]])];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[T#4[S#2]])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=T#18[T#4[S#2]]} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=(\ X#6.S#9)} in (app (var X#1) S#8))]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),(app [.] S#8)),
             ((\ X#6.S#9),(app [.] S#8)),
             ((app (dummy3 ) S#8),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(app [.] S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[[.]];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[[.]],
           T#17         |->  [.],
           T#4          |->  (app [.] S#8),
           T#18         |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=(\ X#6.S#9)} in (app (var X#1) S#8))];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=S#2} in (app (\ X#6.S#9) T#18[(var X#1)]))]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {X#6=T#18[S#2]} in S#9)];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),(app (\ X#6.S#9) T#18)),
             (S#2,(app (\ X#6.S#9) T#18)),
             ((app (\ X#6.S#9) T#18[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[S#2],(\ X#6.[.])),
             (T#18[S#2],(letrec {X#6=[.]} in S#9)),
             ((var X#1),(app (\ X#6.S#9) T#18[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[[.]];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[[.]],
           T#17         |->  [.],
           T#4          |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[S#2])];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=S#2} in (app (\ X#6.S#9) T#18[(var X#1)]))];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[S#2])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=T#18[S#2]} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=(app (\ X#6.S#9) S#8)} in (var X#1))]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {A#15,T#12,T#3,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((app (\ X#6.S#9) S#8),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#6.S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[[.]];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[[.]],
           T#17         |->  [.],
           T#4          |->  [.],
           S#2          |->  (app (\ X#6.S#9) S#8)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=(app (\ X#6.S#9) S#8)} in (var X#1))];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=(\ X#6.S#9)} in A#18[(app (var X#1) S#8)])]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[A#18[(letrec {X#6=S#8} in S#9)]];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#19,A#17,T#4,A#15,T#12,T#3,A#16,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),A#18[(app [.] S#8)]),
             ((\ X#6.S#9),A#18[(app [.] S#8)]),
             (A#18[(app (dummy3 ) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#18[(app [.] S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#18[[.2]]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16[A#18],
           T#12         |->  A#16,
           A#17         |->  A#18,
           T#4          |->  A#18[(app [.] S#8)],
           T#19         |->  (app [.] S#8),
           T#20         |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#5=A#16[A#18[(app (\ X#6.S#9) S#8)]];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=(\ X#6.S#9)} in A#18[(app (var X#1) S#8)])];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#18[(app (\ X#6.S#9) S#8)]];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[A#18[(letrec {X#6=S#8} in S#9)]];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=S#2} in A#18[(app (\ X#6.S#9) T#20[(var X#1)])])]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[A#18[(letrec {X#6=T#20[S#2]} in S#9)]]
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#17,T#4,A#15,T#12,T#3,A#16,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),A#18[(app (\ X#6.S#9) T#20)]),
             (S#2,A#18[(app (\ X#6.S#9) T#20)]),
             (A#18[(app (\ X#6.S#9) T#20[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#20[S#2],(\ X#6.[.])),
             (T#20[S#2],(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#18[(app (\ X#6.S#9) T#20[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#18[[.2]]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16[A#18],
           T#12         |->  A#16,
           A#17         |->  A#18,
           T#4          |->  A#18[(app (\ X#6.S#9) T#20)],
           T#19         |->  (app (\ X#6.S#9) T#20),
           S#8          |->  T#20[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[A#18[(app (\ X#6.S#9) T#20[S#2])]];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=S#2} in A#18[(app (\ X#6.S#9) T#20[(var X#1)])])];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#18[(app (\ X#6.S#9) T#20[S#2])]];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[A#18[(letrec {X#6=T#20[S#2]} in S#9)]];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=(app (\ X#6.S#9) S#8)} in A#18[(var X#1)])]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[A#18[(letrec {X#6=S#8} in S#9)]];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {A#17,T#4,A#15,T#12,T#3,A#16,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),A#18[[.]]),
             ((app (\ X#6.S#9) S#8),A#18[[.]]),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#6.S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#18[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#18[[.2]]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16[A#18],
           T#12         |->  A#16,
           A#17         |->  A#18,
           T#4          |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  (app (\ X#6.S#9) S#8)}

and instantiated rules:

                                  (letrec {X#5=A#16[A#18[(app (\ X#6.S#9) S#8)]];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=(app (\ X#6.S#9) S#8)} in A#18[(var X#1)])];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#18[(app (\ X#6.S#9) S#8)]];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[A#18[(letrec {X#6=S#8} in S#9)]];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=A#19[(app (\ X#6.S#9) S#8)]} in A#18[(var X#1)])]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[A#18[A#19[(letrec {X#6=S#8} in S#9)]]]
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#17,T#4,A#15,T#12,T#3,A#16,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),A#18),
             (A#19[(app (\ X#6.S#9) S#8)],A#18),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(app (\ X#6.S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#18[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#18[A#19[[.2]]]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16[A#18[A#19]],
           T#12         |->  A#16,
           A#17         |->  A#18[A#19],
           T#4          |->  A#18,
           S#2          |->  A#19[(app (\ X#6.S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#5=A#16[A#18[A#19[(app (\ X#6.S#9) S#8)]]];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=A#19[(app (\ X#6.S#9) S#8)]} in A#18[(var X#1)])];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#18[A#19[(app (\ X#6.S#9) S#8)]]];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[A#18[A#19[(letrec {X#6=S#8} in S#9)]]];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=S#2} in A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(var X#1)])])]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[S#2])]]
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#17,T#4,A#15,T#12,T#3,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)]),
             (S#2,A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)]),
             (A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#18[(app A#19[[.2]] T#20[S#2])]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16[A#18[(app A#19 T#20[S#2])]],
           T#12         |->  A#16,
           T#4          |->  A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)],
           A#17         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#5=A#16[A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[S#2])]];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=S#2} in A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(var X#1)])])];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[S#2])]];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[S#2])]];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=(\ X#6.S#9)} in (app (var X#1) S#8))]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),(app [.] S#8)),
             ((\ X#6.S#9),(app [.] S#8)),
             ((app (dummy3 ) S#8),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(app [.] S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16[[.]],
           T#12         |->  A#16,
           A#17         |->  [.],
           T#4          |->  (app [.] S#8),
           T#18         |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=(\ X#6.S#9)} in (app (var X#1) S#8))];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=S#2} in (app (\ X#6.S#9) T#18[(var X#1)]))]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {X#6=T#18[S#2]} in S#9)];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),(app (\ X#6.S#9) T#18)),
             (S#2,(app (\ X#6.S#9) T#18)),
             ((app (\ X#6.S#9) T#18[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[S#2],(\ X#6.[.])),
             (T#18[S#2],(letrec {X#6=[.]} in S#9)),
             ((var X#1),(app (\ X#6.S#9) T#18[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16[[.]],
           T#12         |->  A#16,
           A#17         |->  [.],
           T#4          |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[S#2])];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=S#2} in (app (\ X#6.S#9) T#18[(var X#1)]))];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[S#2])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=T#18[S#2]} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=A#17[(app (\ X#6.S#9) S#8)]} in (var X#1))]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[A#17[(letrec {X#6=S#8} in S#9)]];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {A#15,T#12,T#3,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#17[(app (\ X#6.S#9) S#8)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#17[(app (\ X#6.S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#17[[.2]]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16[A#17],
           T#12         |->  A#16,
           T#4          |->  [.],
           S#2          |->  A#17[(app (\ X#6.S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#5=A#16[A#17[(app (\ X#6.S#9) S#8)]];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=A#17[(app (\ X#6.S#9) S#8)]} in (var X#1))];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#17[(app (\ X#6.S#9) S#8)]];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[A#17[(letrec {X#6=S#8} in S#9)]];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(app A#17[(letrec {X#6=S#8} in S#9)] T#18[T#4[S#2]])]
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[T#4[S#2]])]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           T#12         |->  A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[T#4[S#2]])];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[T#4[S#2]])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(app A#17[(letrec {X#6=S#8} in S#9)] T#18[T#4[S#2]])];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {X#1=(\ X#6.S#9)} in (var X#1)) S#8)
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=(letrec {X#6=S#8} in S#9);E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#12,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((\ X#6.S#9),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(app [.] S#8);E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#16         |->  [.],
           T#4          |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#5=(app (\ X#6.S#9) S#8);E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(app (letrec {X#1=(\ X#6.S#9)} in (var X#1)) S#8);E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (\ X#6.S#9) S#8);E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=(letrec {X#6=S#8} in S#9);E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (\ X#6.S#9) T#16[(letrec {X#1=S#2} in T#4[(var X#1)])])
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=(letrec {X#6=T#16[T#4[S#2]]} in S#9);E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#12,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#16[T#4[S#2]],(\ X#6.[.])),
             (T#16[T#4[S#2]],(letrec {X#6=[.]} in S#9)),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(app (\ X#6.S#9) T#16);E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  [.],
           T#12         |->  (app (\ X#6.S#9) T#16),
           S#8          |->  T#16[T#4[S#2]]}

and instantiated rules:

                                  (letrec {X#5=(app (\ X#6.S#9) T#16[T#4[S#2]]);E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(app (\ X#6.S#9) T#16[(letrec {X#1=S#2} in T#4[(var X#1)])]);E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (\ X#6.S#9) T#16[T#4[S#2]]);E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=(letrec {X#6=T#16[T#4[S#2]]} in S#9);E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=(\ X#6.S#9)} in A#16[(app (var X#1) S#8)])
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#17,A#15,T#4,T#3,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),A#16[(app [.] S#8)]),
             ((\ X#6.S#9),A#16[(app [.] S#8)]),
             (A#16[(app (dummy3 ) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#16[(app [.] S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           T#12         |->  [.],
           A#15         |->  A#16,
           T#4          |->  A#16[(app [.] S#8)],
           T#17         |->  (app [.] S#8),
           T#18         |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=(\ X#6.S#9)} in A#16[(app (var X#1) S#8)]);E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=S#2} in A#16[(app (\ X#6.S#9) T#18[(var X#1)])])
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {X#6=T#18[S#2]} in S#9)];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#17,A#15,T#4,T#3,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),A#16[(app (\ X#6.S#9) T#18)]),
             (S#2,A#16[(app (\ X#6.S#9) T#18)]),
             (A#16[(app (\ X#6.S#9) T#18[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[S#2],(\ X#6.[.])),
             (T#18[S#2],(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#16[(app (\ X#6.S#9) T#18[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           T#12         |->  [.],
           A#15         |->  A#16,
           T#4          |->  A#16[(app (\ X#6.S#9) T#18)],
           T#17         |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[S#2])];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in A#16[(app (\ X#6.S#9) T#18[(var X#1)])]);E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[S#2])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=T#18[S#2]} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=(app (\ X#6.S#9) S#8)} in A#16[(var X#1)])
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {A#15,T#4,T#3,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),A#16[[.]]),
             ((app (\ X#6.S#9) S#8),A#16[[.]]),
             (A#16[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#6.S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#16[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           T#12         |->  [.],
           A#15         |->  A#16,
           T#4          |->  A#16[[.]],
           T#17         |->  [.],
           S#2          |->  (app (\ X#6.S#9) S#8)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=(app (\ X#6.S#9) S#8)} in A#16[(var X#1)]);E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=A#17[(app (\ X#6.S#9) S#8)]} in A#16[(var X#1)])
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[A#17[(letrec {X#6=S#8} in S#9)]];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {A#15,T#4,T#3,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),A#16),
             (A#17[(app (\ X#6.S#9) S#8)],A#16),
             (A#16[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#17[(app (\ X#6.S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#16[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#17[[.2]]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           T#12         |->  [.],
           A#15         |->  A#16[A#17],
           T#4          |->  A#16,
           S#2          |->  A#17[(app (\ X#6.S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#5=A#16[A#17[(app (\ X#6.S#9) S#8)]];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=A#17[(app (\ X#6.S#9) S#8)]} in A#16[(var X#1)]);E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#17[(app (\ X#6.S#9) S#8)]];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[A#17[(letrec {X#6=S#8} in S#9)]];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=S#2} in A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(var X#1)])])
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(app A#17[(letrec {X#6=S#8} in S#9)] T#18[S#2])]
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)]),
             (S#2,A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)]),
             (A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[S#2])]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           T#12         |->  [.],
           T#4          |->  A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[S#2])]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[S#2])];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(var X#1)])]);E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[S#2])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(app A#17[(letrec {X#6=S#8} in S#9)] T#18[S#2])];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=(\ X#6.S#9)} in (app (var X#1) S#8))
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=(letrec {X#6=S#8} in S#9);E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),(app [.] S#8)),
             ((\ X#6.S#9),(app [.] S#8)),
             ((app (dummy3 ) S#8),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(app [.] S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           T#12         |->  [.],
           A#15         |->  [.],
           T#4          |->  (app [.] S#8),
           T#16         |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#5=(app (\ X#6.S#9) S#8);E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=(\ X#6.S#9)} in (app (var X#1) S#8));E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (\ X#6.S#9) S#8);E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=(letrec {X#6=S#8} in S#9);E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=S#2} in (app (\ X#6.S#9) T#16[(var X#1)]))
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=(letrec {X#6=T#16[S#2]} in S#9);E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),(app (\ X#6.S#9) T#16)),
             (S#2,(app (\ X#6.S#9) T#16)),
             ((app (\ X#6.S#9) T#16[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#16[S#2],(\ X#6.[.])),
             (T#16[S#2],(letrec {X#6=[.]} in S#9)),
             ((var X#1),(app (\ X#6.S#9) T#16[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           T#12         |->  [.],
           A#15         |->  [.],
           T#4          |->  (app (\ X#6.S#9) T#16),
           S#8          |->  T#16[S#2]}

and instantiated rules:

                                  (letrec {X#5=(app (\ X#6.S#9) T#16[S#2]);E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in (app (\ X#6.S#9) T#16[(var X#1)]));E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (\ X#6.S#9) T#16[S#2]);E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=(letrec {X#6=T#16[S#2]} in S#9);E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=A#15[(app (\ X#6.S#9) S#8)]} in (var X#1))
       ;E#7
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#15[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#15[(app (\ X#6.S#9) S#8)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(app (\ X#6.S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#15[(app (\ X#6.S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#5=A#15[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=A#15[(app (\ X#6.S#9) S#8)]} in (var X#1));E#7} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#15[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#15[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(letrec {X#1=(var X#16)} in (var X#1))]
       ;E#7
       ;EE#17[X#16,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(var X#16)]
       ;E#7
       ;EE#17[X#16,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#16),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#16),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#18[[.]];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(var X#16)];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#5=A#18[(var X#16)];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#18[(letrec {X#1=(var X#16)} in (var X#1))];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(var X#16)];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#18[(var X#16)];E#7;EE#17[X#16,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(letrec {X#1=(var X#16)} in A#20[(var X#1)])]
       ;E#7
       ;EE#17[X#16,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[A#20[(var X#16)]]
       ;E#7
       ;EE#17[X#16,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {}
   Delta3 = {((var X#1),A#20[[.]]),
             ((var X#16),A#20[[.]]),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#16),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#20[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#18;E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#20[(var X#16)]];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]},
           A#15         |->  A#18[A#20],
           T#12         |->  A#18,
           A#19         |->  A#20,
           T#4          |->  A#20[[.]],
           T#21         |->  [.],
           S#2          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#5=A#18[A#20[(var X#16)]];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#18[(letrec {X#1=(var X#16)} in A#20[(var X#1)])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[A#20[(var X#16)]];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#18[A#20[(var X#16)]];E#7;EE#17[X#16,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(letrec {X#1=A#21[(var X#16)]} in A#20[(var X#1)])]
       ;E#7
       ;EE#17[X#16,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[A#20[A#21[(var X#16)]]]
       ;E#7
       ;EE#17[X#16,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {}
   Delta3 = {((var X#1),A#20),
             (A#21[(var X#16)],A#20),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#21[(var X#16)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#20[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#18;E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#20[A#21[(var X#16)]]];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]},
           A#15         |->  A#18[A#20[A#21]],
           T#12         |->  A#18,
           A#19         |->  A#20[A#21],
           T#4          |->  A#20,
           S#2          |->  A#21[(var X#16)]}

and instantiated rules:

                                  (letrec {X#5=A#18[A#20[A#21[(var X#16)]]];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#18[(letrec {X#1=A#21[(var X#16)]} in A#20[(var X#1)])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[A#20[A#21[(var X#16)]]];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#18[A#20[A#21[(var X#16)]]];E#7;EE#17[X#16,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(letrec {X#1=S#2} in A#20[(app A#21[(var X#16)] T#22[(var X#1)])])]
       ;E#7
       ;EE#17[X#16,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]]
       ;E#7
       ;EE#17[X#16,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),A#20[(app A#21[(var X#16)] T#22)]),
             (S#2,A#20[(app A#21[(var X#16)] T#22)]),
             (A#20[(app A#21[(var X#16)] T#22[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#20[(app A#21[(var X#16)] T#22[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#18;E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]},
           A#15         |->  A#18[A#20[(app A#21 T#22[S#2])]],
           T#12         |->  A#18,
           T#4          |->  A#20[(app A#21[(var X#16)] T#22)],
           A#19         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#5=A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#18[(letrec {X#1=S#2} in A#20[(app A#21[(var X#16)] T#22[(var X#1)])])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]];E#7;EE#17[X#16,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(letrec {X#1=A#19[(var X#16)]} in (var X#1))]
       ;E#7
       ;EE#17[X#16,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[A#19[(var X#16)]]
       ;E#7
       ;EE#17[X#16,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#19[(var X#16)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(var X#16)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#18;E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#19[(var X#16)]];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]},
           A#15         |->  A#18[A#19],
           T#12         |->  A#18,
           T#4          |->  [.],
           S#2          |->  A#19[(var X#16)]}

and instantiated rules:

                                  (letrec {X#5=A#18[A#19[(var X#16)]];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#18[(letrec {X#1=A#19[(var X#16)]} in (var X#1))];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[A#19[(var X#16)]];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#18[A#19[(var X#16)]];E#7;EE#17[X#16,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#7
       ;EE#17[X#16,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])]
       ;E#7
       ;EE#17[X#16,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])];E#7;EE#17[X#16,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=(var X#16)} in A#18[(var X#1)])
       ;E#7
       ;EE#17[X#16,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(var X#16)]
       ;E#7
       ;EE#17[X#16,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),A#18[[.]]),
             ((var X#16),A#18[[.]]),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#16),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#18[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(var X#16)];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]},
           T#12         |->  [.],
           A#15         |->  A#18,
           T#4          |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#5=A#18[(var X#16)];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=(var X#16)} in A#18[(var X#1)]);E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(var X#16)];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#18[(var X#16)];E#7;EE#17[X#16,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=A#19[(var X#16)]} in A#18[(var X#1)])
       ;E#7
       ;EE#17[X#16,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[A#19[(var X#16)]]
       ;E#7
       ;EE#17[X#16,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),A#18),
             (A#19[(var X#16)],A#18),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(var X#16)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#18[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#19[(var X#16)]];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]},
           T#12         |->  [.],
           A#15         |->  A#18[A#19],
           T#4          |->  A#18,
           S#2          |->  A#19[(var X#16)]}

and instantiated rules:

                                  (letrec {X#5=A#18[A#19[(var X#16)]];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=A#19[(var X#16)]} in A#18[(var X#1)]);E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[A#19[(var X#16)]];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#18[A#19[(var X#16)]];E#7;EE#17[X#16,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=S#2} in A#18[(app A#19[(var X#16)] T#20[(var X#1)])])
       ;E#7
       ;EE#17[X#16,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[S#2])]
       ;E#7
       ;EE#17[X#16,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),A#18[(app A#19[(var X#16)] T#20)]),
             (S#2,A#18[(app A#19[(var X#16)] T#20)]),
             (A#18[(app A#19[(var X#16)] T#20[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#18[(app A#19[(var X#16)] T#20[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[S#2])];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]},
           T#12         |->  [.],
           T#4          |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[S#2])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in A#18[(app A#19[(var X#16)] T#20[(var X#1)])]);E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[S#2])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[S#2])];E#7;EE#17[X#16,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=A#15[(var X#16)]} in (var X#1))
       ;E#7
       ;EE#17[X#16,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#15[(var X#16)]
       ;E#7
       ;EE#17[X#16,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#15[(var X#16)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(var X#16)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#15[(var X#16)];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#15[(var X#16)]}

and instantiated rules:

                                  (letrec {X#5=A#15[(var X#16)];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=A#15[(var X#16)]} in (var X#1));E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#15[(var X#16)];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#15[(var X#16)];E#7;EE#17[X#16,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {X#1=(var X#17)} in (var X#1))]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(var X#17)]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#20}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#17),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20[[.]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]},
           A#15         |->  A#20,
           T#12         |->  A#20[[.]],
           T#21         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#16=A#20[(var X#17)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#20[(letrec {X#1=(var X#17)} in (var X#1))];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(var X#17)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#20[(var X#17)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {X#1=(var X#17)} in A#22[(var X#1)])]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[A#22[(var X#17)]]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#21,T#4,A#15,T#12,T#3,A#20,A#22}
   Delta2 = {}
   Delta3 = {((var X#1),A#22[[.]]),
             ((var X#17),A#22[[.]]),
             (A#22[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#22[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20;E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#22[(var X#17)]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]},
           A#15         |->  A#20[A#22],
           T#12         |->  A#20,
           A#21         |->  A#22,
           T#4          |->  A#22[[.]],
           T#23         |->  [.],
           S#2          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#16=A#20[A#22[(var X#17)]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#20[(letrec {X#1=(var X#17)} in A#22[(var X#1)])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[A#22[(var X#17)]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#20[A#22[(var X#17)]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {X#1=A#23[(var X#17)]} in A#22[(var X#1)])]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[A#22[A#23[(var X#17)]]]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#21,T#4,A#15,T#12,T#3,A#20,A#22}
   Delta2 = {}
   Delta3 = {((var X#1),A#22),
             (A#23[(var X#17)],A#22),
             (A#22[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#23[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#22[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20;E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#22[A#23[(var X#17)]]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]},
           A#15         |->  A#20[A#22[A#23]],
           T#12         |->  A#20,
           A#21         |->  A#22[A#23],
           T#4          |->  A#22,
           S#2          |->  A#23[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#22[A#23[(var X#17)]]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#20[(letrec {X#1=A#23[(var X#17)]} in A#22[(var X#1)])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[A#22[A#23[(var X#17)]]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#20[A#22[A#23[(var X#17)]]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {X#1=S#2} in A#22[(app A#23[(var X#17)] T#24[(var X#1)])])]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#21,T#4,A#15,T#12,T#3,A#20}
   Delta2 = {}
   Delta3 = {((var X#1),A#22[(app A#23[(var X#17)] T#24)]),
             (S#2,A#22[(app A#23[(var X#17)] T#24)]),
             (A#22[(app A#23[(var X#17)] T#24[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#22[(app A#23[(var X#17)] T#24[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20;E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]},
           A#15         |->  A#20[A#22[(app A#23 T#24[S#2])]],
           T#12         |->  A#20,
           T#4          |->  A#22[(app A#23[(var X#17)] T#24)],
           A#21         |->  A#22[(app A#23 T#24[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#20[(letrec {X#1=S#2} in A#22[(app A#23[(var X#17)] T#24[(var X#1)])])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {X#1=A#21[(var X#17)]} in (var X#1))]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[A#21[(var X#17)]]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#20}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#21[(var X#17)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#21[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20;E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#21[(var X#17)]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]},
           A#15         |->  A#20[A#21],
           T#12         |->  A#20,
           T#4          |->  [.],
           S#2          |->  A#21[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#21[(var X#17)]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#20[(letrec {X#1=A#21[(var X#17)]} in (var X#1))];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[A#21[(var X#17)]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#20[A#21[(var X#17)]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=(var X#17)} in A#20[(var X#1)])
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(var X#17)]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#20}
   Delta2 = {}
   Delta3 = {((var X#1),A#20[[.]]),
             ((var X#17),A#20[[.]]),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#20[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]},
           T#12         |->  [.],
           A#15         |->  A#20,
           T#4          |->  A#20[[.]],
           T#21         |->  [.],
           S#2          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#16=A#20[(var X#17)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=(var X#17)} in A#20[(var X#1)]);E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(var X#17)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#20[(var X#17)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=A#21[(var X#17)]} in A#20[(var X#1)])
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[A#21[(var X#17)]]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#20}
   Delta2 = {}
   Delta3 = {((var X#1),A#20),
             (A#21[(var X#17)],A#20),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#21[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#20[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#21[(var X#17)]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]},
           T#12         |->  [.],
           A#15         |->  A#20[A#21],
           T#4          |->  A#20,
           S#2          |->  A#21[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#21[(var X#17)]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=A#21[(var X#17)]} in A#20[(var X#1)]);E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[A#21[(var X#17)]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#20[A#21[(var X#17)]];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=S#2} in A#20[(app A#21[(var X#17)] T#22[(var X#1)])])
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[S#2])]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),A#20[(app A#21[(var X#17)] T#22)]),
             (S#2,A#20[(app A#21[(var X#17)] T#22)]),
             (A#20[(app A#21[(var X#17)] T#22[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#20[(app A#21[(var X#17)] T#22[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]},
           T#12         |->  [.],
           T#4          |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=S#2} in A#20[(app A#21[(var X#17)] T#22[(var X#1)])]);E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=A#15[(var X#17)]} in (var X#1))
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (\ X#6.S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#15[(var X#17)]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#15[(var X#17)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#15[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#15[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#15[(var X#17)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=A#15[(var X#17)]} in (var X#1));E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#15[(var X#17)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#15[(var X#17)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {X#1=(\ X#6.S#9)} in (var X#1)) S#8)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=S#8} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((\ X#6.S#9),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[(app [.] S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app [.] S#8)],
           T#19         |->  (app [.] S#8),
           T#20         |->  [.],
           T#4          |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(app (letrec {X#1=(\ X#6.S#9)} in (var X#1)) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=S#8} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (\ X#6.S#9) T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=T#20[T#4[S#2]]} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#20[T#4[S#2]],(\ X#6.[.])),
             (T#20[T#4[S#2]],(letrec {X#6=[.]} in S#9)),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (\ X#6.S#9) T#20)],
           T#19         |->  (app (\ X#6.S#9) T#20),
           S#8          |->  T#20[T#4[S#2]]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[T#4[S#2]])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[T#4[S#2]])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=T#20[T#4[S#2]]} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=(\ X#6.S#9)} in (app (var X#1) S#8))]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=S#8} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),(app [.] S#8)),
             ((\ X#6.S#9),(app [.] S#8)),
             ((app (dummy3 ) S#8),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(app [.] S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[[.]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           T#4          |->  (app [.] S#8),
           T#20         |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=(\ X#6.S#9)} in (app (var X#1) S#8))];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=S#8} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=S#2} in (app (\ X#6.S#9) T#20[(var X#1)]))]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=T#20[S#2]} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),(app (\ X#6.S#9) T#20)),
             (S#2,(app (\ X#6.S#9) T#20)),
             ((app (\ X#6.S#9) T#20[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#20[S#2],(\ X#6.[.])),
             (T#20[S#2],(letrec {X#6=[.]} in S#9)),
             ((var X#1),(app (\ X#6.S#9) T#20[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[[.]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           T#4          |->  (app (\ X#6.S#9) T#20),
           S#8          |->  T#20[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[S#2])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=S#2} in (app (\ X#6.S#9) T#20[(var X#1)]))];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[S#2])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=T#20[S#2]} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=(app (\ X#6.S#9) S#8)} in (var X#1))]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=S#8} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((app (\ X#6.S#9) S#8),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#6.S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[[.]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           T#4          |->  [.],
           S#2          |->  (app (\ X#6.S#9) S#8)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=(app (\ X#6.S#9) S#8)} in (var X#1))];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=S#8} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=(\ X#6.S#9)} in A#20[(app (var X#1) S#8)])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#20[(letrec {X#6=S#8} in S#9)]]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#21,A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {}
   Delta3 = {((var X#1),A#20[(app [.] S#8)]),
             ((\ X#6.S#9),A#20[(app [.] S#8)]),
             (A#20[(app (dummy3 ) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#20[(app [.] S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#20[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#20],
           T#12         |->  A#18,
           A#19         |->  A#20,
           T#4          |->  A#20[(app [.] S#8)],
           T#21         |->  (app [.] S#8),
           T#22         |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[(app (\ X#6.S#9) S#8)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=(\ X#6.S#9)} in A#20[(app (var X#1) S#8)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[(app (\ X#6.S#9) S#8)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[A#20[(letrec {X#6=S#8} in S#9)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=S#2} in A#20[(app (\ X#6.S#9) T#22[(var X#1)])])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#20[(letrec {X#6=T#22[S#2]} in S#9)]]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#21,A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {}
   Delta3 = {((var X#1),A#20[(app (\ X#6.S#9) T#22)]),
             (S#2,A#20[(app (\ X#6.S#9) T#22)]),
             (A#20[(app (\ X#6.S#9) T#22[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#22[S#2],(\ X#6.[.])),
             (T#22[S#2],(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#20[(app (\ X#6.S#9) T#22[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#20[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#20],
           T#12         |->  A#18,
           A#19         |->  A#20,
           T#4          |->  A#20[(app (\ X#6.S#9) T#22)],
           T#21         |->  (app (\ X#6.S#9) T#22),
           S#8          |->  T#22[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[(app (\ X#6.S#9) T#22[S#2])]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=S#2} in A#20[(app (\ X#6.S#9) T#22[(var X#1)])])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[(app (\ X#6.S#9) T#22[S#2])]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[A#20[(letrec {X#6=T#22[S#2]} in S#9)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=(app (\ X#6.S#9) S#8)} in A#20[(var X#1)])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#20[(letrec {X#6=S#8} in S#9)]]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {}
   Delta3 = {((var X#1),A#20[[.]]),
             ((app (\ X#6.S#9) S#8),A#20[[.]]),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#6.S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#20[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#20[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#20],
           T#12         |->  A#18,
           A#19         |->  A#20,
           T#4          |->  A#20[[.]],
           T#21         |->  [.],
           S#2          |->  (app (\ X#6.S#9) S#8)}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[(app (\ X#6.S#9) S#8)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=(app (\ X#6.S#9) S#8)} in A#20[(var X#1)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[(app (\ X#6.S#9) S#8)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[A#20[(letrec {X#6=S#8} in S#9)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=A#21[(app (\ X#6.S#9) S#8)]} in A#20[(var X#1)])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#20[A#21[(letrec {X#6=S#8} in S#9)]]]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {}
   Delta3 = {((var X#1),A#20),
             (A#21[(app (\ X#6.S#9) S#8)],A#20),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#21[(app (\ X#6.S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#20[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#20[A#21[[.2]]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#20[A#21]],
           T#12         |->  A#18,
           A#19         |->  A#20[A#21],
           T#4          |->  A#20,
           S#2          |->  A#21[(app (\ X#6.S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[A#21[(app (\ X#6.S#9) S#8)]]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=A#21[(app (\ X#6.S#9) S#8)]} in A#20[(var X#1)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[A#21[(app (\ X#6.S#9) S#8)]]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[A#20[A#21[(letrec {X#6=S#8} in S#9)]]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=S#2} in A#20[(app A#21[(app (\ X#6.S#9) S#8)] T#22[(var X#1)])])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#20[(app A#21[(letrec {X#6=S#8} in S#9)] T#22[S#2])]]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),A#20[(app A#21[(app (\ X#6.S#9) S#8)] T#22)]),
             (S#2,A#20[(app A#21[(app (\ X#6.S#9) S#8)] T#22)]),
             (A#20[(app A#21[(app (\ X#6.S#9) S#8)] T#22[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#20[(app A#21[(app (\ X#6.S#9) S#8)] T#22[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#20[(app A#21[[.2]] T#22[S#2])]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#20[(app A#21 T#22[S#2])]],
           T#12         |->  A#18,
           T#4          |->  A#20[(app A#21[(app (\ X#6.S#9) S#8)] T#22)],
           A#19         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[(app A#21[(app (\ X#6.S#9) S#8)] T#22[S#2])]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=S#2} in A#20[(app A#21[(app (\ X#6.S#9) S#8)] T#22[(var X#1)])])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[(app A#21[(app (\ X#6.S#9) S#8)] T#22[S#2])]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[A#20[(app A#21[(letrec {X#6=S#8} in S#9)] T#22[S#2])]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=(\ X#6.S#9)} in (app (var X#1) S#8))]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=S#8} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),(app [.] S#8)),
             ((\ X#6.S#9),(app [.] S#8)),
             ((app (dummy3 ) S#8),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(app [.] S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[[.]],
           T#12         |->  A#18,
           A#19         |->  [.],
           T#4          |->  (app [.] S#8),
           T#20         |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=(\ X#6.S#9)} in (app (var X#1) S#8))];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=S#8} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=S#2} in (app (\ X#6.S#9) T#20[(var X#1)]))]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=T#20[S#2]} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),(app (\ X#6.S#9) T#20)),
             (S#2,(app (\ X#6.S#9) T#20)),
             ((app (\ X#6.S#9) T#20[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#20[S#2],(\ X#6.[.])),
             (T#20[S#2],(letrec {X#6=[.]} in S#9)),
             ((var X#1),(app (\ X#6.S#9) T#20[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[[.]],
           T#12         |->  A#18,
           A#19         |->  [.],
           T#4          |->  (app (\ X#6.S#9) T#20),
           S#8          |->  T#20[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[S#2])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=S#2} in (app (\ X#6.S#9) T#20[(var X#1)]))];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[S#2])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=T#20[S#2]} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=A#19[(app (\ X#6.S#9) S#8)]} in (var X#1))]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#19[(letrec {X#6=S#8} in S#9)]]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#19[(app (\ X#6.S#9) S#8)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(app (\ X#6.S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#19[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#19],
           T#12         |->  A#18,
           T#4          |->  [.],
           S#2          |->  A#19[(app (\ X#6.S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#19[(app (\ X#6.S#9) S#8)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=A#19[(app (\ X#6.S#9) S#8)]} in (var X#1))];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#19[(app (\ X#6.S#9) S#8)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[A#19[(letrec {X#6=S#8} in S#9)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[T#4[S#2]])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[T#4[S#2]])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           T#12         |->  A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[T#4[S#2]])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[T#4[S#2]])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[T#4[S#2]])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {X#1=(\ X#6.S#9)} in (var X#1)) S#8)
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#6=S#8} in S#9)
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((\ X#6.S#9),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=(app [.] S#8);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#18         |->  [.],
           T#4          |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#16=(app (\ X#6.S#9) S#8);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(app (letrec {X#1=(\ X#6.S#9)} in (var X#1)) S#8);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (\ X#6.S#9) S#8);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=(letrec {X#6=S#8} in S#9);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (\ X#6.S#9) T#18[(letrec {X#1=S#2} in T#4[(var X#1)])])
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#6=T#18[T#4[S#2]]} in S#9)
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[T#4[S#2]],(\ X#6.[.])),
             (T#18[T#4[S#2]],(letrec {X#6=[.]} in S#9)),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=(app (\ X#6.S#9) T#18);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[T#4[S#2]]}

and instantiated rules:

                                  (letrec {X#16=(app (\ X#6.S#9) T#18[T#4[S#2]]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(app (\ X#6.S#9) T#18[(letrec {X#1=S#2} in T#4[(var X#1)])]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (\ X#6.S#9) T#18[T#4[S#2]]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=(letrec {X#6=T#18[T#4[S#2]]} in S#9);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=(\ X#6.S#9)} in A#18[(app (var X#1) S#8)])
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=S#8} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#4,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),A#18[(app [.] S#8)]),
             ((\ X#6.S#9),A#18[(app [.] S#8)]),
             (A#18[(app (dummy3 ) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#18[(app [.] S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  A#18,
           T#4          |->  A#18[(app [.] S#8)],
           T#19         |->  (app [.] S#8),
           T#20         |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=(\ X#6.S#9)} in A#18[(app (var X#1) S#8)]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=S#8} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=S#2} in A#18[(app (\ X#6.S#9) T#20[(var X#1)])])
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=T#20[S#2]} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#4,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),A#18[(app (\ X#6.S#9) T#20)]),
             (S#2,A#18[(app (\ X#6.S#9) T#20)]),
             (A#18[(app (\ X#6.S#9) T#20[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#20[S#2],(\ X#6.[.])),
             (T#20[S#2],(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#18[(app (\ X#6.S#9) T#20[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  A#18,
           T#4          |->  A#18[(app (\ X#6.S#9) T#20)],
           T#19         |->  (app (\ X#6.S#9) T#20),
           S#8          |->  T#20[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[S#2])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=S#2} in A#18[(app (\ X#6.S#9) T#20[(var X#1)])]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[S#2])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=T#20[S#2]} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=(app (\ X#6.S#9) S#8)} in A#18[(var X#1)])
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=S#8} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),A#18[[.]]),
             ((app (\ X#6.S#9) S#8),A#18[[.]]),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#6.S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#18[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  A#18,
           T#4          |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  (app (\ X#6.S#9) S#8)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=(app (\ X#6.S#9) S#8)} in A#18[(var X#1)]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=S#8} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=A#19[(app (\ X#6.S#9) S#8)]} in A#18[(var X#1)])
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#19[(letrec {X#6=S#8} in S#9)]]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),A#18),
             (A#19[(app (\ X#6.S#9) S#8)],A#18),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(app (\ X#6.S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#18[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#19[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  A#18[A#19],
           T#4          |->  A#18,
           S#2          |->  A#19[(app (\ X#6.S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#19[(app (\ X#6.S#9) S#8)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=A#19[(app (\ X#6.S#9) S#8)]} in A#18[(var X#1)]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#19[(app (\ X#6.S#9) S#8)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[A#19[(letrec {X#6=S#8} in S#9)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=S#2} in A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(var X#1)])])
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[S#2])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)]),
             (S#2,A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)]),
             (A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[S#2])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           T#4          |->  A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[S#2])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=S#2} in A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(var X#1)])]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[S#2])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[S#2])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=(\ X#6.S#9)} in (app (var X#1) S#8))
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#6=S#8} in S#9)
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),(app [.] S#8)),
             ((\ X#6.S#9),(app [.] S#8)),
             ((app (dummy3 ) S#8),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(app [.] S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  [.],
           T#4          |->  (app [.] S#8),
           T#18         |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#16=(app (\ X#6.S#9) S#8);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=(\ X#6.S#9)} in (app (var X#1) S#8));E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (\ X#6.S#9) S#8);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=(letrec {X#6=S#8} in S#9);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=S#2} in (app (\ X#6.S#9) T#18[(var X#1)]))
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#6=T#18[S#2]} in S#9)
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),(app (\ X#6.S#9) T#18)),
             (S#2,(app (\ X#6.S#9) T#18)),
             ((app (\ X#6.S#9) T#18[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[S#2],(\ X#6.[.])),
             (T#18[S#2],(letrec {X#6=[.]} in S#9)),
             ((var X#1),(app (\ X#6.S#9) T#18[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  [.],
           T#4          |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[S#2]}

and instantiated rules:

                                  (letrec {X#16=(app (\ X#6.S#9) T#18[S#2]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=S#2} in (app (\ X#6.S#9) T#18[(var X#1)]));E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (\ X#6.S#9) T#18[S#2]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=(letrec {X#6=T#18[S#2]} in S#9);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=A#15[(app (\ X#6.S#9) S#8)]} in (var X#1))
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#15[(letrec {X#6=S#8} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#15[(app (\ X#6.S#9) S#8)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(app (\ X#6.S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#15[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#15[(app (\ X#6.S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#16=A#15[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=A#15[(app (\ X#6.S#9) S#8)]} in (var X#1));E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#15[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#15[(letrec {X#6=S#8} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           E#7
          ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
        in
           A#13[(app A#14[(var X#5)] T#15[(var X#1)])]
        )
     )
    ,
     (letrec
        E#7
       ;EE#11[X#5,(letrec {X#6=S#8} in S#9)]
     in
        A#13[(app A#14[(var X#5)] T#15[S#2])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)])),
             (S#2,(letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)])),
             ((letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[[.]])])),
             ((var X#5),A#13[(app A#14[[.]] T#15[S#2])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[S#2])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#5)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[S#2])]}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[S#2])])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(var X#1)])]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[S#2])])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#13[(app A#14[(var X#5)] T#15[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#13= T#12[(var X#1)]
          ;E#15
          ;EE#11[X#5,(app (\ X#6.S#9) S#8)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#13= T#12[S#2]
       ;E#15
       ;EE#11[X#5,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#13=T#12;E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#13=T#12;E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])),
             ((letrec {X#13=T#12[(dummy3 )];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#13=T#12[[.]];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#13=T#12;E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           E#7   |->  {X#13=T#12[S#2];E#15},
           E#14  |->  {E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[S#2];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#13=T#12[(var X#1)];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#13=T#12[S#2];E#15;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#13=T#12[S#2];E#15;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#6.S#9)
     in
        (letrec {X#5=A#16[(app (var X#1) S#8)];E#7} in A#10[(var X#5)])
     )
    ,
     (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=A#16[(app [.] S#8)];E#7} in A#10[(var X#5)])),
             ((\ X#6.S#9),(letrec {X#5=A#16[(app [.] S#8)];E#7} in A#10[(var X#5)])),
             ((letrec {X#5=A#16[(app (dummy3 ) S#8)];E#7} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#5=A#16[(app [.] S#8)];E#7} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=A#16[(app [.] S#8)];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[(app [.] S#8)],
           T#17         |->  (app [.] S#8),
           T#18         |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=(\ X#6.S#9)} in (letrec {X#5=A#16[(app (var X#1) S#8)];E#7} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(var X#1)])];E#7} in A#10[(var X#5)])
     )
    ,
     (letrec {X#5=A#16[(letrec {X#6=T#18[S#2]} in S#9)];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=A#16[(app (\ X#6.S#9) T#18)];E#7} in A#10[(var X#5)])),
             (S#2,(letrec {X#5=A#16[(app (\ X#6.S#9) T#18)];E#7} in A#10[(var X#5)])),
             ((letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(dummy3 )])];E#7} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[S#2],(\ X#6.[.])),
             (T#18[S#2],(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#5=A#16[(app (\ X#6.S#9) T#18[[.]])];E#7} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18)];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (\ X#6.S#9) T#18)],
           T#17         |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[S#2])];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[(var X#1)])];E#7} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) T#18[S#2])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=T#18[S#2]} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (app (\ X#6.S#9) S#8)
     in
        (letrec {X#5=A#16[(var X#1)];E#7} in A#10[(var X#5)])
     )
    ,
     (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {A#15,T#12,T#4,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=A#16[[.]];E#7} in A#10[(var X#5)])),
             ((app (\ X#6.S#9) S#8),(letrec {X#5=A#16[[.]];E#7} in A#10[(var X#5)])),
             ((letrec {X#5=A#16[(dummy3 )];E#7} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#6.S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#5=A#16[[.]];E#7} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=A#16[[.]];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16,
           T#12         |->  A#16[[.]],
           T#17         |->  [.],
           S#2          |->  (app (\ X#6.S#9) S#8)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=(app (\ X#6.S#9) S#8)} in (letrec {X#5=A#16[(var X#1)];E#7} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#16[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#17[(app (\ X#6.S#9) S#8)]
     in
        (letrec {X#5=A#16[(var X#1)];E#7} in A#10[(var X#5)])
     )
    ,
     (letrec {X#5=A#16[A#17[(letrec {X#6=S#8} in S#9)]];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {A#15,T#12,T#4,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=A#16;E#7} in A#10[(var X#5)])),
             (A#17[(app (\ X#6.S#9) S#8)],(letrec {X#5=A#16;E#7} in A#10[(var X#5)])),
             ((letrec {X#5=A#16[(dummy3 )];E#7} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (A#17[(app (\ X#6.S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#5=A#16[[.]];E#7} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=A#16;E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#17[[.2]]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  A#16[A#17],
           T#12         |->  A#16,
           S#2          |->  A#17[(app (\ X#6.S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#5=A#16[A#17[(app (\ X#6.S#9) S#8)]];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=A#17[(app (\ X#6.S#9) S#8)]} in (letrec {X#5=A#16[(var X#1)];E#7} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#16[A#17[(app (\ X#6.S#9) S#8)]];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[A#17[(letrec {X#6=S#8} in S#9)]];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(var X#1)])]
          ;E#7
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#5= A#16[(app A#17[(letrec {X#6=S#8} in S#9)] T#18[S#2])]
       ;E#7
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)];E#7} in A#10[(var X#5)])),
             (S#2,(letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)];E#7} in A#10[(var X#5)])),
             ((letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(dummy3 )])];E#7} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[[.]])];E#7} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[S#2])]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           T#12         |->  A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[S#2])]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[S#2])];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[(var X#1)])];E#7} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#16[(app A#17[(app (\ X#6.S#9) S#8)] T#18[S#2])];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#16[(app A#17[(letrec {X#6=S#8} in S#9)] T#18[S#2])];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#6.S#9)
     in
        (letrec {X#5=(app (var X#1) S#8);E#7} in A#10[(var X#5)])
     )
    ,
     (letrec {X#5=(letrec {X#6=S#8} in S#9);E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=(app [.] S#8);E#7} in A#10[(var X#5)])),
             ((\ X#6.S#9),(letrec {X#5=(app [.] S#8);E#7} in A#10[(var X#5)])),
             ((letrec {X#5=(app (dummy3 ) S#8);E#7} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#5=(app [.] S#8);E#7} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(app [.] S#8);E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#16         |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#5=(app (\ X#6.S#9) S#8);E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=(\ X#6.S#9)} in (letrec {X#5=(app (var X#1) S#8);E#7} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=(app (\ X#6.S#9) S#8);E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=(letrec {X#6=S#8} in S#9);E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {X#5=(app (\ X#6.S#9) T#16[(var X#1)]);E#7} in A#10[(var X#5)])
     )
    ,
     (letrec {X#5=(letrec {X#6=T#16[S#2]} in S#9);E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=(app (\ X#6.S#9) T#16);E#7} in A#10[(var X#5)])),
             (S#2,(letrec {X#5=(app (\ X#6.S#9) T#16);E#7} in A#10[(var X#5)])),
             ((letrec {X#5=(app (\ X#6.S#9) T#16[(dummy3 )]);E#7} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#16[S#2],(\ X#6.[.])),
             (T#16[S#2],(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#5=(app (\ X#6.S#9) T#16[[.]]);E#7} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(app (\ X#6.S#9) T#16);E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           A#15         |->  [.],
           T#12         |->  (app (\ X#6.S#9) T#16),
           S#8          |->  T#16[S#2]}

and instantiated rules:

                                  (letrec {X#5=(app (\ X#6.S#9) T#16[S#2]);E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(app (\ X#6.S#9) T#16[(var X#1)]);E#7} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=(app (\ X#6.S#9) T#16[S#2]);E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=(letrec {X#6=T#16[S#2]} in S#9);E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#15[(app (\ X#6.S#9) S#8)]
     in
        (letrec {X#5=(var X#1);E#7} in A#10[(var X#5)])
     )
    ,
     (letrec {X#5=A#15[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=[.];E#7} in A#10[(var X#5)])),
             (A#15[(app (\ X#6.S#9) S#8)],(letrec {X#5=[.];E#7} in A#10[(var X#5)])),
             ((letrec {X#5=(dummy3 );E#7} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(app (\ X#6.S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#5=[.];E#7} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=[.];E#7} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7},
           T#12         |->  [.],
           S#2          |->  A#15[(app (\ X#6.S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#5=A#15[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=A#15[(app (\ X#6.S#9) S#8)]} in (letrec {X#5=(var X#1);E#7} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#15[(app (\ X#6.S#9) S#8)];E#7} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#15[(letrec {X#6=S#8} in S#9)];E#7} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= A#18[(app A#19[(var X#16)] T#20[(var X#1)])]
          ;E#7
          ;EE#17[X#16,(app (\ X#6.S#9) S#8)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[S#2])]
       ;E#7
       ;EE#17[X#16,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])),
             ((letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(dummy3 )])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#5=A#18[(app A#19[(var X#16)] T#20[[.]])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[S#2])];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[S#2])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(var X#1)])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[S#2])];E#7;EE#17[X#16,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[S#2])];E#7;EE#17[X#16,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#16= A#20[(app A#21[(var X#17)] T#22[(var X#1)])]
          ;E#7
          ;EE#18[X#5,(var X#16)]
          ;EE#19[X#17,(app (\ X#6.S#9) S#8)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[S#2])]
       ;E#7
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {X#6=S#8} in S#9)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])),
             ((letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(dummy3 )])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#16=A#20[(app A#21[(var X#17)] T#22[[.]])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(var X#1)])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#7;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#6.S#9)
     in
        (letrec
           X#16= A#18[(app (var X#1) S#8)]
          ;E#7
          ;EE#17[X#5,(var X#16)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=S#8} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#16=A#18[(app [.] S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((\ X#6.S#9),(letrec {X#16=A#18[(app [.] S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=A#18[(app (dummy3 ) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#16=A#18[(app [.] S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#18[(app [.] S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app [.] S#8)],
           T#19         |->  (app [.] S#8),
           T#20         |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=(\ X#6.S#9)} in (letrec {X#16=A#18[(app (var X#1) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=S#8} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#16= A#18[(app (\ X#6.S#9) T#20[(var X#1)])]
          ;E#7
          ;EE#17[X#5,(var X#16)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=T#20[S#2]} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#16=A#18[(app (\ X#6.S#9) T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#16=A#18[(app (\ X#6.S#9) T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=A#18[(app (\ X#6.S#9) T#20[(dummy3 )])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#20[S#2],(\ X#6.[.])),
             (T#20[S#2],(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#16=A#18[(app (\ X#6.S#9) T#20[[.]])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (\ X#6.S#9) T#20)],
           T#19         |->  (app (\ X#6.S#9) T#20),
           S#8          |->  T#20[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[S#2])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[(var X#1)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) T#20[S#2])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=T#20[S#2]} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (app (\ X#6.S#9) S#8)
     in
        (letrec {X#16=A#18[(var X#1)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#6=S#8} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#16=A#18[[.]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((app (\ X#6.S#9) S#8),(letrec {X#16=A#18[[.]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=A#18[(dummy3 )];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             ((app (\ X#6.S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#16=A#18[[.]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#18[[.]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  (app (\ X#6.S#9) S#8)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=(app (\ X#6.S#9) S#8)} in (letrec {X#16=A#18[(var X#1)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#18[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(letrec {X#6=S#8} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#19[(app (\ X#6.S#9) S#8)]
     in
        (letrec {X#16=A#18[(var X#1)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
     )
    ,
     (letrec
        X#16= A#18[A#19[(letrec {X#6=S#8} in S#9)]]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#16=A#18;E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             (A#19[(app (\ X#6.S#9) S#8)],(letrec {X#16=A#18;E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=A#18[(dummy3 )];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(app (\ X#6.S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#16=A#18[[.]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#18;E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#19[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#19],
           T#12         |->  A#18,
           S#2          |->  A#19[(app (\ X#6.S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#19[(app (\ X#6.S#9) S#8)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=A#19[(app (\ X#6.S#9) S#8)]} in (letrec {X#16=A#18[(var X#1)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#18[A#19[(app (\ X#6.S#9) S#8)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[A#19[(letrec {X#6=S#8} in S#9)]];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#16= A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(var X#1)])]
          ;E#7
          ;EE#17[X#5,(var X#16)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[S#2])]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(dummy3 )])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[[.]])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[S#2])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           T#12         |->  A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[S#2])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[(var X#1)])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (\ X#6.S#9) S#8)] T#20[S#2])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#18[(app A#19[(letrec {X#6=S#8} in S#9)] T#20[S#2])];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#6.S#9)
     in
        (letrec {X#16=(app (var X#1) S#8);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
     )
    ,
     (letrec
        X#16= (letrec {X#6=S#8} in S#9)
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#16=(app [.] S#8);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((\ X#6.S#9),(letrec {X#16=(app [.] S#8);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=(app (dummy3 ) S#8);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#16=(app [.] S#8);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=(app [.] S#8);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#18         |->  [.],
           S#2          |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#16=(app (\ X#6.S#9) S#8);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=(\ X#6.S#9)} in (letrec {X#16=(app (var X#1) S#8);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=(app (\ X#6.S#9) S#8);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=(letrec {X#6=S#8} in S#9);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#16= (app (\ X#6.S#9) T#18[(var X#1)])
          ;E#7
          ;EE#17[X#5,(var X#16)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#16= (letrec {X#6=T#18[S#2]} in S#9)
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#16=(app (\ X#6.S#9) T#18);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#16=(app (\ X#6.S#9) T#18);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=(app (\ X#6.S#9) T#18[(dummy3 )]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[S#2],(\ X#6.[.])),
             (T#18[S#2],(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#16=(app (\ X#6.S#9) T#18[[.]]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=(app (\ X#6.S#9) T#18);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (\ X#6.S#9) T#18),
           S#8          |->  T#18[S#2]}

and instantiated rules:

                                  (letrec {X#16=(app (\ X#6.S#9) T#18[S#2]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#16=(app (\ X#6.S#9) T#18[(var X#1)]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=(app (\ X#6.S#9) T#18[S#2]);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=(letrec {X#6=T#18[S#2]} in S#9);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#15[(app (\ X#6.S#9) S#8)]
     in
        (letrec {X#16=(var X#1);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
     )
    ,
     (letrec
        X#16= A#15[(letrec {X#6=S#8} in S#9)]
       ;E#7
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#16=[.];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             (A#15[(app (\ X#6.S#9) S#8)],(letrec {X#16=[.];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=(dummy3 );E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(app (\ X#6.S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),(letrec {X#16=[.];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=[.];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#15[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#7;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           S#2          |->  A#15[(app (\ X#6.S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#16=A#15[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=A#15[(app (\ X#6.S#9) S#8)]} in (letrec {X#16=(var X#1);E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#15[(app (\ X#6.S#9) S#8)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {X#16=A#15[(letrec {X#6=S#8} in S#9)];E#7;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
     in
        (var X#1)
     )
    ,
     (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(\ X#6.[.])),
             (S#8,(letrec {X#6=[.]} in S#9)),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lbeta3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    and constraints: (S#8,(\ X#6.[.])), (S#8,(letrec {X#6=[.]} in S#9))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(\ X#6.[.])),(S#8,(letrec {X#6=[.]} in S#9)),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  [.],
           S#2  |->  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])}

and instantiated rules:

                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=(letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])} in (var X#1))
    ................................................................................
                                  (letrec {E#7;EE#11[X#5,(app (\ X#6.S#9) S#8)]} in A#10[(var X#5)])
    -SR,lbeta3->                  (letrec {E#7;EE#11[X#5,(letrec {X#6=S#8} in S#9)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(letrec {X#1=(var X#5)} in (var X#1))])
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(\ X#6.S#8)])
  )

where

   Delta1 = {A#9,T#10,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#5),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[[.]]),
           A#9   |->  A#11,
           T#10  |->  A#11[[.]],
           T#12  |->  [.],
           T#4   |->  [.],
           S#2   |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(var X#5)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(letrec {X#1=(var X#5)} in (var X#1))])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#8)
       ;E#7
     in
        A#11[(letrec {X#1=(var X#5)} in A#13[(var X#1)])]
     )
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#13[(\ X#6.S#8)]])
  )

where

   Delta1 = {A#12,T#4,A#9,T#10,T#3,A#11,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),A#13[[.]]),
             ((var X#5),A#13[[.]]),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#13[[.]]),
             ((var X#5),A#11[A#13[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#8);E#7} in A#11),
           A#9   |->  A#11[A#13],
           T#10  |->  A#11,
           A#12  |->  A#13,
           T#4   |->  A#13[[.]],
           T#14  |->  [.],
           S#2   |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#13[(var X#5)]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(letrec {X#1=(var X#5)} in A#13[(var X#1)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#13[(var X#5)]])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#13[(\ X#6.S#8)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#8)
       ;E#7
     in
        A#11[(letrec {X#1=A#14[(var X#5)]} in A#13[(var X#1)])]
     )
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#13[A#14[(\ X#6.S#8)]]])
  )

where

   Delta1 = {A#12,T#4,A#9,T#10,T#3,A#11,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),A#13),
             (A#14[(var X#5)],A#13),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#13[[.]]),
             ((var X#5),A#11[A#13[A#14[[.]]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#8);E#7} in A#11),
           A#9   |->  A#11[A#13[A#14]],
           T#10  |->  A#11,
           A#12  |->  A#13[A#14],
           T#4   |->  A#13,
           S#2   |->  A#14[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#13[A#14[(var X#5)]]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(letrec {X#1=A#14[(var X#5)]} in A#13[(var X#1)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#13[A#14[(var X#5)]]])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#13[A#14[(\ X#6.S#8)]]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#8)
       ;E#7
     in
        A#11[(letrec {X#1=S#2} in A#13[(app A#14[(var X#5)] T#15[(var X#1)])])]
     )
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#13[(app A#14[(\ X#6.S#8)] T#15[S#2])]])
  )

where

   Delta1 = {A#12,T#4,A#9,T#10,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),A#13[(app A#14[(var X#5)] T#15)]),
             (S#2,A#13[(app A#14[(var X#5)] T#15)]),
             (A#13[(app A#14[(var X#5)] T#15[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#13[(app A#14[(var X#5)] T#15[[.]])]),
             ((var X#5),A#11[A#13[(app A#14[[.]] T#15[S#2])]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#8);E#7} in A#11),
           A#9   |->  A#11[A#13[(app A#14 T#15[S#2])]],
           T#10  |->  A#11,
           T#4   |->  A#13[(app A#14[(var X#5)] T#15)],
           A#12  |->  A#13[(app A#14 T#15[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#13[(app A#14[(var X#5)] T#15[S#2])]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(letrec {X#1=S#2} in A#13[(app A#14[(var X#5)] T#15[(var X#1)])])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#13[(app A#14[(var X#5)] T#15[S#2])]])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#13[(app A#14[(\ X#6.S#8)] T#15[S#2])]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#8)
       ;E#7
     in
        A#11[(letrec {X#1=A#12[(var X#5)]} in (var X#1))]
     )
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#12[(\ X#6.S#8)]])
  )

where

   Delta1 = {A#9,T#10,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#12[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#11[A#12[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#8);E#7} in A#11),
           A#9   |->  A#11[A#12],
           T#10  |->  A#11,
           T#4   |->  [.],
           S#2   |->  A#12[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#12[(var X#5)]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(letrec {X#1=A#12[(var X#5)]} in (var X#1))])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#12[(var X#5)]])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#12[(\ X#6.S#8)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#8)
       ;E#7
     in
        A#11[(app A#12[(var X#5)] T#13[(letrec {X#1=S#2} in T#4[(var X#1)])])]
     )
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(\ X#6.S#8)] T#13[T#4[S#2]])])
  )

where

   Delta1 = {A#9,T#10,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#11[(app A#12[[.]] T#13[T#4[S#2]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)]),
           T#10  |->  A#11[(app A#12[(var X#5)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[T#4[S#2]])])
    -ucp3->                       (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {X#1=S#2} in T#4[(var X#1)])])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[T#4[S#2]])])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(\ X#6.S#8)] T#13[T#4[S#2]])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(\ X#6.S#8);E#7} in (letrec {X#1=(var X#5)} in A#11[(var X#1)]))
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(\ X#6.S#8)])
  )

where

   Delta1 = {A#9,T#4,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),A#11[[.]]),
             ((var X#5),A#11[[.]]),
             (A#11[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#11[[.]]),
             ((var X#5),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#8);E#7} in [.]),
           T#10  |->  [.],
           A#9   |->  A#11,
           T#4   |->  A#11[[.]],
           T#12  |->  [.],
           S#2   |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(var X#5)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#8);E#7} in (letrec {X#1=(var X#5)} in A#11[(var X#1)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#8)
       ;E#7
     in
        (letrec {X#1=A#12[(var X#5)]} in A#11[(var X#1)])
     )
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#12[(\ X#6.S#8)]])
  )

where

   Delta1 = {A#9,T#4,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),A#11),
             (A#12[(var X#5)],A#11),
             (A#11[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#11[[.]]),
             ((var X#5),A#11[A#12[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#8);E#7} in [.]),
           T#10  |->  [.],
           A#9   |->  A#11[A#12],
           T#4   |->  A#11,
           S#2   |->  A#12[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#12[(var X#5)]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#8);E#7} in (letrec {X#1=A#12[(var X#5)]} in A#11[(var X#1)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#12[(var X#5)]])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[A#12[(\ X#6.S#8)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#8)
       ;E#7
     in
        (letrec {X#1=S#2} in A#11[(app A#12[(var X#5)] T#13[(var X#1)])])
     )
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(\ X#6.S#8)] T#13[S#2])])
  )

where

   Delta1 = {A#9,T#4,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),A#11[(app A#12[(var X#5)] T#13)]),
             (S#2,A#11[(app A#12[(var X#5)] T#13)]),
             (A#11[(app A#12[(var X#5)] T#13[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#11[(app A#12[(var X#5)] T#13[[.]])]),
             ((var X#5),A#11[(app A#12[[.]] T#13[S#2])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#8);E#7} in [.]),
           T#10  |->  [.],
           T#4   |->  A#11[(app A#12[(var X#5)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[S#2])])
    -ucp3->                       (letrec {X#5=(\ X#6.S#8);E#7} in (letrec {X#1=S#2} in A#11[(app A#12[(var X#5)] T#13[(var X#1)])]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[S#2])])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(\ X#6.S#8)] T#13[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(\ X#6.S#8);E#7} in (letrec {X#1=A#9[(var X#5)]} in (var X#1)))
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#9[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#8);E#7} in [.]),
           T#10  |->  [.],
           T#4   |->  [.],
           S#2   |->  A#9[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#8);E#7} in (letrec {X#1=A#9[(var X#5)]} in (var X#1)))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#5=(letrec {X#1=(\ X#6.S#8)} in (var X#1));E#7} in A#9[(var X#5)])
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((\ X#6.S#8),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=[.];E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  [.],
           T#4   |->  [.],
           S#2   |->  (\ X#6.S#8)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=(\ X#6.S#8)} in (var X#1));E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(letrec {X#1=S#2} in T#4[(var X#1)])]
       ;X#5= (\ X#6.S#8)
       ;E#13
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#11=T#10[T#4[S#2]];X#5=(\ X#6.S#8);E#13} in A#9[(\ X#6.S#8)])
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#11=T#10;X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)]),
           E#7   |->  {X#11=T#10[T#4[S#2]];E#13},
           E#12  |->  {X#5=(\ X#6.S#8);E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[T#4[S#2]];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#11=T#10[(letrec {X#1=S#2} in T#4[(var X#1)])];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#11=T#10[T#4[S#2]];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#11=T#10[T#4[S#2]];X#5=(\ X#6.S#8);E#13} in A#9[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(var X#1)])])
     )
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(\ X#6.S#8)] T#13[S#2])])
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)])),
             (S#2,(letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)])),
             ((letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[[.]])])),
             ((var X#5),A#11[(app A#12[[.]] T#13[S#2])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)]),
           T#10  |->  A#11[(app A#12[(var X#5)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[S#2])])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(var X#1)])]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[S#2])])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#11[(app A#12[(\ X#6.S#8)] T#13[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(\ X#6.S#8)} in (letrec {X#5=(var X#1);E#7} in A#9[(var X#5)]))
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=[.];E#7} in A#9[(var X#5)])),
             ((\ X#6.S#8),(letrec {X#5=[.];E#7} in A#9[(var X#5)])),
             ((letrec {X#5=(dummy3 );E#7} in A#9[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=[.];E#7} in A#9[(var X#5)])),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=[.];E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  [.],
           S#2   |->  (\ X#6.S#8)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#1=(\ X#6.S#8)} in (letrec {X#5=(var X#1);E#7} in A#9[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {X#11=T#10[(var X#1)];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
     )
    ,
     (letrec {X#11=T#10[S#2];X#5=(\ X#6.S#8);E#13} in A#9[(\ X#6.S#8)])
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#11=T#10;X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])),
             (S#2,(letrec {X#11=T#10;X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])),
             ((letrec {X#11=T#10[(dummy3 )];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#11=T#10[[.]];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#11=T#10;X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)]),
           E#7   |->  {X#11=T#10[S#2];E#13},
           E#12  |->  {X#5=(\ X#6.S#8);E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[S#2];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#11=T#10[(var X#1)];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)]))
    ................................................................................
                                  (letrec {X#11=T#10[S#2];X#5=(\ X#6.S#8);E#13} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#11=T#10[S#2];X#5=(\ X#6.S#8);E#13} in A#9[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])} in (var X#1))
    ,
     (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)]),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  [.],
           S#2  |->  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#1=(letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])} in (var X#1))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(var X#5)])
    -SR,cp-in1->                  (letrec {X#5=(\ X#6.S#8);E#7} in A#9[(\ X#6.S#8)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(letrec {X#1=(var X#7)} in (var X#1))]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(\ X#6.S#9)])
  )

where

   Delta1 = {A#10,T#12,T#3,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#7),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#7),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#13[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[[.]]),
           A#10  |->  A#13,
           T#12  |->  A#13[[.]],
           T#14  |->  [.],
           T#4   |->  [.],
           S#2   |->  (var X#7)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(letrec {X#1=(var X#7)} in (var X#1))])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(letrec {X#1=(var X#7)} in A#15[(var X#1)])]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#15[(\ X#6.S#9)]])
  )

where

   Delta1 = {A#14,T#4,A#10,T#12,T#3,A#13,A#15}
   Delta2 = {}
   Delta3 = {((var X#1),A#15[[.]]),
             ((var X#7),A#15[[.]]),
             (A#15[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#7),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#15[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#13[A#15[[.]]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13),
           A#10  |->  A#13[A#15],
           T#12  |->  A#13,
           A#14  |->  A#15,
           T#4   |->  A#15[[.]],
           T#16  |->  [.],
           S#2   |->  (var X#7)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#15[(var X#7)]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(letrec {X#1=(var X#7)} in A#15[(var X#1)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#15[(var X#7)]])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#15[(\ X#6.S#9)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(letrec {X#1=A#16[(var X#7)]} in A#15[(var X#1)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[A#15[A#16[(\ X#6.S#9)]]]
     )
  )

where

   Delta1 = {A#14,T#4,A#10,T#12,T#3,A#13,A#15}
   Delta2 = {}
   Delta3 = {((var X#1),A#15),
             (A#16[(var X#7)],A#15),
             (A#15[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#16[(var X#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#15[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#13[A#15[A#16[[.]]]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13),
           A#10  |->  A#13[A#15[A#16]],
           T#12  |->  A#13,
           A#14  |->  A#15[A#16],
           T#4   |->  A#15,
           S#2   |->  A#16[(var X#7)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#15[A#16[(var X#7)]]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(letrec {X#1=A#16[(var X#7)]} in A#15[(var X#1)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#15[A#16[(var X#7)]]])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#15[A#16[(\ X#6.S#9)]]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(letrec {X#1=S#2} in A#15[(app A#16[(var X#7)] T#17[(var X#1)])])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[A#15[(app A#16[(\ X#6.S#9)] T#17[S#2])]]
     )
  )

where

   Delta1 = {A#14,T#4,A#10,T#12,T#3,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),A#15[(app A#16[(var X#7)] T#17)]),
             (S#2,A#15[(app A#16[(var X#7)] T#17)]),
             (A#15[(app A#16[(var X#7)] T#17[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#15[(app A#16[(var X#7)] T#17[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#13[A#15[(app A#16[[.]] T#17[S#2])]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13),
           A#10  |->  A#13[A#15[(app A#16 T#17[S#2])]],
           T#12  |->  A#13,
           T#4   |->  A#15[(app A#16[(var X#7)] T#17)],
           A#14  |->  A#15[(app A#16 T#17[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#15[(app A#16[(var X#7)] T#17[S#2])]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(letrec {X#1=S#2} in A#15[(app A#16[(var X#7)] T#17[(var X#1)])])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#15[(app A#16[(var X#7)] T#17[S#2])]])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#15[(app A#16[(\ X#6.S#9)] T#17[S#2])]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(letrec {X#1=A#14[(var X#7)]} in (var X#1))]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#14[(\ X#6.S#9)]])
  )

where

   Delta1 = {A#10,T#12,T#3,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#14[(var X#7)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(var X#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#13[A#14[[.]]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13),
           A#10  |->  A#13[A#14],
           T#12  |->  A#13,
           T#4   |->  [.],
           S#2   |->  A#14[(var X#7)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#14[(var X#7)]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(letrec {X#1=A#14[(var X#7)]} in (var X#1))])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#14[(var X#7)]])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#14[(\ X#6.S#9)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=S#2} in T#4[(var X#1)])])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(app A#14[(\ X#6.S#9)] T#15[T#4[S#2]])]
     )
  )

where

   Delta1 = {A#10,T#12,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#13[(app A#14[[.]] T#15[T#4[S#2]])]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#7)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[T#4[S#2]])])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[(letrec {X#1=S#2} in T#4[(var X#1)])])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[T#4[S#2]])])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(\ X#6.S#9)] T#15[T#4[S#2]])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        (letrec {X#1=(var X#7)} in A#13[(var X#1)])
     )
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(\ X#6.S#9)])
  )

where

   Delta1 = {A#10,T#4,T#3,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),A#13[[.]]),
             ((var X#7),A#13[[.]]),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#7),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#13[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#13[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in [.]),
           T#12  |->  [.],
           A#10  |->  A#13,
           T#4   |->  A#13[[.]],
           T#14  |->  [.],
           S#2   |->  (var X#7)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in (letrec {X#1=(var X#7)} in A#13[(var X#1)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        (letrec {X#1=A#14[(var X#7)]} in A#13[(var X#1)])
     )
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#14[(\ X#6.S#9)]])
  )

where

   Delta1 = {A#10,T#4,T#3,A#13}
   Delta2 = {}
   Delta3 = {((var X#1),A#13),
             (A#14[(var X#7)],A#13),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(var X#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#13[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#13[A#14[[.]]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in [.]),
           T#12  |->  [.],
           A#10  |->  A#13[A#14],
           T#4   |->  A#13,
           S#2   |->  A#14[(var X#7)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#14[(var X#7)]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in (letrec {X#1=A#14[(var X#7)]} in A#13[(var X#1)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#14[(var X#7)]])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[A#14[(\ X#6.S#9)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        (letrec {X#1=S#2} in A#13[(app A#14[(var X#7)] T#15[(var X#1)])])
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(app A#14[(\ X#6.S#9)] T#15[S#2])]
     )
  )

where

   Delta1 = {A#10,T#4,T#3}
   Delta2 = {}
   Delta3 = {((var X#1),A#13[(app A#14[(var X#7)] T#15)]),
             (S#2,A#13[(app A#14[(var X#7)] T#15)]),
             (A#13[(app A#14[(var X#7)] T#15[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#13[(app A#14[(var X#7)] T#15[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#13[(app A#14[[.]] T#15[S#2])]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in [.]),
           T#12  |->  [.],
           T#4   |->  A#13[(app A#14[(var X#7)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[S#2])])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in (letrec {X#1=S#2} in A#13[(app A#14[(var X#7)] T#15[(var X#1)])]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[S#2])])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(\ X#6.S#9)] T#15[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        (letrec {X#1=A#10[(var X#7)]} in (var X#1))
     )
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#10[(var X#7)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in [.]),
           T#12  |->  [.],
           T#4   |->  [.],
           S#2   |->  A#10[(var X#7)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in (letrec {X#1=A#10[(var X#7)]} in (var X#1)))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=(\ X#6.S#9)} in (var X#1))
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#10[(var X#7)]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((\ X#6.S#9),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=[.];E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;VV#11|X#7,(var X#5)|},
           T#12  |->  [.],
           T#4   |->  [.],
           S#2   |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=(\ X#6.S#9)} in (var X#1));E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=S#2} in T#4[(var X#1)])]
       ;X#5= (\ X#6.S#9)
       ;E#15
       ;VV#11|X#7,(var X#5)|
     in
        A#10[(var X#7)]
     )
    ,
     (letrec
        X#13= T#12[T#4[S#2]]
       ;X#5= (\ X#6.S#9)
       ;E#15
       ;VV#11|X#7,(var X#5)|
     in
        A#10[(\ X#6.S#9)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3   |->  (letrec {X#13=T#12;X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)]),
           E#8   |->  {X#13=T#12[T#4[S#2]];E#15},
           E#14  |->  {X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|}}

and instantiated rules:

                                  (letrec {X#13=T#12[T#4[S#2]];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -ucp3->                       (letrec {X#13=T#12[(letrec {X#1=S#2} in T#4[(var X#1)])];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    ................................................................................
                                  (letrec {X#13=T#12[T#4[S#2]];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#13=T#12[T#4[S#2]];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=(var X#5)} in (var X#1))
       ;E#8
     in
        A#10[(var X#7)]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);X#7=(var X#5);E#8} in A#10[(\ X#6.S#9)])
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#5),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8} in A#10[(var X#7)]),
           VV#11|.1,.2| |-> {[.1]=[.2]},
           X#13         |->  X#7,
           E#14         |->  {X#5=(\ X#6.S#9);E#8},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=(var X#5);E#8} in A#10[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=(var X#5)} in (var X#1));E#8} in A#10[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=(var X#5);E#8} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);X#7=(var X#5);E#8} in A#10[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=(var X#16)} in (var X#1))
       ;E#8
       ;VV#17|X#16,(var X#5)|
     in
        A#10[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (var X#16)
       ;E#8
       ;VV#17|X#16,(var X#5)|
     in
        A#10[(\ X#6.S#9)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#16),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#16),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8;VV#17|X#16,(var X#5)|} in A#10[(var X#7)]),
           VV#11|.1,.2| |-> {[.1]=(var X#16);VV#17|X#16,[.2]|},
           X#13         |->  X#7,
           E#14         |->  {X#5=(\ X#6.S#9);E#8;VV#17|X#16,(var X#5)|},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=(var X#16);E#8;VV#17|X#16,(var X#5)|} in A#10[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=(var X#16)} in (var X#1));E#8;VV#17|X#16,(var X#5)|} in A#10[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=(var X#16);E#8;VV#17|X#16,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);X#7=(var X#16);E#8;VV#17|X#16,(var X#5)|} in A#10[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=(var X#17)} in (var X#1))
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;VV#18|X#7,(var X#16)|
       ;VV#19|X#17,(var X#5)|
     in
        A#10[(var X#7)]
     )
    ,
     (letrec
        X#16= (var X#17)
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;VV#18|X#7,(var X#16)|
       ;VV#19|X#17,(var X#5)|
     in
        A#10[(\ X#6.S#9)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#17),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];X#5=(\ X#6.S#9);E#8;VV#18|X#7,(var X#16)|;VV#19|X#17,(var X#5)|} in A#10[(var X#7)]),
           VV#11|.1,.2| |-> {X#16=(var X#17);VV#18|[.1],(var X#16)|;VV#19|X#17,[.2]|},
           X#13         |->  X#16,
           E#14         |->  {X#5=(\ X#6.S#9);E#8;VV#18|X#7,(var X#16)|;VV#19|X#17,(var X#5)|},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#16=(var X#17);X#5=(\ X#6.S#9);E#8;VV#18|X#7,(var X#16)|;VV#19|X#17,(var X#5)|} in A#10[(var X#7)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=(var X#17)} in (var X#1));X#5=(\ X#6.S#9);E#8;VV#18|X#7,(var X#16)|;VV#19|X#17,(var X#5)|} in A#10[(var X#7)])
    ................................................................................
                                  (letrec {X#16=(var X#17);X#5=(\ X#6.S#9);E#8;VV#18|X#7,(var X#16)|;VV#19|X#17,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#16=(var X#17);X#5=(\ X#6.S#9);E#8;VV#18|X#7,(var X#16)|;VV#19|X#17,(var X#5)|} in A#10[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=(var X#5)} in (var X#1))
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;VV#17|X#7,(var X#16)|
     in
        A#10[(var X#7)]
     )
    ,
     (letrec
        X#16= (var X#5)
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;VV#17|X#7,(var X#16)|
     in
        A#10[(\ X#6.S#9)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#5),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];X#5=(\ X#6.S#9);E#8;VV#17|X#7,(var X#16)|} in A#10[(var X#7)]),
           VV#11|.1,.2| |-> {X#16=[.2];VV#17|[.1],(var X#16)|},
           X#13         |->  X#16,
           E#14         |->  {X#5=(\ X#6.S#9);E#8;VV#17|X#7,(var X#16)|},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#16=(var X#5);X#5=(\ X#6.S#9);E#8;VV#17|X#7,(var X#16)|} in A#10[(var X#7)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=(var X#5)} in (var X#1));X#5=(\ X#6.S#9);E#8;VV#17|X#7,(var X#16)|} in A#10[(var X#7)])
    ................................................................................
                                  (letrec {X#16=(var X#5);X#5=(\ X#6.S#9);E#8;VV#17|X#7,(var X#16)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#16=(var X#5);X#5=(\ X#6.S#9);E#8;VV#17|X#7,(var X#16)|} in A#10[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (\ X#6.S#9)
          ;E#8
          ;VV#11|X#7,(var X#5)|
        in
           A#13[(app A#14[(var X#7)] T#15[(var X#1)])]
        )
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;VV#11|X#7,(var X#5)|
     in
        A#13[(app A#14[(\ X#6.S#9)] T#15[S#2])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15)])),
             (S#2,(letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15)])),
             ((letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[[.]])])),
             ((var X#5),[.]),
             ((var X#7),A#13[(app A#14[[.]] T#15[S#2])]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#7)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[S#2])])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[(var X#1)])]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(var X#7)] T#15[S#2])])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#13[(app A#14[(\ X#6.S#9)] T#15[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#6.S#9)
     in
        (letrec {X#5=(var X#1);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
     )
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=[.];E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])),
             ((\ X#6.S#9),(letrec {X#5=[.];E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])),
             ((letrec {X#5=(dummy3 );E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=[.];E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])),
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=[.];E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;VV#11|X#7,(var X#5)|},
           T#12  |->  [.],
           S#2   |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -ucp3->                       (letrec {X#1=(\ X#6.S#9)} in (letrec {X#5=(var X#1);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#13= T#12[(var X#1)]
          ;X#5= (\ X#6.S#9)
          ;E#15
          ;VV#11|X#7,(var X#5)|
        in
           A#10[(var X#7)]
        )
     )
    ,
     (letrec
        X#13= T#12[S#2]
       ;X#5= (\ X#6.S#9)
       ;E#15
       ;VV#11|X#7,(var X#5)|
     in
        A#10[(\ X#6.S#9)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#13=T#12;X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])),
             (S#2,(letrec {X#13=T#12;X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])),
             ((letrec {X#13=T#12[(dummy3 )];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#13=T#12[[.]];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])),
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#13=T#12;X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)]),
           E#8   |->  {X#13=T#12[S#2];E#15},
           E#14  |->  {X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|}}

and instantiated rules:

                                  (letrec {X#13=T#12[S#2];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#13=T#12[(var X#1)];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)]))
    ................................................................................
                                  (letrec {X#13=T#12[S#2];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#13=T#12[S#2];X#5=(\ X#6.S#9);E#15;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
     in
        (var X#1)
     )
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
  )

where

   Delta1 = {}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)]),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#10[[.]]),
             ((var X#5),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-in2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    and constraints: 

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}
      Delta1=  {}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#10[[.]]),((var X#5),[.])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  [.],
           S#2  |->  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -ucp3->                       (letrec {X#1=(letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])} in (var X#1))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(var X#7)])
    -SR,cp-in2->                  (letrec {X#5=(\ X#6.S#9);E#8;VV#11|X#7,(var X#5)|} in A#10[(\ X#6.S#9)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#14[(letrec {X#1=(var X#7)} in (var X#1))]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[(var X#7)])
  )

where

   Delta1 = {A#11,T#13,T#3,A#10,A#14}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#7),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#7),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#14[[.]]),
             ((var X#7),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[[.]]),
           A#11  |->  A#14,
           T#13  |->  A#14[[.]],
           T#15  |->  [.],
           T#4   |->  [.],
           S#2   |->  (var X#7)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(letrec {X#1=(var X#7)} in (var X#1))])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#14[(letrec {X#1=(var X#7)} in A#16[(var X#1)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#14[A#16[(var X#7)]]
     )
  )

where

   Delta1 = {A#15,T#4,A#11,T#13,T#3,A#10,A#14,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),A#16[[.]]),
             ((var X#7),A#16[[.]]),
             (A#16[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#7),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#16[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#14[A#16[[.]]]),
             ((var X#7),A#14[A#16[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14),
           A#11  |->  A#14[A#16],
           T#13  |->  A#14,
           A#15  |->  A#16,
           T#4   |->  A#16[[.]],
           T#17  |->  [.],
           S#2   |->  (var X#7)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[A#16[(var X#7)]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(letrec {X#1=(var X#7)} in A#16[(var X#1)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[A#16[(var X#7)]])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[A#16[(var X#7)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#14[(letrec {X#1=A#17[(var X#7)]} in A#16[(var X#1)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#14[A#16[A#17[(var X#7)]]]
     )
  )

where

   Delta1 = {A#15,T#4,A#11,T#13,T#3,A#10,A#14,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),A#16),
             (A#17[(var X#7)],A#16),
             (A#16[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#17[(var X#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#16[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#14[A#16[A#17[[.]]]]),
             ((var X#7),A#14[A#16[A#17[[.]]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14),
           A#11  |->  A#14[A#16[A#17]],
           T#13  |->  A#14,
           A#15  |->  A#16[A#17],
           T#4   |->  A#16,
           S#2   |->  A#17[(var X#7)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[A#16[A#17[(var X#7)]]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(letrec {X#1=A#17[(var X#7)]} in A#16[(var X#1)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[A#16[A#17[(var X#7)]]])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[A#16[A#17[(var X#7)]]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#14[(letrec {X#1=S#2} in A#16[(app A#17[(var X#7)] T#18[(var X#1)])])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#14[A#16[(app A#17[(var X#7)] T#18[S#2])]]
     )
  )

where

   Delta1 = {A#15,T#4,A#11,T#13,T#3,A#10,A#14}
   Delta2 = {}
   Delta3 = {((var X#1),A#16[(app A#17[(var X#7)] T#18)]),
             (S#2,A#16[(app A#17[(var X#7)] T#18)]),
             (A#16[(app A#17[(var X#7)] T#18[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#16[(app A#17[(var X#7)] T#18[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#14[A#16[(app A#17[[.]] T#18[S#2])]]),
             ((var X#7),A#14[A#16[(app A#17[[.]] T#18[S#2])]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14),
           A#11  |->  A#14[A#16[(app A#17 T#18[S#2])]],
           T#13  |->  A#14,
           T#4   |->  A#16[(app A#17[(var X#7)] T#18)],
           A#15  |->  A#16[(app A#17 T#18[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[A#16[(app A#17[(var X#7)] T#18[S#2])]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(letrec {X#1=S#2} in A#16[(app A#17[(var X#7)] T#18[(var X#1)])])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[A#16[(app A#17[(var X#7)] T#18[S#2])]])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[A#16[(app A#17[(var X#7)] T#18[S#2])]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#14[(letrec {X#1=A#15[(var X#7)]} in (var X#1))]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#14[A#15[(var X#7)]]
     )
  )

where

   Delta1 = {A#11,T#13,T#3,A#10,A#14}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#15[(var X#7)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(var X#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#14[A#15[[.]]]),
             ((var X#7),A#14[A#15[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14),
           A#11  |->  A#14[A#15],
           T#13  |->  A#14,
           T#4   |->  [.],
           S#2   |->  A#15[(var X#7)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[A#15[(var X#7)]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(letrec {X#1=A#15[(var X#7)]} in (var X#1))])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[A#15[(var X#7)]])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[A#15[(var X#7)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#14[(app A#15[(var X#7)] T#16[(letrec {X#1=S#2} in T#4[(var X#1)])])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#14[(app A#15[(var X#7)] T#16[T#4[S#2]])]
     )
  )

where

   Delta1 = {A#11,T#13,T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#14[(app A#15[[.]] T#16[T#4[S#2]])]),
             ((var X#7),A#14[(app A#15[[.]] T#16[T#4[S#2]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#7)] T#16)],
           A#11  |->  A#14[(app A#15 T#16[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[T#4[S#2]])])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[(letrec {X#1=S#2} in T#4[(var X#1)])])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[T#4[S#2]])])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[(app A#15[(var X#7)] T#16[T#4[S#2]])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        (letrec {X#1=(var X#7)} in A#14[(var X#1)])
     )
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[(var X#7)])
  )

where

   Delta1 = {A#11,T#4,T#3,A#10,A#14}
   Delta2 = {}
   Delta3 = {((var X#1),A#14[[.]]),
             ((var X#7),A#14[[.]]),
             (A#14[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#7),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#14[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#14[[.]]),
             ((var X#7),A#14[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in [.]),
           T#13  |->  [.],
           A#11  |->  A#14,
           T#4   |->  A#14[[.]],
           T#15  |->  [.],
           S#2   |->  (var X#7)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in (letrec {X#1=(var X#7)} in A#14[(var X#1)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        (letrec {X#1=A#15[(var X#7)]} in A#14[(var X#1)])
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#14[A#15[(var X#7)]]
     )
  )

where

   Delta1 = {A#11,T#4,T#3,A#10,A#14}
   Delta2 = {}
   Delta3 = {((var X#1),A#14),
             (A#15[(var X#7)],A#14),
             (A#14[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(var X#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#14[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#14[A#15[[.]]]),
             ((var X#7),A#14[A#15[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in [.]),
           T#13  |->  [.],
           A#11  |->  A#14[A#15],
           T#4   |->  A#14,
           S#2   |->  A#15[(var X#7)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[A#15[(var X#7)]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in (letrec {X#1=A#15[(var X#7)]} in A#14[(var X#1)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[A#15[(var X#7)]])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[A#15[(var X#7)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        (letrec {X#1=S#2} in A#14[(app A#15[(var X#7)] T#16[(var X#1)])])
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#14[(app A#15[(var X#7)] T#16[S#2])]
     )
  )

where

   Delta1 = {A#11,T#4,T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),A#14[(app A#15[(var X#7)] T#16)]),
             (S#2,A#14[(app A#15[(var X#7)] T#16)]),
             (A#14[(app A#15[(var X#7)] T#16[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#14[(app A#15[(var X#7)] T#16[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#14[(app A#15[[.]] T#16[S#2])]),
             ((var X#7),A#14[(app A#15[[.]] T#16[S#2])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in [.]),
           T#13  |->  [.],
           T#4   |->  A#14[(app A#15[(var X#7)] T#16)],
           A#11  |->  A#14[(app A#15 T#16[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[S#2])])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in (letrec {X#1=S#2} in A#14[(app A#15[(var X#7)] T#16[(var X#1)])]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[S#2])])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[(app A#15[(var X#7)] T#16[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        (letrec {X#1=A#11[(var X#7)]} in (var X#1))
     )
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#11[(var X#7)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(var X#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in [.]),
           T#13  |->  [.],
           T#4   |->  [.],
           S#2   |->  A#11[(var X#7)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in (letrec {X#1=A#11[(var X#7)]} in (var X#1)))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=(\ X#6.S#9)} in (var X#1))
       ;E#8
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((\ X#6.S#9),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=[.];E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)]),
           X#14  |->  X#5,
           E#15  |->  {E#8;EE#12[X#7,A#10[(var X#5)]]},
           T#13  |->  [.],
           T#4   |->  [.],
           S#2   |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=(\ X#6.S#9)} in (var X#1));E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#14= T#13[(letrec {X#1=S#2} in T#4[(var X#1)])]
       ;X#5= (\ X#6.S#9)
       ;E#16
       ;EE#12[X#7,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#14= T#13[T#4[S#2]]
       ;X#5= (\ X#6.S#9)
       ;E#16
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#14=T#13;X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)]),
           E#8   |->  {X#14=T#13[T#4[S#2]];E#16},
           E#15  |->  {X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]}}

and instantiated rules:

                                  (letrec {X#14=T#13[T#4[S#2]];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#14=T#13[(letrec {X#1=S#2} in T#4[(var X#1)])];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#14=T#13[T#4[S#2]];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#14=T#13[T#4[S#2]];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(letrec {X#1=(var X#5)} in (var X#1))]]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {T#18,A#16,T#13,T#3,A#10,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#5),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#19[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[[.]]];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[A#19[[.]]],
           A#10         |->  A#19,
           T#18         |->  A#19[[.]],
           T#20         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(var X#5)]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(letrec {X#1=(var X#5)} in (var X#1))]];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(var X#5)]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(letrec {X#1=(var X#5)} in A#21[(var X#1)])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[A#21[(\ X#6.S#9)]]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,T#18,A#16,T#13,T#3,A#10,A#17,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[[.]]),
             ((var X#5),A#21[[.]]),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),A#19[A#21[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[A#19],
           A#10         |->  A#19[A#21],
           T#18         |->  A#19,
           A#20         |->  A#21,
           T#4          |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[(var X#5)]]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(letrec {X#1=(var X#5)} in A#21[(var X#1)])]];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[(var X#5)]]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[(\ X#6.S#9)]]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(letrec {X#1=A#22[(var X#5)]} in A#21[(var X#1)])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[A#21[A#22[(\ X#6.S#9)]]]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,T#18,A#16,T#13,T#3,A#10,A#17,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21),
             (A#22[(var X#5)],A#21),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),A#19[A#21[A#22[[.]]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[A#19],
           A#10         |->  A#19[A#21[A#22]],
           T#18         |->  A#19,
           A#20         |->  A#21[A#22],
           T#4          |->  A#21,
           S#2          |->  A#22[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[A#22[(var X#5)]]]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(letrec {X#1=A#22[(var X#5)]} in A#21[(var X#1)])]];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[A#22[(var X#5)]]]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[A#22[(\ X#6.S#9)]]]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#5)] T#23[(var X#1)])])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[S#2])]]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,T#18,A#16,T#13,T#3,A#10,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[(app A#22[(var X#5)] T#23)]),
             (S#2,A#21[(app A#22[(var X#5)] T#23)]),
             (A#21[(app A#22[(var X#5)] T#23[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[(app A#22[(var X#5)] T#23[[.]])]),
             ((var X#5),A#19[A#21[(app A#22[[.]] T#23[S#2])]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[A#19],
           A#10         |->  A#19[A#21[(app A#22 T#23[S#2])]],
           T#18         |->  A#19,
           T#4          |->  A#21[(app A#22[(var X#5)] T#23)],
           A#20         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[(app A#22[(var X#5)] T#23[S#2])]]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#5)] T#23[(var X#1)])])]];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[(app A#22[(var X#5)] T#23[S#2])]]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[S#2])]]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(letrec {X#1=A#20[(var X#5)]} in (var X#1))]]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[A#20[(\ X#6.S#9)]]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#18,A#16,T#13,T#3,A#10,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#20[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#20[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#19[A#20[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[A#19],
           A#10         |->  A#19[A#20],
           T#18         |->  A#19,
           T#4          |->  [.],
           S#2          |->  A#20[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[(var X#5)]]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(letrec {X#1=A#20[(var X#5)]} in (var X#1))]];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[(var X#5)]]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[(\ X#6.S#9)]]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[(var X#5)] T#21[(letrec {X#1=S#2} in T#4[(var X#1)])])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[T#4[S#2]])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#18,A#16,T#13,T#3,A#10,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#19[(app A#20[[.]] T#21[T#4[S#2]])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21)]];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[A#19[(app A#20[(var X#5)] T#21)]],
           T#18         |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[T#4[S#2]])]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[(letrec {X#1=S#2} in T#4[(var X#1)])])]];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[T#4[S#2]])]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[T#4[S#2]])]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=(var X#5)} in A#19[(var X#1)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {T#4,A#16,T#13,T#3,A#10,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[[.]]),
             ((var X#5),A#19[[.]]),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),A#19[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[[.]];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[[.]],
           T#18         |->  [.],
           A#10         |->  A#19,
           T#4          |->  A#19[[.]],
           T#20         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(var X#5)]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=(var X#5)} in A#19[(var X#1)])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(var X#5)]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=A#20[(var X#5)]} in A#19[(var X#1)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[A#20[(\ X#6.S#9)]]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#16,T#13,T#3,A#10,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19),
             (A#20[(var X#5)],A#19),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#20[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),A#19[A#20[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[[.]];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[[.]],
           T#18         |->  [.],
           A#10         |->  A#19[A#20],
           T#4          |->  A#19,
           S#2          |->  A#20[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[(var X#5)]]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=A#20[(var X#5)]} in A#19[(var X#1)])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[(var X#5)]]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[(\ X#6.S#9)]]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=S#2} in A#19[(app A#20[(var X#5)] T#21[(var X#1)])])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[S#2])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#16,T#13,T#3,A#10,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[(app A#20[(var X#5)] T#21)]),
             (S#2,A#19[(app A#20[(var X#5)] T#21)]),
             (A#19[(app A#20[(var X#5)] T#21[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[(app A#20[(var X#5)] T#21[[.]])]),
             ((var X#5),A#19[(app A#20[[.]] T#21[S#2])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[[.]];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[[.]],
           T#18         |->  [.],
           T#4          |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[S#2])]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=S#2} in A#19[(app A#20[(var X#5)] T#21[(var X#1)])])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[S#2])]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[S#2])]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=A#10[(var X#5)]} in (var X#1))]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#10[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {A#16,T#13,T#3,A#10,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#10[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[[.]];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[[.]],
           T#18         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#10[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#10[(var X#5)]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=A#10[(var X#5)]} in (var X#1))];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#10[(var X#5)]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#10[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=(var X#5)} in A#19[A#21[(var X#1)]])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[A#21[(\ X#6.S#9)]]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#18,T#4,A#16,T#13,T#3,A#10,A#17,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[A#21[[.]]]),
             ((var X#5),A#19[A#21[[.]]]),
             (A#19[A#21[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[A#21[[.]]]),
             ((var X#5),A#21[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17;E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[A#19[[.2]]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17[A#19],
           T#13         |->  A#17,
           A#18         |->  A#19,
           T#4          |->  A#19[A#21[[.]]],
           A#10         |->  A#21,
           T#20         |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[(var X#5)]]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=(var X#5)} in A#19[A#21[(var X#1)]])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[(var X#5)]]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[(\ X#6.S#9)]]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=A#22[(var X#5)]} in A#19[A#21[(var X#1)]])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[A#21[A#22[(\ X#6.S#9)]]]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#18,T#4,A#16,T#13,T#3,A#10,A#17,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[A#21]),
             (A#22[(var X#5)],A#19[A#21]),
             (A#19[A#21[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[A#21[[.]]]),
             ((var X#5),A#21[A#22[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17;E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[A#19[[.2]]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17[A#19],
           T#13         |->  A#17,
           A#18         |->  A#19,
           T#4          |->  A#19[A#21],
           A#10         |->  A#21[A#22],
           T#20         |->  A#21,
           S#2          |->  A#22[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[A#22[(var X#5)]]]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=A#22[(var X#5)]} in A#19[A#21[(var X#1)]])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[A#22[(var X#5)]]]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[A#22[(\ X#6.S#9)]]]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=S#2} in A#19[A#21[(app A#22[(var X#5)] T#23[(var X#1)])]])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[S#2])]]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#18,T#4,A#16,T#13,T#3,A#10,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[A#21[(app A#22[(var X#5)] T#23)]]),
             (S#2,A#19[A#21[(app A#22[(var X#5)] T#23)]]),
             (A#19[A#21[(app A#22[(var X#5)] T#23[(dummy3 )])]],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[A#21[(app A#22[(var X#5)] T#23[[.]])]]),
             ((var X#5),A#21[(app A#22[[.]] T#23[S#2])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17;E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[A#19[[.2]]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17[A#19],
           T#13         |->  A#17,
           A#18         |->  A#19,
           T#4          |->  A#19[A#21[(app A#22[(var X#5)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#5)] T#23)],
           A#10         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[(app A#22[(var X#5)] T#23[S#2])]]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=S#2} in A#19[A#21[(app A#22[(var X#5)] T#23[(var X#1)])]])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[(app A#22[(var X#5)] T#23[S#2])]]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[S#2])]]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=A#10[(var X#5)]} in A#19[(var X#1)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[A#10[(\ X#6.S#9)]]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,A#16,T#13,T#3,A#10,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[[.]]),
             (A#10[(var X#5)],A#19[[.]]),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17;E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[A#19[[.2]]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17[A#19],
           T#13         |->  A#17,
           A#18         |->  A#19,
           T#4          |->  A#19[[.]],
           T#20         |->  [.],
           S#2          |->  A#10[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#10[(var X#5)]]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=A#10[(var X#5)]} in A#19[(var X#1)])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#10[(var X#5)]]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#10[(\ X#6.S#9)]]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=A#20[A#10[(var X#5)]]} in A#19[(var X#1)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[A#20[A#10[(\ X#6.S#9)]]]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,A#16,T#13,T#3,A#10,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19),
             (A#20[A#10[(var X#5)]],A#19),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#20[A#10[(var X#5)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17;E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[A#19[A#20[[.2]]]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17[A#19[A#20]],
           T#13         |->  A#17,
           A#18         |->  A#19[A#20],
           T#4          |->  A#19,
           S#2          |->  A#20[A#10[(var X#5)]]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[A#10[(var X#5)]]]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=A#20[A#10[(var X#5)]]} in A#19[(var X#1)])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[A#10[(var X#5)]]]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[A#10[(\ X#6.S#9)]]]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=S#2} in A#19[(app A#20[A#10[(var X#5)]] T#21[(var X#1)])])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[S#2])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,A#16,T#13,T#3,A#10,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[(app A#20[A#10[(var X#5)]] T#21)]),
             (S#2,A#19[(app A#20[A#10[(var X#5)]] T#21)]),
             (A#19[(app A#20[A#10[(var X#5)]] T#21[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[(app A#20[A#10[(var X#5)]] T#21[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17;E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[A#19[(app A#20[[.2]] T#21[S#2])]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17[A#19[(app A#20 T#21[S#2])]],
           T#13         |->  A#17,
           T#4          |->  A#19[(app A#20[A#10[(var X#5)]] T#21)],
           A#18         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[A#10[(var X#5)]] T#21[S#2])]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=S#2} in A#19[(app A#20[A#10[(var X#5)]] T#21[(var X#1)])])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[A#10[(var X#5)]] T#21[S#2])]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[S#2])]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=(var X#5)} in A#19[(var X#1)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {T#4,A#16,T#13,T#3,A#10,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[[.]]),
             ((var X#5),A#19[[.]]),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),A#19[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17;E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17[[.]],
           T#13         |->  A#17,
           A#18         |->  [.],
           A#10         |->  A#19,
           T#4          |->  A#19[[.]],
           T#20         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(var X#5)]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=(var X#5)} in A#19[(var X#1)])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(var X#5)]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=A#20[(var X#5)]} in A#19[(var X#1)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[A#20[(\ X#6.S#9)]]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#16,T#13,T#3,A#10,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19),
             (A#20[(var X#5)],A#19),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#20[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),A#19[A#20[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17;E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17[[.]],
           T#13         |->  A#17,
           A#18         |->  [.],
           A#10         |->  A#19[A#20],
           T#4          |->  A#19,
           S#2          |->  A#20[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[(var X#5)]]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=A#20[(var X#5)]} in A#19[(var X#1)])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[(var X#5)]]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[(\ X#6.S#9)]]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=S#2} in A#19[(app A#20[(var X#5)] T#21[(var X#1)])])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[S#2])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#16,T#13,T#3,A#10,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[(app A#20[(var X#5)] T#21)]),
             (S#2,A#19[(app A#20[(var X#5)] T#21)]),
             (A#19[(app A#20[(var X#5)] T#21[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[(app A#20[(var X#5)] T#21[[.]])]),
             ((var X#5),A#19[(app A#20[[.]] T#21[S#2])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17;E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17[[.]],
           T#13         |->  A#17,
           A#18         |->  [.],
           T#4          |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[S#2])]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=S#2} in A#19[(app A#20[(var X#5)] T#21[(var X#1)])])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[S#2])]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[S#2])]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=A#18[A#10[(var X#5)]]} in (var X#1))]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#18[A#10[(\ X#6.S#9)]]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#3,A#10,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#18[A#10[(var X#5)]],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#18[A#10[(var X#5)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17;E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[A#18[[.2]]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17[A#18],
           T#13         |->  A#17,
           T#4          |->  [.],
           S#2          |->  A#18[A#10[(var X#5)]]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#18[A#10[(var X#5)]]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=A#18[A#10[(var X#5)]]} in (var X#1))];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#18[A#10[(var X#5)]]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#18[A#10[(\ X#6.S#9)]]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[A#10[(var X#5)]] T#19[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[A#10[(\ X#6.S#9)]] T#19[T#4[S#2]])]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19)];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] T#19[T#4[S#2]])]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  A#17[(app A#18[A#10[(var X#5)]] T#19)],
           A#16         |->  A#17[(app A#18 T#19[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[T#4[S#2]])];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[T#4[S#2]])];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(\ X#6.S#9)]] T#19[T#4[S#2]])];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=(var X#5)} in (var X#1))]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);X#7=A#17[(\ X#6.S#9)];E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {T#13,T#3,A#10,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#5),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#17[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[[.]];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  [.],
           A#10         |->  A#17,
           T#13         |->  A#17[[.]],
           T#18         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(var X#5)];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=(var X#5)} in (var X#1))];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(var X#5)];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(\ X#6.S#9)];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=(var X#5)} in A#19[(var X#1)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {A#18,T#4,T#13,T#3,A#10,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[[.]]),
             ((var X#5),A#19[[.]]),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),A#17[A#19[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17;E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  [.],
           A#10         |->  A#17[A#19],
           T#13         |->  A#17,
           A#18         |->  A#19,
           T#4          |->  A#19[[.]],
           T#20         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(var X#5)]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=(var X#5)} in A#19[(var X#1)])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(var X#5)]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=A#20[(var X#5)]} in A#19[(var X#1)])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[A#20[(\ X#6.S#9)]]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,T#13,T#3,A#10,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19),
             (A#20[(var X#5)],A#19),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#20[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),A#17[A#19[A#20[[.]]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17;E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  [.],
           A#10         |->  A#17[A#19[A#20]],
           T#13         |->  A#17,
           A#18         |->  A#19[A#20],
           T#4          |->  A#19,
           S#2          |->  A#20[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[(var X#5)]]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=A#20[(var X#5)]} in A#19[(var X#1)])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[(var X#5)]]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[(\ X#6.S#9)]]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=S#2} in A#19[(app A#20[(var X#5)] T#21[(var X#1)])])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[S#2])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,T#13,T#3,A#10,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[(app A#20[(var X#5)] T#21)]),
             (S#2,A#19[(app A#20[(var X#5)] T#21)]),
             (A#19[(app A#20[(var X#5)] T#21[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[(app A#20[(var X#5)] T#21[[.]])]),
             ((var X#5),A#17[A#19[(app A#20[[.]] T#21[S#2])]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17;E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  [.],
           A#10         |->  A#17[A#19[(app A#20 T#21[S#2])]],
           T#13         |->  A#17,
           T#4          |->  A#19[(app A#20[(var X#5)] T#21)],
           A#18         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[S#2])]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=S#2} in A#19[(app A#20[(var X#5)] T#21[(var X#1)])])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[S#2])]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[S#2])]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(letrec {X#1=A#18[(var X#5)]} in (var X#1))]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#18[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {T#13,T#3,A#10,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#18[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#18[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#17[A#18[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17;E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  [.],
           A#10         |->  A#17[A#18],
           T#13         |->  A#17,
           T#4          |->  [.],
           S#2          |->  A#18[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#18[(var X#5)]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(letrec {X#1=A#18[(var X#5)]} in (var X#1))];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#18[(var X#5)]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#18[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[(var X#5)] T#19[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[(\ X#6.S#9)] T#19[T#4[S#2]])]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#17[(app A#18[[.]] T#19[T#4[S#2]])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19)];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  [.],
           T#13         |->  A#17[(app A#18[(var X#5)] T#19)],
           A#10         |->  A#17[(app A#18 T#19[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[T#4[S#2]])];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[T#4[S#2]])];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(\ X#6.S#9)] T#19[T#4[S#2]])];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=(var X#5)} in A#17[A#19[(var X#1)]])
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {T#18,A#16,T#4,T#3,A#10,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#17[A#19[[.]]]),
             ((var X#5),A#17[A#19[[.]]]),
             (A#17[A#19[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#17[A#19[[.]]]),
             ((var X#5),A#19[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  [.],
           A#16         |->  A#17,
           T#4          |->  A#17[A#19[[.]]],
           A#10         |->  A#19,
           T#18         |->  A#19[[.]],
           T#20         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(var X#5)]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=(var X#5)} in A#17[A#19[(var X#1)]]);E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(var X#5)]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=A#20[(var X#5)]} in A#17[A#19[(var X#1)]])
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[A#20[(\ X#6.S#9)]]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#18,A#16,T#4,T#3,A#10,A#17,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#17[A#19]),
             (A#20[(var X#5)],A#17[A#19]),
             (A#17[A#19[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             (A#20[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#17[A#19[[.]]]),
             ((var X#5),A#19[A#20[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  [.],
           A#16         |->  A#17,
           T#4          |->  A#17[A#19],
           A#10         |->  A#19[A#20],
           T#18         |->  A#19,
           S#2          |->  A#20[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[(var X#5)]]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=A#20[(var X#5)]} in A#17[A#19[(var X#1)]]);E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[(var X#5)]]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[A#20[(\ X#6.S#9)]]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=S#2} in A#17[A#19[(app A#20[(var X#5)] T#21[(var X#1)])]])
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[S#2])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#18,A#16,T#4,T#3,A#10,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),A#17[A#19[(app A#20[(var X#5)] T#21)]]),
             (S#2,A#17[A#19[(app A#20[(var X#5)] T#21)]]),
             (A#17[A#19[(app A#20[(var X#5)] T#21[(dummy3 )])]],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#17[A#19[(app A#20[(var X#5)] T#21[[.]])]]),
             ((var X#5),A#19[(app A#20[[.]] T#21[S#2])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  [.],
           A#16         |->  A#17,
           T#4          |->  A#17[A#19[(app A#20[(var X#5)] T#21)]],
           T#18         |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[S#2])]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=S#2} in A#17[A#19[(app A#20[(var X#5)] T#21[(var X#1)])]]);E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[S#2])]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[S#2])]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=A#10[(var X#5)]} in A#17[(var X#1)])
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#10[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {A#16,T#4,T#3,A#10,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),A#17[[.]]),
             (A#10[(var X#5)],A#17[[.]]),
             (A#17[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#17[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  [.],
           A#16         |->  A#17,
           T#4          |->  A#17[[.]],
           T#18         |->  [.],
           S#2          |->  A#10[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#10[(var X#5)]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=A#10[(var X#5)]} in A#17[(var X#1)]);E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#10[(var X#5)]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#10[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=A#18[A#10[(var X#5)]]} in A#17[(var X#1)])
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#18[A#10[(\ X#6.S#9)]]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#4,T#3,A#10,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),A#17),
             (A#18[A#10[(var X#5)]],A#17),
             (A#17[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#18[A#10[(var X#5)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#17[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[A#18[[.2]]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  [.],
           A#16         |->  A#17[A#18],
           T#4          |->  A#17,
           S#2          |->  A#18[A#10[(var X#5)]]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#18[A#10[(var X#5)]]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=A#18[A#10[(var X#5)]]} in A#17[(var X#1)]);E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#18[A#10[(var X#5)]]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#18[A#10[(\ X#6.S#9)]]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=S#2} in A#17[(app A#18[A#10[(var X#5)]] T#19[(var X#1)])])
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[A#10[(\ X#6.S#9)]] T#19[S#2])]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#4,T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),A#17[(app A#18[A#10[(var X#5)]] T#19)]),
             (S#2,A#17[(app A#18[A#10[(var X#5)]] T#19)]),
             (A#17[(app A#18[A#10[(var X#5)]] T#19[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#17[(app A#18[A#10[(var X#5)]] T#19[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] T#19[S#2])]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  [.],
           T#4          |->  A#17[(app A#18[A#10[(var X#5)]] T#19)],
           A#16         |->  A#17[(app A#18 T#19[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[S#2])];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=S#2} in A#17[(app A#18[A#10[(var X#5)]] T#19[(var X#1)])]);E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[S#2])];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(\ X#6.S#9)]] T#19[S#2])];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=(var X#5)} in A#17[(var X#1)])
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);X#7=A#17[(\ X#6.S#9)];E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {T#4,T#3,A#10,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),A#17[[.]]),
             ((var X#5),A#17[[.]]),
             (A#17[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#17[[.]]),
             ((var X#5),A#17[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  [.],
           A#16         |->  [.],
           A#10         |->  A#17,
           T#4          |->  A#17[[.]],
           T#18         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(var X#5)];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=(var X#5)} in A#17[(var X#1)]);E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(var X#5)];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(\ X#6.S#9)];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=A#18[(var X#5)]} in A#17[(var X#1)])
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#18[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {T#4,T#3,A#10,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),A#17),
             (A#18[(var X#5)],A#17),
             (A#17[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#18[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#17[[.]]),
             ((var X#5),A#17[A#18[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  [.],
           A#16         |->  [.],
           A#10         |->  A#17[A#18],
           T#4          |->  A#17,
           S#2          |->  A#18[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#18[(var X#5)]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=A#18[(var X#5)]} in A#17[(var X#1)]);E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#18[(var X#5)]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#18[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=S#2} in A#17[(app A#18[(var X#5)] T#19[(var X#1)])])
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[(\ X#6.S#9)] T#19[S#2])]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),A#17[(app A#18[(var X#5)] T#19)]),
             (S#2,A#17[(app A#18[(var X#5)] T#19)]),
             (A#17[(app A#18[(var X#5)] T#19[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#17[(app A#18[(var X#5)] T#19[[.]])]),
             ((var X#5),A#17[(app A#18[[.]] T#19[S#2])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  [.],
           A#16         |->  [.],
           T#4          |->  A#17[(app A#18[(var X#5)] T#19)],
           A#10         |->  A#17[(app A#18 T#19[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[S#2])];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=S#2} in A#17[(app A#18[(var X#5)] T#19[(var X#1)])]);E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[S#2])];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(\ X#6.S#9)] T#19[S#2])];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=A#16[A#10[(var X#5)]]} in (var X#1))
       ;E#8
     in
        A#11[(var X#7)]
     )
    ,
     (letrec {X#5=(\ X#6.S#9);X#7=A#16[A#10[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#16[A#10[(var X#5)]],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#16[A#10[(var X#5)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#16[A#10[(var X#5)]]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#16[A#10[(var X#5)]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=A#16[A#10[(var X#5)]]} in (var X#1));E#8} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#16[A#10[(var X#5)]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#16[A#10[(\ X#6.S#9)]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(letrec {X#1=(var X#17)} in (var X#1))]
       ;E#8
       ;EE#18[X#17,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(var X#17)]
       ;E#8
       ;EE#18[X#17,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#17),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#19[[.]];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[(var X#17)];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#17,A#10[(var X#5)]]},
           A#16         |->  A#19,
           T#13         |->  A#19[[.]],
           T#20         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(var X#17)];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#19[(letrec {X#1=(var X#17)} in (var X#1))];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(var X#17)];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#19[(var X#17)];E#8;EE#18[X#17,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(letrec {X#1=(var X#17)} in A#21[(var X#1)])]
       ;E#8
       ;EE#18[X#17,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[A#21[(var X#17)]]
       ;E#8
       ;EE#18[X#17,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,A#16,T#13,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[[.]]),
             ((var X#17),A#21[[.]]),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#19;E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[A#21[(var X#17)]];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#17,A#10[(var X#5)]]},
           A#16         |->  A#19[A#21],
           T#13         |->  A#19,
           A#20         |->  A#21,
           T#4          |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[A#21[(var X#17)]];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#19[(letrec {X#1=(var X#17)} in A#21[(var X#1)])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[A#21[(var X#17)]];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#19[A#21[(var X#17)]];E#8;EE#18[X#17,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(letrec {X#1=A#22[(var X#17)]} in A#21[(var X#1)])]
       ;E#8
       ;EE#18[X#17,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[A#21[A#22[(var X#17)]]]
       ;E#8
       ;EE#18[X#17,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,A#16,T#13,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21),
             (A#22[(var X#17)],A#21),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#19;E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[A#21[A#22[(var X#17)]]];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#17,A#10[(var X#5)]]},
           A#16         |->  A#19[A#21[A#22]],
           T#13         |->  A#19,
           A#20         |->  A#21[A#22],
           T#4          |->  A#21,
           S#2          |->  A#22[(var X#17)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[A#21[A#22[(var X#17)]]];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#19[(letrec {X#1=A#22[(var X#17)]} in A#21[(var X#1)])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[A#21[A#22[(var X#17)]]];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#19[A#21[A#22[(var X#17)]]];E#8;EE#18[X#17,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#17)] T#23[(var X#1)])])]
       ;E#8
       ;EE#18[X#17,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[A#21[(app A#22[(var X#17)] T#23[S#2])]]
       ;E#8
       ;EE#18[X#17,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,A#16,T#13,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[(app A#22[(var X#17)] T#23)]),
             (S#2,A#21[(app A#22[(var X#17)] T#23)]),
             (A#21[(app A#22[(var X#17)] T#23[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[(app A#22[(var X#17)] T#23[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#19;E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[A#21[(app A#22[(var X#17)] T#23[S#2])]];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#17,A#10[(var X#5)]]},
           A#16         |->  A#19[A#21[(app A#22 T#23[S#2])]],
           T#13         |->  A#19,
           T#4          |->  A#21[(app A#22[(var X#17)] T#23)],
           A#20         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[A#21[(app A#22[(var X#17)] T#23[S#2])]];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#17)] T#23[(var X#1)])])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[A#21[(app A#22[(var X#17)] T#23[S#2])]];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#19[A#21[(app A#22[(var X#17)] T#23[S#2])]];E#8;EE#18[X#17,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(letrec {X#1=A#20[(var X#17)]} in (var X#1))]
       ;E#8
       ;EE#18[X#17,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[A#20[(var X#17)]]
       ;E#8
       ;EE#18[X#17,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#20[(var X#17)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#20[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#19;E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[A#20[(var X#17)]];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#17,A#10[(var X#5)]]},
           A#16         |->  A#19[A#20],
           T#13         |->  A#19,
           T#4          |->  [.],
           S#2          |->  A#20[(var X#17)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[A#20[(var X#17)]];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#19[(letrec {X#1=A#20[(var X#17)]} in (var X#1))];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[A#20[(var X#17)]];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#19[A#20[(var X#17)]];E#8;EE#18[X#17,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#8
       ;EE#18[X#17,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(app A#20[(var X#17)] T#21[T#4[S#2]])]
       ;E#8
       ;EE#18[X#17,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21)];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] T#21[T#4[S#2]])];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#17,A#10[(var X#5)]]},
           T#13         |->  A#19[(app A#20[(var X#17)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[T#4[S#2]])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[T#4[S#2]])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[T#4[S#2]])];E#8;EE#18[X#17,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=(var X#17)} in A#19[(var X#1)])
       ;E#8
       ;EE#18[X#17,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(var X#17)]
       ;E#8
       ;EE#18[X#17,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#4,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[[.]]),
             ((var X#17),A#19[[.]]),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[(var X#17)];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#17,A#10[(var X#5)]]},
           T#13         |->  [.],
           A#16         |->  A#19,
           T#4          |->  A#19[[.]],
           T#20         |->  [.],
           S#2          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(var X#17)];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=(var X#17)} in A#19[(var X#1)]);E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(var X#17)];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#19[(var X#17)];E#8;EE#18[X#17,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=A#20[(var X#17)]} in A#19[(var X#1)])
       ;E#8
       ;EE#18[X#17,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[A#20[(var X#17)]]
       ;E#8
       ;EE#18[X#17,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#4,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19),
             (A#20[(var X#17)],A#19),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#20[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[A#20[(var X#17)]];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#17,A#10[(var X#5)]]},
           T#13         |->  [.],
           A#16         |->  A#19[A#20],
           T#4          |->  A#19,
           S#2          |->  A#20[(var X#17)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[A#20[(var X#17)]];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=A#20[(var X#17)]} in A#19[(var X#1)]);E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[A#20[(var X#17)]];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#19[A#20[(var X#17)]];E#8;EE#18[X#17,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=S#2} in A#19[(app A#20[(var X#17)] T#21[(var X#1)])])
       ;E#8
       ;EE#18[X#17,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(app A#20[(var X#17)] T#21[S#2])]
       ;E#8
       ;EE#18[X#17,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#4,T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[(app A#20[(var X#17)] T#21)]),
             (S#2,A#19[(app A#20[(var X#17)] T#21)]),
             (A#19[(app A#20[(var X#17)] T#21[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[(app A#20[(var X#17)] T#21[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] T#21[S#2])];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#17,A#10[(var X#5)]]},
           T#13         |->  [.],
           T#4          |->  A#19[(app A#20[(var X#17)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[S#2])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=S#2} in A#19[(app A#20[(var X#17)] T#21[(var X#1)])]);E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[S#2])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[S#2])];E#8;EE#18[X#17,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= (letrec {X#1=A#16[(var X#17)]} in (var X#1))
       ;E#8
       ;EE#18[X#17,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#16[(var X#17)]
       ;E#8
       ;EE#18[X#17,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#16[(var X#17)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#16[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#9);X#7=[.];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#16[(var X#17)];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#17,A#10[(var X#5)]]},
           T#13         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#16[(var X#17)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#16[(var X#17)];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#9);X#7=(letrec {X#1=A#16[(var X#17)]} in (var X#1));E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#16[(var X#17)];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#16[(var X#17)];E#8;EE#18[X#17,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(letrec {X#1=(var X#18)} in (var X#1))]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#21[(var X#18)]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#3,A#10,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#18),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#18),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#21[[.]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[(var X#18)];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]},
           A#16         |->  A#21,
           T#13         |->  A#21[[.]],
           T#22         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#18)}

and instantiated rules:

                                  (letrec {X#17=A#21[(var X#18)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#21[(letrec {X#1=(var X#18)} in (var X#1))];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#21[(var X#18)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#21[(var X#18)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(letrec {X#1=(var X#18)} in A#23[(var X#1)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#21[A#23[(var X#18)]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,A#16,T#13,T#3,A#10,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[[.]]),
             ((var X#18),A#23[[.]]),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#18),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#21;X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[A#23[(var X#18)]];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]},
           A#16         |->  A#21[A#23],
           T#13         |->  A#21,
           A#22         |->  A#23,
           T#4          |->  A#23[[.]],
           T#24         |->  [.],
           S#2          |->  (var X#18)}

and instantiated rules:

                                  (letrec {X#17=A#21[A#23[(var X#18)]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#21[(letrec {X#1=(var X#18)} in A#23[(var X#1)])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#21[A#23[(var X#18)]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#21[A#23[(var X#18)]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(letrec {X#1=A#24[(var X#18)]} in A#23[(var X#1)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#21[A#23[A#24[(var X#18)]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,A#16,T#13,T#3,A#10,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23),
             (A#24[(var X#18)],A#23),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#24[(var X#18)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#21;X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[A#23[A#24[(var X#18)]]];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]},
           A#16         |->  A#21[A#23[A#24]],
           T#13         |->  A#21,
           A#22         |->  A#23[A#24],
           T#4          |->  A#23,
           S#2          |->  A#24[(var X#18)]}

and instantiated rules:

                                  (letrec {X#17=A#21[A#23[A#24[(var X#18)]]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#21[(letrec {X#1=A#24[(var X#18)]} in A#23[(var X#1)])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#21[A#23[A#24[(var X#18)]]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#21[A#23[A#24[(var X#18)]]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(letrec {X#1=S#2} in A#23[(app A#24[(var X#18)] T#25[(var X#1)])])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#21[A#23[(app A#24[(var X#18)] T#25[S#2])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,A#16,T#13,T#3,A#10,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[(app A#24[(var X#18)] T#25)]),
             (S#2,A#23[(app A#24[(var X#18)] T#25)]),
             (A#23[(app A#24[(var X#18)] T#25[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[(app A#24[(var X#18)] T#25[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#21;X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[A#23[(app A#24[(var X#18)] T#25[S#2])]];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]},
           A#16         |->  A#21[A#23[(app A#24 T#25[S#2])]],
           T#13         |->  A#21,
           T#4          |->  A#23[(app A#24[(var X#18)] T#25)],
           A#22         |->  A#23[(app A#24 T#25[S#2])]}

and instantiated rules:

                                  (letrec {X#17=A#21[A#23[(app A#24[(var X#18)] T#25[S#2])]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#21[(letrec {X#1=S#2} in A#23[(app A#24[(var X#18)] T#25[(var X#1)])])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#21[A#23[(app A#24[(var X#18)] T#25[S#2])]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#21[A#23[(app A#24[(var X#18)] T#25[S#2])]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(letrec {X#1=A#22[(var X#18)]} in (var X#1))]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#21[A#22[(var X#18)]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#3,A#10,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#22[(var X#18)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#18)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#21;X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[A#22[(var X#18)]];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]},
           A#16         |->  A#21[A#22],
           T#13         |->  A#21,
           T#4          |->  [.],
           S#2          |->  A#22[(var X#18)]}

and instantiated rules:

                                  (letrec {X#17=A#21[A#22[(var X#18)]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#21[(letrec {X#1=A#22[(var X#18)]} in (var X#1))];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#21[A#22[(var X#18)]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#21[A#22[(var X#18)]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[T#4[S#2]])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] T#23[T#4[S#2]])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]},
           T#13         |->  A#21[(app A#22[(var X#18)] T#23)],
           A#16         |->  A#21[(app A#22 T#23[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[T#4[S#2]])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(letrec {X#1=S#2} in T#4[(var X#1)])])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[T#4[S#2]])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[T#4[S#2]])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (letrec {X#1=(var X#18)} in A#21[(var X#1)])
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#21[(var X#18)]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#4,T#3,A#10,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[[.]]),
             ((var X#18),A#21[[.]]),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#18),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=[.];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[(var X#18)];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]},
           T#13         |->  [.],
           A#16         |->  A#21,
           T#4          |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  (var X#18)}

and instantiated rules:

                                  (letrec {X#17=A#21[(var X#18)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=(letrec {X#1=(var X#18)} in A#21[(var X#1)]);X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#21[(var X#18)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#21[(var X#18)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (letrec {X#1=A#22[(var X#18)]} in A#21[(var X#1)])
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#21[A#22[(var X#18)]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#4,T#3,A#10,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21),
             (A#22[(var X#18)],A#21),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#18)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=[.];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[A#22[(var X#18)]];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]},
           T#13         |->  [.],
           A#16         |->  A#21[A#22],
           T#4          |->  A#21,
           S#2          |->  A#22[(var X#18)]}

and instantiated rules:

                                  (letrec {X#17=A#21[A#22[(var X#18)]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=(letrec {X#1=A#22[(var X#18)]} in A#21[(var X#1)]);X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#21[A#22[(var X#18)]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#21[A#22[(var X#18)]];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (letrec {X#1=S#2} in A#21[(app A#22[(var X#18)] T#23[(var X#1)])])
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[S#2])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#4,T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[(app A#22[(var X#18)] T#23)]),
             (S#2,A#21[(app A#22[(var X#18)] T#23)]),
             (A#21[(app A#22[(var X#18)] T#23[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[(app A#22[(var X#18)] T#23[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=[.];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] T#23[S#2])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]},
           T#13         |->  [.],
           T#4          |->  A#21[(app A#22[(var X#18)] T#23)],
           A#16         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[S#2])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=(letrec {X#1=S#2} in A#21[(app A#22[(var X#18)] T#23[(var X#1)])]);X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[S#2])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[S#2])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (letrec {X#1=A#16[(var X#18)]} in (var X#1))
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(var X#5)]]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#16[(var X#18)]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#16[(var X#18)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#16[(var X#18)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=[.];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#16[(var X#18)];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]},
           T#13         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#16[(var X#18)]}

and instantiated rules:

                                  (letrec {X#17=A#16[(var X#18)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=(letrec {X#1=A#16[(var X#18)]} in (var X#1));X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#16[(var X#18)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#16[(var X#18)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[A#21[(letrec {X#1=(var X#5)} in (var X#1))]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(\ X#6.S#9)]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#16,T#13,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#5),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#21[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19[A#21[[.]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[A#21[[.]]],
           A#10         |->  A#21,
           T#20         |->  A#21[[.]],
           T#22         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[A#21[(letrec {X#1=(var X#5)} in (var X#1))]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(\ X#6.S#9)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[A#21[(letrec {X#1=(var X#5)} in A#23[(var X#1)])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[A#23[(\ X#6.S#9)]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,T#20,A#16,T#13,T#3,A#10,A#19,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[[.]]),
             ((var X#5),A#23[[.]]),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),A#21[A#23[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19[A#21];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[A#21],
           A#10         |->  A#21[A#23],
           T#20         |->  A#21,
           A#22         |->  A#23,
           T#4          |->  A#23[[.]],
           T#24         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[A#23[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[A#21[(letrec {X#1=(var X#5)} in A#23[(var X#1)])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[A#23[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[A#23[(\ X#6.S#9)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[A#21[(letrec {X#1=A#24[(var X#5)]} in A#23[(var X#1)])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[A#23[A#24[(\ X#6.S#9)]]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,T#20,A#16,T#13,T#3,A#10,A#19,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23),
             (A#24[(var X#5)],A#23),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#24[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),A#21[A#23[A#24[[.]]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19[A#21];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[A#21],
           A#10         |->  A#21[A#23[A#24]],
           T#20         |->  A#21,
           A#22         |->  A#23[A#24],
           T#4          |->  A#23,
           S#2          |->  A#24[(var X#5)]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[A#23[A#24[(var X#5)]]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[A#21[(letrec {X#1=A#24[(var X#5)]} in A#23[(var X#1)])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[A#23[A#24[(var X#5)]]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[A#23[A#24[(\ X#6.S#9)]]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[A#21[(letrec {X#1=S#2} in A#23[(app A#24[(var X#5)] T#25[(var X#1)])])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[A#23[(app A#24[(\ X#6.S#9)] T#25[S#2])]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,T#20,A#16,T#13,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[(app A#24[(var X#5)] T#25)]),
             (S#2,A#23[(app A#24[(var X#5)] T#25)]),
             (A#23[(app A#24[(var X#5)] T#25[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[(app A#24[(var X#5)] T#25[[.]])]),
             ((var X#5),A#21[A#23[(app A#24[[.]] T#25[S#2])]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19[A#21];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[A#21],
           A#10         |->  A#21[A#23[(app A#24 T#25[S#2])]],
           T#20         |->  A#21,
           T#4          |->  A#23[(app A#24[(var X#5)] T#25)],
           A#22         |->  A#23[(app A#24 T#25[S#2])]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[A#23[(app A#24[(var X#5)] T#25[S#2])]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[A#21[(letrec {X#1=S#2} in A#23[(app A#24[(var X#5)] T#25[(var X#1)])])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[A#23[(app A#24[(var X#5)] T#25[S#2])]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[A#23[(app A#24[(\ X#6.S#9)] T#25[S#2])]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[A#21[(letrec {X#1=A#22[(var X#5)]} in (var X#1))]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[A#22[(\ X#6.S#9)]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#16,T#13,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#22[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#21[A#22[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19[A#21];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[A#21],
           A#10         |->  A#21[A#22],
           T#20         |->  A#21,
           T#4          |->  [.],
           S#2          |->  A#22[(var X#5)]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[A#22[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[A#21[(letrec {X#1=A#22[(var X#5)]} in (var X#1))]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[A#22[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[A#22[(\ X#6.S#9)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[A#21[(app A#22[(var X#5)] T#23[(letrec {X#1=S#2} in T#4[(var X#1)])])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[T#4[S#2]])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#16,T#13,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#21[(app A#22[[.]] T#23[T#4[S#2]])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[A#21[(app A#22[(var X#5)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#5)] T#23)],
           A#10         |->  A#21[(app A#22 T#23[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[T#4[S#2]])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[(letrec {X#1=S#2} in T#4[(var X#1)])])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[T#4[S#2]])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[T#4[S#2]])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=(var X#5)} in A#21[(var X#1)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(\ X#6.S#9)]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#16,T#13,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[[.]]),
             ((var X#5),A#21[[.]]),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),A#21[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19[[.]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[[.]],
           T#20         |->  [.],
           A#10         |->  A#21,
           T#4          |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=(var X#5)} in A#21[(var X#1)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(\ X#6.S#9)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=A#22[(var X#5)]} in A#21[(var X#1)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[A#22[(\ X#6.S#9)]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#16,T#13,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21),
             (A#22[(var X#5)],A#21),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),A#21[A#22[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19[[.]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[[.]],
           T#20         |->  [.],
           A#10         |->  A#21[A#22],
           T#4          |->  A#21,
           S#2          |->  A#22[(var X#5)]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[A#22[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=A#22[(var X#5)]} in A#21[(var X#1)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[A#22[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[A#22[(\ X#6.S#9)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#5)] T#23[(var X#1)])])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[S#2])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#16,T#13,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[(app A#22[(var X#5)] T#23)]),
             (S#2,A#21[(app A#22[(var X#5)] T#23)]),
             (A#21[(app A#22[(var X#5)] T#23[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[(app A#22[(var X#5)] T#23[[.]])]),
             ((var X#5),A#21[(app A#22[[.]] T#23[S#2])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19[[.]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[[.]],
           T#20         |->  [.],
           T#4          |->  A#21[(app A#22[(var X#5)] T#23)],
           A#10         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#5)] T#23[(var X#1)])])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=A#10[(var X#5)]} in (var X#1))]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#10[(\ X#6.S#9)]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#10[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19[[.]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[[.]],
           T#20         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#10[(var X#5)]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#10[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=A#10[(var X#5)]} in (var X#1))];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#10[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#10[(\ X#6.S#9)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=(var X#5)} in A#21[A#23[(var X#1)]])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[A#23[(\ X#6.S#9)]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#20,T#4,A#16,T#13,T#3,A#10,A#19,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[A#23[[.]]]),
             ((var X#5),A#21[A#23[[.]]]),
             (A#21[A#23[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[A#23[[.]]]),
             ((var X#5),A#23[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19;X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[A#21[[.2]]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19[A#21],
           T#13         |->  A#19,
           A#20         |->  A#21,
           T#4          |->  A#21[A#23[[.]]],
           A#10         |->  A#23,
           T#22         |->  A#23[[.]],
           T#24         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[A#23[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=(var X#5)} in A#21[A#23[(var X#1)]])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[A#23[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[A#23[(\ X#6.S#9)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=A#24[(var X#5)]} in A#21[A#23[(var X#1)]])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[A#23[A#24[(\ X#6.S#9)]]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#20,T#4,A#16,T#13,T#3,A#10,A#19,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[A#23]),
             (A#24[(var X#5)],A#21[A#23]),
             (A#21[A#23[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             (A#24[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[A#23[[.]]]),
             ((var X#5),A#23[A#24[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19;X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[A#21[[.2]]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19[A#21],
           T#13         |->  A#19,
           A#20         |->  A#21,
           T#4          |->  A#21[A#23],
           A#10         |->  A#23[A#24],
           T#22         |->  A#23,
           S#2          |->  A#24[(var X#5)]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[A#23[A#24[(var X#5)]]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=A#24[(var X#5)]} in A#21[A#23[(var X#1)]])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[A#23[A#24[(var X#5)]]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[A#23[A#24[(\ X#6.S#9)]]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=S#2} in A#21[A#23[(app A#24[(var X#5)] T#25[(var X#1)])]])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[A#23[(app A#24[(\ X#6.S#9)] T#25[S#2])]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#20,T#4,A#16,T#13,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[A#23[(app A#24[(var X#5)] T#25)]]),
             (S#2,A#21[A#23[(app A#24[(var X#5)] T#25)]]),
             (A#21[A#23[(app A#24[(var X#5)] T#25[(dummy3 )])]],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[A#23[(app A#24[(var X#5)] T#25[[.]])]]),
             ((var X#5),A#23[(app A#24[[.]] T#25[S#2])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19;X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[A#21[[.2]]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19[A#21],
           T#13         |->  A#19,
           A#20         |->  A#21,
           T#4          |->  A#21[A#23[(app A#24[(var X#5)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#5)] T#25)],
           A#10         |->  A#23[(app A#24 T#25[S#2])]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[A#23[(app A#24[(var X#5)] T#25[S#2])]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=S#2} in A#21[A#23[(app A#24[(var X#5)] T#25[(var X#1)])]])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[A#23[(app A#24[(var X#5)] T#25[S#2])]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[A#23[(app A#24[(\ X#6.S#9)] T#25[S#2])]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=A#10[(var X#5)]} in A#21[(var X#1)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[A#10[(\ X#6.S#9)]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,A#16,T#13,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[[.]]),
             (A#10[(var X#5)],A#21[[.]]),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19;X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[A#21[[.2]]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19[A#21],
           T#13         |->  A#19,
           A#20         |->  A#21,
           T#4          |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  A#10[(var X#5)]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[A#10[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=A#10[(var X#5)]} in A#21[(var X#1)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[A#10[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[A#10[(\ X#6.S#9)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=A#22[A#10[(var X#5)]]} in A#21[(var X#1)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[A#22[A#10[(\ X#6.S#9)]]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,A#16,T#13,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21),
             (A#22[A#10[(var X#5)]],A#21),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[A#10[(var X#5)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19;X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[A#21[A#22[[.2]]]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19[A#21[A#22]],
           T#13         |->  A#19,
           A#20         |->  A#21[A#22],
           T#4          |->  A#21,
           S#2          |->  A#22[A#10[(var X#5)]]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[A#22[A#10[(var X#5)]]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=A#22[A#10[(var X#5)]]} in A#21[(var X#1)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[A#22[A#10[(var X#5)]]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[A#22[A#10[(\ X#6.S#9)]]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=S#2} in A#21[(app A#22[A#10[(var X#5)]] T#23[(var X#1)])])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(app A#22[A#10[(\ X#6.S#9)]] T#23[S#2])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,A#16,T#13,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[(app A#22[A#10[(var X#5)]] T#23)]),
             (S#2,A#21[(app A#22[A#10[(var X#5)]] T#23)]),
             (A#21[(app A#22[A#10[(var X#5)]] T#23[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[(app A#22[A#10[(var X#5)]] T#23[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19;X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[A#21[(app A#22[[.2]] T#23[S#2])]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19[A#21[(app A#22 T#23[S#2])]],
           T#13         |->  A#19,
           T#4          |->  A#21[(app A#22[A#10[(var X#5)]] T#23)],
           A#20         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(app A#22[A#10[(var X#5)]] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=S#2} in A#21[(app A#22[A#10[(var X#5)]] T#23[(var X#1)])])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(app A#22[A#10[(var X#5)]] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(app A#22[A#10[(\ X#6.S#9)]] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=(var X#5)} in A#21[(var X#1)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(\ X#6.S#9)]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#16,T#13,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[[.]]),
             ((var X#5),A#21[[.]]),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),A#21[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19;X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19[[.]],
           T#13         |->  A#19,
           A#20         |->  [.],
           A#10         |->  A#21,
           T#4          |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=(var X#5)} in A#21[(var X#1)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(\ X#6.S#9)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=A#22[(var X#5)]} in A#21[(var X#1)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[A#22[(\ X#6.S#9)]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#16,T#13,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21),
             (A#22[(var X#5)],A#21),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),A#21[A#22[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19;X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19[[.]],
           T#13         |->  A#19,
           A#20         |->  [.],
           A#10         |->  A#21[A#22],
           T#4          |->  A#21,
           S#2          |->  A#22[(var X#5)]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[A#22[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=A#22[(var X#5)]} in A#21[(var X#1)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[A#22[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[A#22[(\ X#6.S#9)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#5)] T#23[(var X#1)])])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[S#2])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#16,T#13,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[(app A#22[(var X#5)] T#23)]),
             (S#2,A#21[(app A#22[(var X#5)] T#23)]),
             (A#21[(app A#22[(var X#5)] T#23[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[(app A#22[(var X#5)] T#23[[.]])]),
             ((var X#5),A#21[(app A#22[[.]] T#23[S#2])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19;X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19[[.]],
           T#13         |->  A#19,
           A#20         |->  [.],
           T#4          |->  A#21[(app A#22[(var X#5)] T#23)],
           A#10         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#5)] T#23[(var X#1)])])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=A#20[A#10[(var X#5)]]} in (var X#1))]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#20[A#10[(\ X#6.S#9)]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#20[A#10[(var X#5)]],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#20[A#10[(var X#5)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19;X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[A#20[[.2]]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19[A#20],
           T#13         |->  A#19,
           T#4          |->  [.],
           S#2          |->  A#20[A#10[(var X#5)]]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#20[A#10[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=A#20[A#10[(var X#5)]]} in (var X#1))];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#20[A#10[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#20[A#10[(\ X#6.S#9)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[A#10[(var X#5)]] T#21[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[T#4[S#2]])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] T#21[T#4[S#2]])];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  A#19[(app A#20[A#10[(var X#5)]] T#21)],
           A#16         |->  A#19[(app A#20 T#21[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[T#4[S#2]])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[(letrec {X#1=S#2} in T#4[(var X#1)])])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[T#4[S#2]])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[T#4[S#2]])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=(var X#5)} in (var X#1))]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(\ X#6.S#9)]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#5),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#19[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19[[.]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  [.],
           A#10         |->  A#19,
           T#13         |->  A#19[[.]],
           T#20         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#17=A#19[(var X#5)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=(var X#5)} in (var X#1))];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(var X#5)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(\ X#6.S#9)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=(var X#5)} in A#21[(var X#1)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(\ X#6.S#9)]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,T#13,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[[.]]),
             ((var X#5),A#21[[.]]),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),A#19[A#21[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19;X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  [.],
           A#10         |->  A#19[A#21],
           T#13         |->  A#19,
           A#20         |->  A#21,
           T#4          |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=(var X#5)} in A#21[(var X#1)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(\ X#6.S#9)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=A#22[(var X#5)]} in A#21[(var X#1)])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[A#22[(\ X#6.S#9)]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,T#13,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21),
             (A#22[(var X#5)],A#21),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),A#19[A#21[A#22[[.]]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19;X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  [.],
           A#10         |->  A#19[A#21[A#22]],
           T#13         |->  A#19,
           A#20         |->  A#21[A#22],
           T#4          |->  A#21,
           S#2          |->  A#22[(var X#5)]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[A#22[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=A#22[(var X#5)]} in A#21[(var X#1)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[A#22[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[A#22[(\ X#6.S#9)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#5)] T#23[(var X#1)])])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[S#2])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,T#13,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[(app A#22[(var X#5)] T#23)]),
             (S#2,A#21[(app A#22[(var X#5)] T#23)]),
             (A#21[(app A#22[(var X#5)] T#23[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[(app A#22[(var X#5)] T#23[[.]])]),
             ((var X#5),A#19[A#21[(app A#22[[.]] T#23[S#2])]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19;X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  [.],
           A#10         |->  A#19[A#21[(app A#22 T#23[S#2])]],
           T#13         |->  A#19,
           T#4          |->  A#21[(app A#22[(var X#5)] T#23)],
           A#20         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#5)] T#23[(var X#1)])])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(letrec {X#1=A#20[(var X#5)]} in (var X#1))]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#20[(\ X#6.S#9)]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#20[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#20[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#19[A#20[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19;X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  [.],
           A#10         |->  A#19[A#20],
           T#13         |->  A#19,
           T#4          |->  [.],
           S#2          |->  A#20[(var X#5)]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#20[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(letrec {X#1=A#20[(var X#5)]} in (var X#1))];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#20[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#20[(\ X#6.S#9)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= A#19[(app A#20[(var X#5)] T#21[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(\ X#6.S#9)] T#21[T#4[S#2]])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#19[(app A#20[[.]] T#21[T#4[S#2]])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[T#4[S#2]])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[(letrec {X#1=S#2} in T#4[(var X#1)])])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[T#4[S#2]])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[(\ X#6.S#9)] T#21[T#4[S#2]])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (letrec {X#1=(var X#5)} in A#19[A#21[(var X#1)]])
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(\ X#6.S#9)]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#16,T#4,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[A#21[[.]]]),
             ((var X#5),A#19[A#21[[.]]]),
             (A#19[A#21[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[A#21[[.]]]),
             ((var X#5),A#21[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=[.];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  [.],
           A#16         |->  A#19,
           T#4          |->  A#19[A#21[[.]]],
           A#10         |->  A#21,
           T#20         |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=(letrec {X#1=(var X#5)} in A#19[A#21[(var X#1)]]);X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(\ X#6.S#9)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (letrec {X#1=A#22[(var X#5)]} in A#19[A#21[(var X#1)]])
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[A#22[(\ X#6.S#9)]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#16,T#4,T#3,A#10,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[A#21]),
             (A#22[(var X#5)],A#19[A#21]),
             (A#19[A#21[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[A#21[[.]]]),
             ((var X#5),A#21[A#22[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=[.];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  [.],
           A#16         |->  A#19,
           T#4          |->  A#19[A#21],
           A#10         |->  A#21[A#22],
           T#20         |->  A#21,
           S#2          |->  A#22[(var X#5)]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[A#22[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=(letrec {X#1=A#22[(var X#5)]} in A#19[A#21[(var X#1)]]);X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[A#22[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[A#22[(\ X#6.S#9)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (letrec {X#1=S#2} in A#19[A#21[(app A#22[(var X#5)] T#23[(var X#1)])]])
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[S#2])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#16,T#4,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[A#21[(app A#22[(var X#5)] T#23)]]),
             (S#2,A#19[A#21[(app A#22[(var X#5)] T#23)]]),
             (A#19[A#21[(app A#22[(var X#5)] T#23[(dummy3 )])]],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[A#21[(app A#22[(var X#5)] T#23[[.]])]]),
             ((var X#5),A#21[(app A#22[[.]] T#23[S#2])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=[.];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  [.],
           A#16         |->  A#19,
           T#4          |->  A#19[A#21[(app A#22[(var X#5)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#5)] T#23)],
           A#10         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=(letrec {X#1=S#2} in A#19[A#21[(app A#22[(var X#5)] T#23[(var X#1)])]]);X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (letrec {X#1=A#10[(var X#5)]} in A#19[(var X#1)])
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#10[(\ X#6.S#9)]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#4,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[[.]]),
             (A#10[(var X#5)],A#19[[.]]),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=[.];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  [.],
           A#16         |->  A#19,
           T#4          |->  A#19[[.]],
           T#20         |->  [.],
           S#2          |->  A#10[(var X#5)]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#10[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=(letrec {X#1=A#10[(var X#5)]} in A#19[(var X#1)]);X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#10[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#10[(\ X#6.S#9)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (letrec {X#1=A#20[A#10[(var X#5)]]} in A#19[(var X#1)])
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#20[A#10[(\ X#6.S#9)]]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#4,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19),
             (A#20[A#10[(var X#5)]],A#19),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#20[A#10[(var X#5)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=[.];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[A#20[[.2]]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  [.],
           A#16         |->  A#19[A#20],
           T#4          |->  A#19,
           S#2          |->  A#20[A#10[(var X#5)]]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#20[A#10[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=(letrec {X#1=A#20[A#10[(var X#5)]]} in A#19[(var X#1)]);X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#20[A#10[(var X#5)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#20[A#10[(\ X#6.S#9)]]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (letrec {X#1=S#2} in A#19[(app A#20[A#10[(var X#5)]] T#21[(var X#1)])])
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[S#2])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#4,T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[(app A#20[A#10[(var X#5)]] T#21)]),
             (S#2,A#19[(app A#20[A#10[(var X#5)]] T#21)]),
             (A#19[(app A#20[A#10[(var X#5)]] T#21[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[(app A#20[A#10[(var X#5)]] T#21[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=[.];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] T#21[S#2])];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  [.],
           T#4          |->  A#19[(app A#20[A#10[(var X#5)]] T#21)],
           A#16         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[S#2])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=(letrec {X#1=S#2} in A#19[(app A#20[A#10[(var X#5)]] T#21[(var X#1)])]);X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[S#2])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[S#2])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (letrec {X#1=(var X#5)} in A#19[(var X#1)])
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(\ X#6.S#9)]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[[.]]),
             ((var X#5),A#19[[.]]),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),A#19[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=[.];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  [.],
           A#16         |->  [.],
           A#10         |->  A#19,
           T#4          |->  A#19[[.]],
           T#20         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#17=A#19[(var X#5)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=(letrec {X#1=(var X#5)} in A#19[(var X#1)]);X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(var X#5)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(\ X#6.S#9)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (letrec {X#1=A#20[(var X#5)]} in A#19[(var X#1)])
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[A#20[(\ X#6.S#9)]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,T#3,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19),
             (A#20[(var X#5)],A#19),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#20[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),A#19[A#20[[.]]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=[.];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  [.],
           A#16         |->  [.],
           A#10         |->  A#19[A#20],
           T#4          |->  A#19,
           S#2          |->  A#20[(var X#5)]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#20[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=(letrec {X#1=A#20[(var X#5)]} in A#19[(var X#1)]);X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[A#20[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#20[(\ X#6.S#9)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (letrec {X#1=S#2} in A#19[(app A#20[(var X#5)] T#21[(var X#1)])])
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(\ X#6.S#9)] T#21[S#2])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[(app A#20[(var X#5)] T#21)]),
             (S#2,A#19[(app A#20[(var X#5)] T#21)]),
             (A#19[(app A#20[(var X#5)] T#21[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[(app A#20[(var X#5)] T#21[[.]])]),
             ((var X#5),A#19[(app A#20[[.]] T#21[S#2])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=[.];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  [.],
           A#16         |->  [.],
           T#4          |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[S#2])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=(letrec {X#1=S#2} in A#19[(app A#20[(var X#5)] T#21[(var X#1)])]);X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[S#2])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[(\ X#6.S#9)] T#21[S#2])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#17= (letrec {X#1=A#16[A#10[(var X#5)]]} in (var X#1))
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
    ,
     (letrec
        X#17= A#16[A#10[(\ X#6.S#9)]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#3,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#16[A#10[(var X#5)]],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#16[A#10[(var X#5)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#17=[.];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#16[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#16[A#10[(var X#5)]]}

and instantiated rules:

                                  (letrec {X#17=A#16[A#10[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#17=(letrec {X#1=A#16[A#10[(var X#5)]]} in (var X#1));X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    ................................................................................
                                  (letrec {X#17=A#16[A#10[(var X#5)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#16[A#10[(\ X#6.S#9)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (\ X#6.S#9)
          ;E#8
          ;EE#12[X#7,A#10[(var X#5)]]
        in
           A#14[(app A#15[(var X#7)] T#16[(var X#1)])]
        )
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;E#8
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#14[(app A#15[(var X#7)] T#16[S#2])]
     )
  )

where

   Delta1 = {A#11,T#13,T#4,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16)])),
             (S#2,(letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16)])),
             ((letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[[.]])])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#14[(app A#15[[.]] T#16[S#2])]),
             ((var X#7),A#14[(app A#15[[.]] T#16[S#2])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16)]),
           T#13  |->  A#14[(app A#15[(var X#7)] T#16)],
           A#11  |->  A#14[(app A#15 T#16[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[S#2])])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[(var X#1)])]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#14[(app A#15[(var X#7)] T#16[S#2])])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#14[(app A#15[(var X#7)] T#16[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#6.S#9)
     in
        (letrec {X#5=(var X#1);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
     )
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
  )

where

   Delta1 = {T#4,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=[.];E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])),
             ((\ X#6.S#9),(letrec {X#5=[.];E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])),
             ((letrec {X#5=(dummy3 );E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#9),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=[.];E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=[.];E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)]),
           X#14  |->  X#5,
           E#15  |->  {E#8;EE#12[X#7,A#10[(var X#5)]]},
           T#13  |->  [.],
           S#2   |->  (\ X#6.S#9)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#1=(\ X#6.S#9)} in (letrec {X#5=(var X#1);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#14= T#13[(var X#1)]
          ;X#5= (\ X#6.S#9)
          ;E#16
          ;EE#12[X#7,A#10[(var X#5)]]
        in
           A#11[(var X#7)]
        )
     )
    ,
     (letrec
        X#14= T#13[S#2]
       ;X#5= (\ X#6.S#9)
       ;E#16
       ;EE#12[X#7,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#14=T#13;X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])),
             (S#2,(letrec {X#14=T#13;X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])),
             ((letrec {X#14=T#13[(dummy3 )];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#14=T#13[[.]];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#14=T#13;X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)]),
           E#8   |->  {X#14=T#13[S#2];E#16},
           E#15  |->  {X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]}}

and instantiated rules:

                                  (letrec {X#14=T#13[S#2];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#14=T#13[(var X#1)];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)]))
    ................................................................................
                                  (letrec {X#14=T#13[S#2];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#14=T#13[S#2];X#5=(\ X#6.S#9);E#16;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (\ X#6.S#9)
          ;X#7= A#17[A#19[(app A#20[(var X#5)] T#21[(var X#1)])]]
          ;E#8
        in
           A#11[(var X#7)]
        )
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[S#2])]]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#18,A#16,T#13,T#4,A#10,A#17}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21)]];E#8} in A#11[(var X#7)])),
             (S#2,(letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21)]];E#8} in A#11[(var X#7)])),
             ((letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[(dummy3 )])]];E#8} in A#11[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[[.]])]];E#8} in A#11[(var X#7)])),
             ((var X#5),A#19[(app A#20[[.]] T#21[S#2])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21)]];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  A#17,
           T#13         |->  A#17[A#19[(app A#20[(var X#5)] T#21)]],
           T#18         |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[S#2])]];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[(var X#1)])]];E#8} in A#11[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(var X#5)] T#21[S#2])]];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[A#19[(app A#20[(\ X#6.S#9)] T#21[S#2])]];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (\ X#6.S#9)
          ;X#7= A#17[(app A#18[A#10[(var X#5)]] T#19[(var X#1)])]
          ;E#8
        in
           A#11[(var X#7)]
        )
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[A#10[(\ X#6.S#9)]] T#19[S#2])]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19)];E#8} in A#11[(var X#7)])),
             (S#2,(letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19)];E#8} in A#11[(var X#7)])),
             ((letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[(dummy3 )])];E#8} in A#11[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[[.]])];E#8} in A#11[(var X#7)])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19)];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#17[(app A#18[[.2]] T#19[S#2])]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           T#13         |->  A#17[(app A#18[A#10[(var X#5)]] T#19)],
           A#16         |->  A#17[(app A#18 T#19[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[S#2])];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[(var X#1)])];E#8} in A#11[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(var X#5)]] T#19[S#2])];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[A#10[(\ X#6.S#9)]] T#19[S#2])];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (\ X#6.S#9)
          ;X#7= A#17[(app A#18[(var X#5)] T#19[(var X#1)])]
          ;E#8
        in
           A#11[(var X#7)]
        )
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#17[(app A#18[(\ X#6.S#9)] T#19[S#2])]
       ;E#8
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#4,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19)];E#8} in A#11[(var X#7)])),
             (S#2,(letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19)];E#8} in A#11[(var X#7)])),
             ((letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[(dummy3 )])];E#8} in A#11[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[[.]])];E#8} in A#11[(var X#7)])),
             ((var X#5),A#17[(app A#18[[.]] T#19[S#2])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19)];E#8} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=[.2]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8},
           A#16         |->  [.],
           T#13         |->  A#17[(app A#18[(var X#5)] T#19)],
           A#10         |->  A#17[(app A#18 T#19[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[S#2])];E#8} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[(var X#1)])];E#8} in A#11[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(var X#5)] T#19[S#2])];E#8} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#17[(app A#18[(\ X#6.S#9)] T#19[S#2])];E#8} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (\ X#6.S#9)
          ;X#7= A#19[(app A#20[(var X#17)] T#21[(var X#1)])]
          ;E#8
          ;EE#18[X#17,A#10[(var X#5)]]
        in
           A#11[(var X#7)]
        )
     )
    ,
     (letrec
        X#5= (\ X#6.S#9)
       ;X#7= A#19[(app A#20[(var X#17)] T#21[S#2])]
       ;E#8
       ;EE#18[X#17,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21)];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])),
             (S#2,(letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21)];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])),
             ((letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(dummy3 )])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[[.]])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21)];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {[.1]=A#19[(app A#20[(var X#17)] T#21[S#2])];EE#18[X#17,[.2]]},
           X#14         |->  X#7,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#17,A#10[(var X#5)]]},
           T#13         |->  A#19[(app A#20[(var X#17)] T#21)],
           A#16         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[S#2])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[(var X#1)])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[S#2])];E#8;EE#18[X#17,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);X#7=A#19[(app A#20[(var X#17)] T#21[S#2])];E#8;EE#18[X#17,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#17= A#21[(app A#22[(var X#18)] T#23[(var X#1)])]
          ;X#5= (\ X#6.S#9)
          ;E#8
          ;EE#19[X#7,(var X#17)]
          ;EE#20[X#18,A#10[(var X#5)]]
        in
           A#11[(var X#7)]
        )
     )
    ,
     (letrec
        X#17= A#21[(app A#22[(var X#18)] T#23[S#2])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#19[X#7,(var X#17)]
       ;EE#20[X#18,A#10[(\ X#6.S#9)]]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#17=A#21[(app A#22[(var X#18)] T#23)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])),
             (S#2,(letrec {X#17=A#21[(app A#22[(var X#18)] T#23)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])),
             ((letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(dummy3 )])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#17=A#21[(app A#22[(var X#18)] T#23[[.]])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23)];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#21[(app A#22[(var X#18)] T#23[S#2])];EE#19[[.1],(var X#17)];EE#20[X#18,[.2]]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]},
           T#13         |->  A#21[(app A#22[(var X#18)] T#23)],
           A#16         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[S#2])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[(var X#1)])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)]))
    ................................................................................
                                  (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[S#2])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#21[(app A#22[(var X#18)] T#23[S#2])];X#5=(\ X#6.S#9);E#8;EE#19[X#7,(var X#17)];EE#20[X#18,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#17= A#19[A#21[(app A#22[(var X#5)] T#23[(var X#1)])]]
          ;X#5= (\ X#6.S#9)
          ;E#8
          ;EE#18[X#7,(var X#17)]
        in
           A#11[(var X#7)]
        )
     )
    ,
     (letrec
        X#17= A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[S#2])]]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#16,T#13,T#4,A#10,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])),
             (S#2,(letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])),
             ((letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[(dummy3 )])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[[.]])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])),
             ((var X#5),A#21[(app A#22[[.]] T#23[S#2])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23)]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[[.2]];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  A#19,
           T#13         |->  A#19[A#21[(app A#22[(var X#5)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#5)] T#23)],
           A#10         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[(var X#1)])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]))
    ................................................................................
                                  (letrec {X#17=A#19[A#21[(app A#22[(var X#5)] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[A#21[(app A#22[(\ X#6.S#9)] T#23[S#2])]];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#17= A#19[(app A#20[A#10[(var X#5)]] T#21[(var X#1)])]
          ;X#5= (\ X#6.S#9)
          ;E#8
          ;EE#18[X#7,(var X#17)]
        in
           A#11[(var X#7)]
        )
     )
    ,
     (letrec
        X#17= A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[S#2])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {A#16,T#13,T#4,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])),
             (S#2,(letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])),
             ((letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[(dummy3 )])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[[.]])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=A#19[(app A#20[[.2]] T#21[S#2])];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           T#13         |->  A#19[(app A#20[A#10[(var X#5)]] T#21)],
           A#16         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[S#2])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[(var X#1)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]))
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[A#10[(var X#5)]] T#21[S#2])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[A#10[(\ X#6.S#9)]] T#21[S#2])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#17= A#19[(app A#20[(var X#5)] T#21[(var X#1)])]
          ;X#5= (\ X#6.S#9)
          ;E#8
          ;EE#18[X#7,(var X#17)]
        in
           A#11[(var X#7)]
        )
     )
    ,
     (letrec
        X#17= A#19[(app A#20[(\ X#6.S#9)] T#21[S#2])]
       ;X#5= (\ X#6.S#9)
       ;E#8
       ;EE#18[X#7,(var X#17)]
     in
        A#11[(var X#7)]
     )
  )

where

   Delta1 = {T#13,T#4,A#10}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#17=A#19[(app A#20[(var X#5)] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])),
             (S#2,(letrec {X#17=A#19[(app A#20[(var X#5)] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])),
             ((letrec {X#17=A#19[(app A#20[(var X#5)] T#21[(dummy3 )])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#17=A#19[(app A#20[(var X#5)] T#21[[.]])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])),
             ((var X#5),A#19[(app A#20[[.]] T#21[S#2])]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21)];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]),
           EE#12[.1,.2] |-> {X#17=[.2];EE#18[[.1],(var X#17)]},
           X#14         |->  X#17,
           E#15         |->  {X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]},
           A#16         |->  [.],
           T#13         |->  A#19[(app A#20[(var X#5)] T#21)],
           A#10         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[S#2])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[(var X#1)])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)]))
    ................................................................................
                                  (letrec {X#17=A#19[(app A#20[(var X#5)] T#21[S#2])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#17=A#19[(app A#20[(\ X#6.S#9)] T#21[S#2])];X#5=(\ X#6.S#9);E#8;EE#18[X#7,(var X#17)]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
     in
        (var X#1)
     )
    ,
     (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
  )

where

   Delta1 = {A#10}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)]),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#7),A#11[[.]]),
             ((var X#7),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    and constraints: A#10/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}
      Delta1=  {A#10}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#7),A#11[[.]]),((var X#7),A#11[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  [.],
           S#2  |->  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -ucp3->                       (letrec {X#1=(letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])} in (var X#1))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(var X#5)]]} in A#11[(var X#7)])
    -SR,cp-e1->                   (letrec {X#5=(\ X#6.S#9);E#8;EE#12[X#7,A#10[(\ X#6.S#9)]]} in A#11[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(letrec {X#1=(var X#7)} in (var X#1))]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(var X#7)]
     )
  )

where

   Delta1 = {A#12,T#15,T#3,A#11,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#7),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#7),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#16[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[[.]]),
           A#12  |->  A#16,
           T#15  |->  A#16[[.]],
           T#17  |->  [.],
           T#4   |->  [.],
           S#2   |->  (var X#7)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(letrec {X#1=(var X#7)} in (var X#1))])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#16[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(letrec {X#1=(var X#7)} in A#18[(var X#1)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[A#18[(var X#7)]]
     )
  )

where

   Delta1 = {A#17,T#4,A#12,T#15,T#3,A#11,A#16,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),A#18[[.]]),
             ((var X#7),A#18[[.]]),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#7),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#18[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[A#18[[.]]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[A#18[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16),
           A#12  |->  A#16[A#18],
           T#15  |->  A#16,
           A#17  |->  A#18,
           T#4   |->  A#18[[.]],
           T#19  |->  [.],
           S#2   |->  (var X#7)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[A#18[(var X#7)]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(letrec {X#1=(var X#7)} in A#18[(var X#1)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[A#18[(var X#7)]])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#16[A#18[(var X#7)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(letrec {X#1=A#19[(var X#7)]} in A#18[(var X#1)])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[A#18[A#19[(var X#7)]]]
     )
  )

where

   Delta1 = {A#17,T#4,A#12,T#15,T#3,A#11,A#16,A#18}
   Delta2 = {}
   Delta3 = {((var X#1),A#18),
             (A#19[(var X#7)],A#18),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(var X#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#18[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[A#18[A#19[[.]]]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[A#18[A#19[[.]]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16),
           A#12  |->  A#16[A#18[A#19]],
           T#15  |->  A#16,
           A#17  |->  A#18[A#19],
           T#4   |->  A#18,
           S#2   |->  A#19[(var X#7)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[A#18[A#19[(var X#7)]]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(letrec {X#1=A#19[(var X#7)]} in A#18[(var X#1)])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[A#18[A#19[(var X#7)]]])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#16[A#18[A#19[(var X#7)]]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(letrec {X#1=S#2} in A#18[(app A#19[(var X#7)] T#20[(var X#1)])])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[A#18[(app A#19[(var X#7)] T#20[S#2])]]
     )
  )

where

   Delta1 = {A#17,T#4,A#12,T#15,T#3,A#11,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),A#18[(app A#19[(var X#7)] T#20)]),
             (S#2,A#18[(app A#19[(var X#7)] T#20)]),
             (A#18[(app A#19[(var X#7)] T#20[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#18[(app A#19[(var X#7)] T#20[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#16[A#18[(app A#19[[.]] T#20[S#2])]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[A#18[(app A#19[[.]] T#20[S#2])]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16),
           A#12  |->  A#16[A#18[(app A#19 T#20[S#2])]],
           T#15  |->  A#16,
           T#4   |->  A#18[(app A#19[(var X#7)] T#20)],
           A#17  |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[A#18[(app A#19[(var X#7)] T#20[S#2])]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(letrec {X#1=S#2} in A#18[(app A#19[(var X#7)] T#20[(var X#1)])])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[A#18[(app A#19[(var X#7)] T#20[S#2])]])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#16[A#18[(app A#19[(var X#7)] T#20[S#2])]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(letrec {X#1=A#17[(var X#7)]} in (var X#1))]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[A#17[(var X#7)]]
     )
  )

where

   Delta1 = {A#12,T#15,T#3,A#11,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#17[(var X#7)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#17[(var X#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#16[A#17[[.]]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[A#17[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16),
           A#12  |->  A#16[A#17],
           T#15  |->  A#16,
           T#4   |->  [.],
           S#2   |->  A#17[(var X#7)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[A#17[(var X#7)]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(letrec {X#1=A#17[(var X#7)]} in (var X#1))])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[A#17[(var X#7)]])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#16[A#17[(var X#7)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(app A#17[(var X#7)] T#18[(letrec {X#1=S#2} in T#4[(var X#1)])])]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(app A#17[(var X#7)] T#18[T#4[S#2]])]
     )
  )

where

   Delta1 = {A#12,T#15,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[(app A#17[[.]] T#18[T#4[S#2]])]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[(app A#17[[.]] T#18[T#4[S#2]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#7)] T#18)],
           A#12  |->  A#16[(app A#17 T#18[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[T#4[S#2]])])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(letrec {X#1=S#2} in T#4[(var X#1)])])])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[T#4[S#2]])])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[T#4[S#2]])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        (letrec {X#1=(var X#7)} in A#16[(var X#1)])
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(var X#7)]
     )
  )

where

   Delta1 = {A#12,T#4,T#3,A#11,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),A#16[[.]]),
             ((var X#7),A#16[[.]]),
             (A#16[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#7),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#16[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in [.]),
           T#15  |->  [.],
           A#12  |->  A#16,
           T#4   |->  A#16[[.]],
           T#17  |->  [.],
           S#2   |->  (var X#7)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in (letrec {X#1=(var X#7)} in A#16[(var X#1)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#16[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        (letrec {X#1=A#17[(var X#7)]} in A#16[(var X#1)])
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[A#17[(var X#7)]]
     )
  )

where

   Delta1 = {A#12,T#4,T#3,A#11,A#16}
   Delta2 = {}
   Delta3 = {((var X#1),A#16),
             (A#17[(var X#7)],A#16),
             (A#16[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#17[(var X#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#16[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[A#17[[.]]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[A#17[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in [.]),
           T#15  |->  [.],
           A#12  |->  A#16[A#17],
           T#4   |->  A#16,
           S#2   |->  A#17[(var X#7)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[A#17[(var X#7)]])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in (letrec {X#1=A#17[(var X#7)]} in A#16[(var X#1)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[A#17[(var X#7)]])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#16[A#17[(var X#7)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        (letrec {X#1=S#2} in A#16[(app A#17[(var X#7)] T#18[(var X#1)])])
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(app A#17[(var X#7)] T#18[S#2])]
     )
  )

where

   Delta1 = {A#12,T#4,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),A#16[(app A#17[(var X#7)] T#18)]),
             (S#2,A#16[(app A#17[(var X#7)] T#18)]),
             (A#16[(app A#17[(var X#7)] T#18[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#16[(app A#17[(var X#7)] T#18[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#16[(app A#17[[.]] T#18[S#2])]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[(app A#17[[.]] T#18[S#2])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in [.]),
           T#15  |->  [.],
           T#4   |->  A#16[(app A#17[(var X#7)] T#18)],
           A#12  |->  A#16[(app A#17 T#18[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[S#2])])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in (letrec {X#1=S#2} in A#16[(app A#17[(var X#7)] T#18[(var X#1)])]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[S#2])])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        (letrec {X#1=A#12[(var X#7)]} in (var X#1))
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#12[(var X#7)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(var X#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in [.]),
           T#15  |->  [.],
           T#4   |->  [.],
           S#2   |->  A#12[(var X#7)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in (letrec {X#1=A#12[(var X#7)]} in (var X#1)))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=(\ X#6.S#10)} in (var X#1))
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((\ X#6.S#10),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#10),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=[.];E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           X#16  |->  X#5,
           E#17  |->  {E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15  |->  [.],
           T#4   |->  [.],
           S#2   |->  (\ X#6.S#10)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=(\ X#6.S#10)} in (var X#1));E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= T#15[(letrec {X#1=S#2} in T#4[(var X#1)])]
       ;X#5= (\ X#6.S#10)
       ;E#18
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#16= T#15[T#4[S#2]]
       ;X#5= (\ X#6.S#10)
       ;E#18
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#16=T#15;X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           E#9   |->  {X#16=T#15[T#4[S#2]];E#18},
           E#17  |->  {X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|}}

and instantiated rules:

                                  (letrec {X#16=T#15[T#4[S#2]];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#16=T#15[(letrec {X#1=S#2} in T#4[(var X#1)])];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#16=T#15[T#4[S#2]];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#16=T#15[T#4[S#2]];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#8= (letrec {X#1=(var X#5)} in (var X#1))
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#8= (var X#5)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#5),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#8=[.];E#9;EE#13[X#7,A#11[(var X#8)]]} in A#12[(var X#7)]),
           VV#14|.1,.2| |-> {[.1]=[.2]},
           X#16         |->  X#8,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]]},
           T#15         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#8=(var X#5);E#9;EE#13[X#7,A#11[(var X#8)]]} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#8=(letrec {X#1=(var X#5)} in (var X#1));E#9;EE#13[X#7,A#11[(var X#8)]]} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#8=(var X#5);E#9;EE#13[X#7,A#11[(var X#8)]]} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#8=(var X#5);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]]} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#8= (letrec {X#1=(var X#19)} in (var X#1))
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#20|X#19,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#8= (var X#19)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#20|X#19,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#19),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#19),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#8=[.];E#9;EE#13[X#7,A#11[(var X#8)]];VV#20|X#19,(var X#5)|} in A#12[(var X#7)]),
           VV#14|.1,.2| |-> {[.1]=(var X#19);VV#20|X#19,[.2]|},
           X#16         |->  X#8,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#20|X#19,(var X#5)|},
           T#15         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#19)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#8=(var X#19);E#9;EE#13[X#7,A#11[(var X#8)]];VV#20|X#19,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#8=(letrec {X#1=(var X#19)} in (var X#1));E#9;EE#13[X#7,A#11[(var X#8)]];VV#20|X#19,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#8=(var X#19);E#9;EE#13[X#7,A#11[(var X#8)]];VV#20|X#19,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#8=(var X#19);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#20|X#19,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=(var X#20)} in (var X#1))
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#21|X#8,(var X#19)|
       ;VV#22|X#20,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= (var X#20)
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#21|X#8,(var X#19)|
       ;VV#22|X#20,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#20),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#20),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#21|X#8,(var X#19)|;VV#22|X#20,(var X#5)|} in A#12[(var X#7)]),
           VV#14|.1,.2| |-> {X#19=(var X#20);VV#21|[.1],(var X#19)|;VV#22|X#20,[.2]|},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#21|X#8,(var X#19)|;VV#22|X#20,(var X#5)|},
           T#15         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#20)}

and instantiated rules:

                                  (letrec {X#19=(var X#20);X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#21|X#8,(var X#19)|;VV#22|X#20,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=(var X#20)} in (var X#1));X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#21|X#8,(var X#19)|;VV#22|X#20,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=(var X#20);X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#21|X#8,(var X#19)|;VV#22|X#20,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=(var X#20);X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#21|X#8,(var X#19)|;VV#22|X#20,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=(var X#5)} in (var X#1))
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(var X#8)]]
       ;VV#20|X#8,(var X#19)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= (var X#5)
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#20|X#8,(var X#19)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#5),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#20|X#8,(var X#19)|} in A#12[(var X#7)]),
           VV#14|.1,.2| |-> {X#19=[.2];VV#20|[.1],(var X#19)|},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#20|X#8,(var X#19)|},
           T#15         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#19=(var X#5);X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#20|X#8,(var X#19)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=(var X#5)} in (var X#1));X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#20|X#8,(var X#19)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=(var X#5);X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#20|X#8,(var X#19)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=(var X#5);X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#20|X#8,(var X#19)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(letrec {X#1=(var X#8)} in (var X#1))]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(\ X#6.S#10)]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#3,A#11,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#8),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[[.]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19,
           T#15         |->  A#19[A#21[[.]]],
           A#11         |->  A#21,
           T#20         |->  A#21[[.]],
           T#22         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(letrec {X#1=(var X#8)} in (var X#1))]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(\ X#6.S#10)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(letrec {X#1=(var X#8)} in A#23[(var X#1)])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[A#23[(\ X#6.S#10)]]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,T#20,A#18,T#15,T#3,A#11,A#19,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[[.]]),
             ((var X#8),A#23[[.]]),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[A#23[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19,
           T#15         |->  A#19[A#21],
           A#11         |->  A#21[A#23],
           T#20         |->  A#21,
           A#22         |->  A#23,
           T#4          |->  A#23[[.]],
           T#24         |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(letrec {X#1=(var X#8)} in A#23[(var X#1)])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[(\ X#6.S#10)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(letrec {X#1=A#24[(var X#8)]} in A#23[(var X#1)])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[A#23[A#24[(\ X#6.S#10)]]]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,T#20,A#18,T#15,T#3,A#11,A#19,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23),
             (A#24[(var X#8)],A#23),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#24[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[A#23[A#24[[.]]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19,
           T#15         |->  A#19[A#21],
           A#11         |->  A#21[A#23[A#24]],
           T#20         |->  A#21,
           A#22         |->  A#23[A#24],
           T#4          |->  A#23,
           S#2          |->  A#24[(var X#8)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[A#24[(var X#8)]]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(letrec {X#1=A#24[(var X#8)]} in A#23[(var X#1)])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[A#24[(var X#8)]]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[A#24[(\ X#6.S#10)]]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(letrec {X#1=S#2} in A#23[(app A#24[(var X#8)] T#25[(var X#1)])])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[S#2])]]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,T#20,A#18,T#15,T#3,A#11,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[(app A#24[(var X#8)] T#25)]),
             (S#2,A#23[(app A#24[(var X#8)] T#25)]),
             (A#23[(app A#24[(var X#8)] T#25[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[(app A#24[(var X#8)] T#25[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[A#23[(app A#24[[.]] T#25[S#2])]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19,
           T#15         |->  A#19[A#21],
           A#11         |->  A#21[A#23[(app A#24 T#25[S#2])]],
           T#20         |->  A#21,
           T#4          |->  A#23[(app A#24[(var X#8)] T#25)],
           A#22         |->  A#23[(app A#24 T#25[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[(app A#24[(var X#8)] T#25[S#2])]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(letrec {X#1=S#2} in A#23[(app A#24[(var X#8)] T#25[(var X#1)])])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[(app A#24[(var X#8)] T#25[S#2])]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[S#2])]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(letrec {X#1=A#22[(var X#8)]} in (var X#1))]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[A#22[(\ X#6.S#10)]]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#3,A#11,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#22[(var X#8)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[A#22[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19,
           T#15         |->  A#19[A#21],
           A#11         |->  A#21[A#22],
           T#20         |->  A#21,
           T#4          |->  [.],
           S#2          |->  A#22[(var X#8)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(letrec {X#1=A#22[(var X#8)]} in (var X#1))]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[(\ X#6.S#10)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=S#2} in T#4[(var X#1)])])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[T#4[S#2]])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#3,A#11,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[T#4[S#2]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19,
           T#15         |->  A#19[A#21[(app A#22[(var X#8)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[T#4[S#2]])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=S#2} in T#4[(var X#1)])])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[T#4[S#2]])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[T#4[S#2]])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=(var X#8)} in A#21[(var X#1)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(\ X#6.S#10)]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#18,T#15,T#3,A#11,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[[.]]),
             ((var X#8),A#21[[.]]),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[[.]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19,
           T#15         |->  A#19[[.]],
           T#20         |->  [.],
           A#11         |->  A#21,
           T#4          |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=(var X#8)} in A#21[(var X#1)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(\ X#6.S#10)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=A#22[(var X#8)]} in A#21[(var X#1)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[A#22[(\ X#6.S#10)]]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#18,T#15,T#3,A#11,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21),
             (A#22[(var X#8)],A#21),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[A#22[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[[.]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19,
           T#15         |->  A#19[[.]],
           T#20         |->  [.],
           A#11         |->  A#21[A#22],
           T#4          |->  A#21,
           S#2          |->  A#22[(var X#8)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=A#22[(var X#8)]} in A#21[(var X#1)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[(\ X#6.S#10)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#8)] T#23[(var X#1)])])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[S#2])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#18,T#15,T#3,A#11,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[(app A#22[(var X#8)] T#23)]),
             (S#2,A#21[(app A#22[(var X#8)] T#23)]),
             (A#21[(app A#22[(var X#8)] T#23[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[(app A#22[(var X#8)] T#23[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[S#2])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[[.]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19,
           T#15         |->  A#19[[.]],
           T#20         |->  [.],
           T#4          |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#8)] T#23[(var X#1)])])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=A#11[(var X#8)]} in (var X#1))]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#11[(\ X#6.S#10)]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#3,A#11,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#11[(var X#8)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[[.]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19,
           T#15         |->  A#19[[.]],
           T#20         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#11[(var X#8)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#11[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=A#11[(var X#8)]} in (var X#1))];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#11[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#11[(\ X#6.S#10)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=(var X#8)} in A#21[A#23[(var X#1)]])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[A#23[(\ X#6.S#10)]]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#20,T#4,A#18,T#15,T#3,A#11,A#19,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[A#23[[.]]]),
             ((var X#8),A#21[A#23[[.]]]),
             (A#21[A#23[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[A#23[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19;E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[A#21[[.2]]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19[A#21],
           T#15         |->  A#19,
           A#20         |->  A#21,
           T#4          |->  A#21[A#23[[.]]],
           A#11         |->  A#23,
           T#22         |->  A#23[[.]],
           T#24         |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=(var X#8)} in A#21[A#23[(var X#1)]])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[(\ X#6.S#10)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=A#24[(var X#8)]} in A#21[A#23[(var X#1)]])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[A#23[A#24[(\ X#6.S#10)]]]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#20,T#4,A#18,T#15,T#3,A#11,A#19,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[A#23]),
             (A#24[(var X#8)],A#21[A#23]),
             (A#21[A#23[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             (A#24[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[A#23[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[A#24[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19;E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[A#21[[.2]]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19[A#21],
           T#15         |->  A#19,
           A#20         |->  A#21,
           T#4          |->  A#21[A#23],
           A#11         |->  A#23[A#24],
           T#22         |->  A#23,
           S#2          |->  A#24[(var X#8)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[A#24[(var X#8)]]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=A#24[(var X#8)]} in A#21[A#23[(var X#1)]])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[A#24[(var X#8)]]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[A#24[(\ X#6.S#10)]]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=S#2} in A#21[A#23[(app A#24[(var X#8)] T#25[(var X#1)])]])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[S#2])]]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#20,T#4,A#18,T#15,T#3,A#11,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[A#23[(app A#24[(var X#8)] T#25)]]),
             (S#2,A#21[A#23[(app A#24[(var X#8)] T#25)]]),
             (A#21[A#23[(app A#24[(var X#8)] T#25[(dummy3 )])]],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[A#23[(app A#24[(var X#8)] T#25[[.]])]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[(app A#24[[.]] T#25[S#2])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19;E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[A#21[[.2]]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19[A#21],
           T#15         |->  A#19,
           A#20         |->  A#21,
           T#4          |->  A#21[A#23[(app A#24[(var X#8)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#8)] T#25)],
           A#11         |->  A#23[(app A#24 T#25[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[(app A#24[(var X#8)] T#25[S#2])]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=S#2} in A#21[A#23[(app A#24[(var X#8)] T#25[(var X#1)])]])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[(app A#24[(var X#8)] T#25[S#2])]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[S#2])]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=A#11[(var X#8)]} in A#21[(var X#1)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[A#11[(\ X#6.S#10)]]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,A#18,T#15,T#3,A#11,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[[.]]),
             (A#11[(var X#8)],A#21[[.]]),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19;E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[A#21[[.2]]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19[A#21],
           T#15         |->  A#19,
           A#20         |->  A#21,
           T#4          |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  A#11[(var X#8)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#11[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=A#11[(var X#8)]} in A#21[(var X#1)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#11[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#11[(\ X#6.S#10)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=A#22[A#11[(var X#8)]]} in A#21[(var X#1)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[A#22[A#11[(\ X#6.S#10)]]]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,A#18,T#15,T#3,A#11,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21),
             (A#22[A#11[(var X#8)]],A#21),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[A#11[(var X#8)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19;E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[A#21[A#22[[.2]]]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19[A#21[A#22]],
           T#15         |->  A#19,
           A#20         |->  A#21[A#22],
           T#4          |->  A#21,
           S#2          |->  A#22[A#11[(var X#8)]]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[A#11[(var X#8)]]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=A#22[A#11[(var X#8)]]} in A#21[(var X#1)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[A#11[(var X#8)]]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[A#11[(\ X#6.S#10)]]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=S#2} in A#21[(app A#22[A#11[(var X#8)]] T#23[(var X#1)])])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[S#2])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,A#18,T#15,T#3,A#11,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[(app A#22[A#11[(var X#8)]] T#23)]),
             (S#2,A#21[(app A#22[A#11[(var X#8)]] T#23)]),
             (A#21[(app A#22[A#11[(var X#8)]] T#23[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[(app A#22[A#11[(var X#8)]] T#23[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19;E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[A#21[(app A#22[[.2]] T#23[S#2])]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19[A#21[(app A#22 T#23[S#2])]],
           T#15         |->  A#19,
           T#4          |->  A#21[(app A#22[A#11[(var X#8)]] T#23)],
           A#20         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[A#11[(var X#8)]] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=S#2} in A#21[(app A#22[A#11[(var X#8)]] T#23[(var X#1)])])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[A#11[(var X#8)]] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=(var X#8)} in A#21[(var X#1)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(\ X#6.S#10)]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#18,T#15,T#3,A#11,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[[.]]),
             ((var X#8),A#21[[.]]),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19;E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19[[.]],
           T#15         |->  A#19,
           A#20         |->  [.],
           A#11         |->  A#21,
           T#4          |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=(var X#8)} in A#21[(var X#1)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(\ X#6.S#10)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=A#22[(var X#8)]} in A#21[(var X#1)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[A#22[(\ X#6.S#10)]]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#18,T#15,T#3,A#11,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21),
             (A#22[(var X#8)],A#21),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[A#22[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19;E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19[[.]],
           T#15         |->  A#19,
           A#20         |->  [.],
           A#11         |->  A#21[A#22],
           T#4          |->  A#21,
           S#2          |->  A#22[(var X#8)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=A#22[(var X#8)]} in A#21[(var X#1)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[(\ X#6.S#10)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#8)] T#23[(var X#1)])])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[S#2])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#18,T#15,T#3,A#11,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[(app A#22[(var X#8)] T#23)]),
             (S#2,A#21[(app A#22[(var X#8)] T#23)]),
             (A#21[(app A#22[(var X#8)] T#23[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[(app A#22[(var X#8)] T#23[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[S#2])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19;E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19[[.]],
           T#15         |->  A#19,
           A#20         |->  [.],
           T#4          |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#8)] T#23[(var X#1)])])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=A#20[A#11[(var X#8)]]} in (var X#1))]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#20[A#11[(\ X#6.S#10)]]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#3,A#11,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#20[A#11[(var X#8)]],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#20[A#11[(var X#8)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19;E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[A#20[[.2]]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19[A#20],
           T#15         |->  A#19,
           T#4          |->  [.],
           S#2          |->  A#20[A#11[(var X#8)]]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#20[A#11[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=A#20[A#11[(var X#8)]]} in (var X#1))];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#20[A#11[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#20[A#11[(\ X#6.S#10)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[A#11[(var X#8)]] T#21[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[A#11[(\ X#6.S#10)]] T#21[T#4[S#2]])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[T#4[S#2]])]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  A#19[(app A#20[A#11[(var X#8)]] T#21)],
           A#18         |->  A#19[(app A#20 T#21[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[T#4[S#2]])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[T#4[S#2]])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(\ X#6.S#10)]] T#21[T#4[S#2]])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=(var X#8)} in (var X#1))]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(\ X#6.S#10)]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#3,A#11,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#8),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#19[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[[.]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           A#11         |->  A#19,
           T#15         |->  A#19[[.]],
           T#20         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(var X#8)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=(var X#8)} in (var X#1))];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(var X#8)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(\ X#6.S#10)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=(var X#8)} in A#21[(var X#1)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(\ X#6.S#10)]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,T#15,T#3,A#11,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[[.]]),
             ((var X#8),A#21[[.]]),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#19[A#21[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19;E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           A#11         |->  A#19[A#21],
           T#15         |->  A#19,
           A#20         |->  A#21,
           T#4          |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=(var X#8)} in A#21[(var X#1)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(\ X#6.S#10)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=A#22[(var X#8)]} in A#21[(var X#1)])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[A#22[(\ X#6.S#10)]]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,T#15,T#3,A#11,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21),
             (A#22[(var X#8)],A#21),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#19[A#21[A#22[[.]]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19;E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           A#11         |->  A#19[A#21[A#22]],
           T#15         |->  A#19,
           A#20         |->  A#21[A#22],
           T#4          |->  A#21,
           S#2          |->  A#22[(var X#8)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=A#22[(var X#8)]} in A#21[(var X#1)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[(\ X#6.S#10)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#8)] T#23[(var X#1)])])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[S#2])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#20,T#4,T#15,T#3,A#11,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[(app A#22[(var X#8)] T#23)]),
             (S#2,A#21[(app A#22[(var X#8)] T#23)]),
             (A#21[(app A#22[(var X#8)] T#23[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[(app A#22[(var X#8)] T#23[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#19[A#21[(app A#22[[.]] T#23[S#2])]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19;E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           A#11         |->  A#19[A#21[(app A#22 T#23[S#2])]],
           T#15         |->  A#19,
           T#4          |->  A#21[(app A#22[(var X#8)] T#23)],
           A#20         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=S#2} in A#21[(app A#22[(var X#8)] T#23[(var X#1)])])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(letrec {X#1=A#20[(var X#8)]} in (var X#1))]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#20[(\ X#6.S#10)]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#3,A#11,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#20[(var X#8)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#20[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#19[A#20[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19;E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           A#11         |->  A#19[A#20],
           T#15         |->  A#19,
           T#4          |->  [.],
           S#2          |->  A#20[(var X#8)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#20[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(letrec {X#1=A#20[(var X#8)]} in (var X#1))];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#20[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#20[(\ X#6.S#10)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[(\ X#6.S#10)] T#21[T#4[S#2]])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#19[(app A#20[[.]] T#21[T#4[S#2]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           T#15         |->  A#19[(app A#20[(var X#8)] T#21)],
           A#11         |->  A#19[(app A#20 T#21[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[T#4[S#2]])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[T#4[S#2]])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(\ X#6.S#10)] T#21[T#4[S#2]])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= (letrec {X#1=(var X#8)} in A#19[A#21[(var X#1)]])
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(\ X#6.S#10)]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#18,T#4,T#3,A#11,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[A#21[[.]]]),
             ((var X#8),A#19[A#21[[.]]]),
             (A#19[A#21[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[A#21[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=[.];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  A#19,
           T#4          |->  A#19[A#21[[.]]],
           A#11         |->  A#21,
           T#20         |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=(letrec {X#1=(var X#8)} in A#19[A#21[(var X#1)]]);E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(\ X#6.S#10)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= (letrec {X#1=A#22[(var X#8)]} in A#19[A#21[(var X#1)]])
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[A#22[(\ X#6.S#10)]]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#18,T#4,T#3,A#11,A#19,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[A#21]),
             (A#22[(var X#8)],A#19[A#21]),
             (A#19[A#21[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[A#21[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[A#22[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=[.];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  A#19,
           T#4          |->  A#19[A#21],
           A#11         |->  A#21[A#22],
           T#20         |->  A#21,
           S#2          |->  A#22[(var X#8)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=(letrec {X#1=A#22[(var X#8)]} in A#19[A#21[(var X#1)]]);E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[A#22[(\ X#6.S#10)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= (letrec {X#1=S#2} in A#19[A#21[(app A#22[(var X#8)] T#23[(var X#1)])]])
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[S#2])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#18,T#4,T#3,A#11,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[A#21[(app A#22[(var X#8)] T#23)]]),
             (S#2,A#19[A#21[(app A#22[(var X#8)] T#23)]]),
             (A#19[A#21[(app A#22[(var X#8)] T#23[(dummy3 )])]],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[A#21[(app A#22[(var X#8)] T#23[[.]])]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[S#2])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=[.];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  A#19,
           T#4          |->  A#19[A#21[(app A#22[(var X#8)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=(letrec {X#1=S#2} in A#19[A#21[(app A#22[(var X#8)] T#23[(var X#1)])]]);E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= (letrec {X#1=A#11[(var X#8)]} in A#19[(var X#1)])
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#11[(\ X#6.S#10)]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,T#3,A#11,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[[.]]),
             (A#11[(var X#8)],A#19[[.]]),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=[.];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  A#19,
           T#4          |->  A#19[[.]],
           T#20         |->  [.],
           S#2          |->  A#11[(var X#8)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#11[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=(letrec {X#1=A#11[(var X#8)]} in A#19[(var X#1)]);E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#11[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#11[(\ X#6.S#10)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= (letrec {X#1=A#20[A#11[(var X#8)]]} in A#19[(var X#1)])
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#20[A#11[(\ X#6.S#10)]]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,T#3,A#11,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19),
             (A#20[A#11[(var X#8)]],A#19),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#20[A#11[(var X#8)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=[.];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[A#20[[.2]]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  A#19[A#20],
           T#4          |->  A#19,
           S#2          |->  A#20[A#11[(var X#8)]]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#20[A#11[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=(letrec {X#1=A#20[A#11[(var X#8)]]} in A#19[(var X#1)]);E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#20[A#11[(var X#8)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#20[A#11[(\ X#6.S#10)]]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= (letrec {X#1=S#2} in A#19[(app A#20[A#11[(var X#8)]] T#21[(var X#1)])])
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[A#11[(\ X#6.S#10)]] T#21[S#2])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[(app A#20[A#11[(var X#8)]] T#21)]),
             (S#2,A#19[(app A#20[A#11[(var X#8)]] T#21)]),
             (A#19[(app A#20[A#11[(var X#8)]] T#21[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[(app A#20[A#11[(var X#8)]] T#21[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=[.];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[S#2])]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           T#4          |->  A#19[(app A#20[A#11[(var X#8)]] T#21)],
           A#18         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[S#2])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=(letrec {X#1=S#2} in A#19[(app A#20[A#11[(var X#8)]] T#21[(var X#1)])]);E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[S#2])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(\ X#6.S#10)]] T#21[S#2])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= (letrec {X#1=(var X#8)} in A#19[(var X#1)])
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(\ X#6.S#10)]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,T#3,A#11,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[[.]]),
             ((var X#8),A#19[[.]]),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#19[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=[.];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  [.],
           A#11         |->  A#19,
           T#4          |->  A#19[[.]],
           T#20         |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(var X#8)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=(letrec {X#1=(var X#8)} in A#19[(var X#1)]);E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(var X#8)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(\ X#6.S#10)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= (letrec {X#1=A#20[(var X#8)]} in A#19[(var X#1)])
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#20[(\ X#6.S#10)]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,T#3,A#11,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),A#19),
             (A#20[(var X#8)],A#19),
             (A#19[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#20[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#19[A#20[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=[.];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  [.],
           A#11         |->  A#19[A#20],
           T#4          |->  A#19,
           S#2          |->  A#20[(var X#8)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#20[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=(letrec {X#1=A#20[(var X#8)]} in A#19[(var X#1)]);E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#20[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#20[(\ X#6.S#10)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= (letrec {X#1=S#2} in A#19[(app A#20[(var X#8)] T#21[(var X#1)])])
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[(\ X#6.S#10)] T#21[S#2])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),A#19[(app A#20[(var X#8)] T#21)]),
             (S#2,A#19[(app A#20[(var X#8)] T#21)]),
             (A#19[(app A#20[(var X#8)] T#21[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#19[(app A#20[(var X#8)] T#21[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#19[(app A#20[[.]] T#21[S#2])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=[.];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  [.],
           T#4          |->  A#19[(app A#20[(var X#8)] T#21)],
           A#11         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[S#2])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=(letrec {X#1=S#2} in A#19[(app A#20[(var X#8)] T#21[(var X#1)])]);E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[S#2])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(\ X#6.S#10)] T#21[S#2])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= (letrec {X#1=A#18[A#11[(var X#8)]]} in (var X#1))
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#18[A#11[(\ X#6.S#10)]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#18[A#11[(var X#8)]],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#18[A#11[(var X#8)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=[.];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#18[A#11[(var X#8)]]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#18[A#11[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=(letrec {X#1=A#18[A#11[(var X#8)]]} in (var X#1));E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#18[A#11[(var X#8)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#18[A#11[(\ X#6.S#10)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(letrec {X#1=(var X#19)} in (var X#1))]
       ;E#9
       ;EE#20[X#19,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(var X#19)]
       ;E#9
       ;EE#20[X#19,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#19),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#19),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#21[[.]];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#21[(var X#19)];EE#20[X#19,[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[[.]],
           T#22         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#19)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(var X#19)];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#21[(letrec {X#1=(var X#19)} in (var X#1))];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(var X#19)];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#21[(var X#19)];E#9;EE#20[X#19,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(letrec {X#1=(var X#19)} in A#23[(var X#1)])]
       ;E#9
       ;EE#20[X#19,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[A#23[(var X#19)]]
       ;E#9
       ;EE#20[X#19,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,A#18,T#15,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[[.]]),
             ((var X#19),A#23[[.]]),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#19),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#21;E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#21[A#23[(var X#19)]];EE#20[X#19,[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21[A#23],
           T#15         |->  A#21,
           A#22         |->  A#23,
           T#4          |->  A#23[[.]],
           T#24         |->  [.],
           S#2          |->  (var X#19)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[A#23[(var X#19)]];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#21[(letrec {X#1=(var X#19)} in A#23[(var X#1)])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[A#23[(var X#19)]];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#21[A#23[(var X#19)]];E#9;EE#20[X#19,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(letrec {X#1=A#24[(var X#19)]} in A#23[(var X#1)])]
       ;E#9
       ;EE#20[X#19,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[A#23[A#24[(var X#19)]]]
       ;E#9
       ;EE#20[X#19,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,A#18,T#15,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23),
             (A#24[(var X#19)],A#23),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#24[(var X#19)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#21;E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#21[A#23[A#24[(var X#19)]]];EE#20[X#19,[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21[A#23[A#24]],
           T#15         |->  A#21,
           A#22         |->  A#23[A#24],
           T#4          |->  A#23,
           S#2          |->  A#24[(var X#19)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[A#23[A#24[(var X#19)]]];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#21[(letrec {X#1=A#24[(var X#19)]} in A#23[(var X#1)])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[A#23[A#24[(var X#19)]]];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#21[A#23[A#24[(var X#19)]]];E#9;EE#20[X#19,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(letrec {X#1=S#2} in A#23[(app A#24[(var X#19)] T#25[(var X#1)])])]
       ;E#9
       ;EE#20[X#19,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[A#23[(app A#24[(var X#19)] T#25[S#2])]]
       ;E#9
       ;EE#20[X#19,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,A#18,T#15,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[(app A#24[(var X#19)] T#25)]),
             (S#2,A#23[(app A#24[(var X#19)] T#25)]),
             (A#23[(app A#24[(var X#19)] T#25[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[(app A#24[(var X#19)] T#25[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#21;E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#21[A#23[(app A#24[(var X#19)] T#25[S#2])]];EE#20[X#19,[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21[A#23[(app A#24 T#25[S#2])]],
           T#15         |->  A#21,
           T#4          |->  A#23[(app A#24[(var X#19)] T#25)],
           A#22         |->  A#23[(app A#24 T#25[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[A#23[(app A#24[(var X#19)] T#25[S#2])]];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#21[(letrec {X#1=S#2} in A#23[(app A#24[(var X#19)] T#25[(var X#1)])])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[A#23[(app A#24[(var X#19)] T#25[S#2])]];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#21[A#23[(app A#24[(var X#19)] T#25[S#2])]];E#9;EE#20[X#19,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(letrec {X#1=A#22[(var X#19)]} in (var X#1))]
       ;E#9
       ;EE#20[X#19,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[A#22[(var X#19)]]
       ;E#9
       ;EE#20[X#19,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#22[(var X#19)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#19)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#21;E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#21[A#22[(var X#19)]];EE#20[X#19,[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21[A#22],
           T#15         |->  A#21,
           T#4          |->  [.],
           S#2          |->  A#22[(var X#19)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[A#22[(var X#19)]];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#21[(letrec {X#1=A#22[(var X#19)]} in (var X#1))];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[A#22[(var X#19)]];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#21[A#22[(var X#19)]];E#9;EE#20[X#19,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#9
       ;EE#20[X#19,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(app A#22[(var X#19)] T#23[T#4[S#2]])]
       ;E#9
       ;EE#20[X#19,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23)];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[T#4[S#2]])];EE#20[X#19,[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[T#4[S#2]])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[T#4[S#2]])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[T#4[S#2]])];E#9;EE#20[X#19,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= (letrec {X#1=(var X#19)} in A#21[(var X#1)])
       ;E#9
       ;EE#20[X#19,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(var X#19)]
       ;E#9
       ;EE#20[X#19,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[[.]]),
             ((var X#19),A#21[[.]]),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#19),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=[.];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#21[(var X#19)];EE#20[X#19,[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  A#21,
           T#4          |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  (var X#19)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(var X#19)];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=(letrec {X#1=(var X#19)} in A#21[(var X#1)]);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(var X#19)];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#21[(var X#19)];E#9;EE#20[X#19,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= (letrec {X#1=A#22[(var X#19)]} in A#21[(var X#1)])
       ;E#9
       ;EE#20[X#19,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[A#22[(var X#19)]]
       ;E#9
       ;EE#20[X#19,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21),
             (A#22[(var X#19)],A#21),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#19)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=[.];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#21[A#22[(var X#19)]];EE#20[X#19,[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  A#21[A#22],
           T#4          |->  A#21,
           S#2          |->  A#22[(var X#19)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[A#22[(var X#19)]];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=(letrec {X#1=A#22[(var X#19)]} in A#21[(var X#1)]);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[A#22[(var X#19)]];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#21[A#22[(var X#19)]];E#9;EE#20[X#19,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= (letrec {X#1=S#2} in A#21[(app A#22[(var X#19)] T#23[(var X#1)])])
       ;E#9
       ;EE#20[X#19,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(app A#22[(var X#19)] T#23[S#2])]
       ;E#9
       ;EE#20[X#19,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[(app A#22[(var X#19)] T#23)]),
             (S#2,A#21[(app A#22[(var X#19)] T#23)]),
             (A#21[(app A#22[(var X#19)] T#23[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[(app A#22[(var X#19)] T#23[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=[.];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[S#2])];EE#20[X#19,[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           T#4          |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[S#2])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=(letrec {X#1=S#2} in A#21[(app A#22[(var X#19)] T#23[(var X#1)])]);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[S#2])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[S#2])];E#9;EE#20[X#19,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= (letrec {X#1=A#18[(var X#19)]} in (var X#1))
       ;E#9
       ;EE#20[X#19,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#18[(var X#19)]
       ;E#9
       ;EE#20[X#19,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#18[(var X#19)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#18[(var X#19)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(\ X#6.S#10);X#7=[.];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#18[(var X#19)];EE#20[X#19,[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#18[(var X#19)]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#18[(var X#19)];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#5=(\ X#6.S#10);X#7=(letrec {X#1=A#18[(var X#19)]} in (var X#1));E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#18[(var X#19)];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#18[(var X#19)];E#9;EE#20[X#19,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(letrec {X#1=(var X#20)} in (var X#1))]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#23[(var X#20)]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#3,A#11,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#20),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#20),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#23[[.]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#23[(var X#20)];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           A#18         |->  A#23,
           T#15         |->  A#23[[.]],
           T#24         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#20)}

and instantiated rules:

                                  (letrec {X#19=A#23[(var X#20)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#23[(letrec {X#1=(var X#20)} in (var X#1))];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#23[(var X#20)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#23[(var X#20)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(letrec {X#1=(var X#20)} in A#25[(var X#1)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#23[A#25[(var X#20)]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#24,T#4,A#18,T#15,T#3,A#11,A#23,A#25}
   Delta2 = {}
   Delta3 = {((var X#1),A#25[[.]]),
             ((var X#20),A#25[[.]]),
             (A#25[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#20),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#25[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#23;X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#23[A#25[(var X#20)]];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           A#18         |->  A#23[A#25],
           T#15         |->  A#23,
           A#24         |->  A#25,
           T#4          |->  A#25[[.]],
           T#26         |->  [.],
           S#2          |->  (var X#20)}

and instantiated rules:

                                  (letrec {X#19=A#23[A#25[(var X#20)]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#23[(letrec {X#1=(var X#20)} in A#25[(var X#1)])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#23[A#25[(var X#20)]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#23[A#25[(var X#20)]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(letrec {X#1=A#26[(var X#20)]} in A#25[(var X#1)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#23[A#25[A#26[(var X#20)]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#24,T#4,A#18,T#15,T#3,A#11,A#23,A#25}
   Delta2 = {}
   Delta3 = {((var X#1),A#25),
             (A#26[(var X#20)],A#25),
             (A#25[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#26[(var X#20)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#25[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#23;X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#23[A#25[A#26[(var X#20)]]];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           A#18         |->  A#23[A#25[A#26]],
           T#15         |->  A#23,
           A#24         |->  A#25[A#26],
           T#4          |->  A#25,
           S#2          |->  A#26[(var X#20)]}

and instantiated rules:

                                  (letrec {X#19=A#23[A#25[A#26[(var X#20)]]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#23[(letrec {X#1=A#26[(var X#20)]} in A#25[(var X#1)])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#23[A#25[A#26[(var X#20)]]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#23[A#25[A#26[(var X#20)]]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(letrec {X#1=S#2} in A#25[(app A#26[(var X#20)] T#27[(var X#1)])])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#23[A#25[(app A#26[(var X#20)] T#27[S#2])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#24,T#4,A#18,T#15,T#3,A#11,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#25[(app A#26[(var X#20)] T#27)]),
             (S#2,A#25[(app A#26[(var X#20)] T#27)]),
             (A#25[(app A#26[(var X#20)] T#27[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#25[(app A#26[(var X#20)] T#27[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#23;X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#23[A#25[(app A#26[(var X#20)] T#27[S#2])]];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           A#18         |->  A#23[A#25[(app A#26 T#27[S#2])]],
           T#15         |->  A#23,
           T#4          |->  A#25[(app A#26[(var X#20)] T#27)],
           A#24         |->  A#25[(app A#26 T#27[S#2])]}

and instantiated rules:

                                  (letrec {X#19=A#23[A#25[(app A#26[(var X#20)] T#27[S#2])]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#23[(letrec {X#1=S#2} in A#25[(app A#26[(var X#20)] T#27[(var X#1)])])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#23[A#25[(app A#26[(var X#20)] T#27[S#2])]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#23[A#25[(app A#26[(var X#20)] T#27[S#2])]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(letrec {X#1=A#24[(var X#20)]} in (var X#1))]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#23[A#24[(var X#20)]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#3,A#11,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#24[(var X#20)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#24[(var X#20)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#23;X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#23[A#24[(var X#20)]];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           A#18         |->  A#23[A#24],
           T#15         |->  A#23,
           T#4          |->  [.],
           S#2          |->  A#24[(var X#20)]}

and instantiated rules:

                                  (letrec {X#19=A#23[A#24[(var X#20)]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#23[(letrec {X#1=A#24[(var X#20)]} in (var X#1))];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#23[A#24[(var X#20)]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#23[A#24[(var X#20)]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[T#4[S#2]])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[T#4[S#2]])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[T#4[S#2]])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(letrec {X#1=S#2} in T#4[(var X#1)])])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[T#4[S#2]])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[T#4[S#2]])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=(var X#20)} in A#23[(var X#1)])
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#23[(var X#20)]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,T#3,A#11,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[[.]]),
             ((var X#20),A#23[[.]]),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#20),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#23[(var X#20)];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  A#23,
           T#4          |->  A#23[[.]],
           T#24         |->  [.],
           S#2          |->  (var X#20)}

and instantiated rules:

                                  (letrec {X#19=A#23[(var X#20)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=(var X#20)} in A#23[(var X#1)]);X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#23[(var X#20)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#23[(var X#20)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=A#24[(var X#20)]} in A#23[(var X#1)])
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#23[A#24[(var X#20)]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,T#3,A#11,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23),
             (A#24[(var X#20)],A#23),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#24[(var X#20)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#23[A#24[(var X#20)]];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  A#23[A#24],
           T#4          |->  A#23,
           S#2          |->  A#24[(var X#20)]}

and instantiated rules:

                                  (letrec {X#19=A#23[A#24[(var X#20)]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=A#24[(var X#20)]} in A#23[(var X#1)]);X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#23[A#24[(var X#20)]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#23[A#24[(var X#20)]];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=S#2} in A#23[(app A#24[(var X#20)] T#25[(var X#1)])])
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[S#2])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[(app A#24[(var X#20)] T#25)]),
             (S#2,A#23[(app A#24[(var X#20)] T#25)]),
             (A#23[(app A#24[(var X#20)] T#25[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[(app A#24[(var X#20)] T#25[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[S#2])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           T#4          |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[S#2])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[S#2])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=S#2} in A#23[(app A#24[(var X#20)] T#25[(var X#1)])]);X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[S#2])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[S#2])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=A#18[(var X#20)]} in (var X#1))
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(var X#8)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#18[(var X#20)]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#18[(var X#20)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#18[(var X#20)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#18[(var X#20)];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#18[(var X#20)]}

and instantiated rules:

                                  (letrec {X#19=A#18[(var X#20)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=A#18[(var X#20)]} in (var X#1));X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#18[(var X#20)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#18[(var X#20)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(letrec {X#1=(var X#8)} in (var X#1))]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(\ X#6.S#10)]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#8),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21[A#23[[.]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[A#23[[.]]],
           A#11         |->  A#23,
           T#22         |->  A#23[[.]],
           T#24         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[A#23[(letrec {X#1=(var X#8)} in (var X#1))]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(\ X#6.S#10)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(letrec {X#1=(var X#8)} in A#25[(var X#1)])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[A#25[(\ X#6.S#10)]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#24,T#4,T#22,A#18,T#15,T#3,A#11,A#21,A#23,A#25}
   Delta2 = {}
   Delta3 = {((var X#1),A#25[[.]]),
             ((var X#8),A#25[[.]]),
             (A#25[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#25[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[A#25[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21[A#23];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[A#23],
           A#11         |->  A#23[A#25],
           T#22         |->  A#23,
           A#24         |->  A#25,
           T#4          |->  A#25[[.]],
           T#26         |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[A#25[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[A#23[(letrec {X#1=(var X#8)} in A#25[(var X#1)])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[A#25[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[A#25[(\ X#6.S#10)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(letrec {X#1=A#26[(var X#8)]} in A#25[(var X#1)])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[A#25[A#26[(\ X#6.S#10)]]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#24,T#4,T#22,A#18,T#15,T#3,A#11,A#21,A#23,A#25}
   Delta2 = {}
   Delta3 = {((var X#1),A#25),
             (A#26[(var X#8)],A#25),
             (A#25[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#26[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#25[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[A#25[A#26[[.]]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21[A#23];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[A#23],
           A#11         |->  A#23[A#25[A#26]],
           T#22         |->  A#23,
           A#24         |->  A#25[A#26],
           T#4          |->  A#25,
           S#2          |->  A#26[(var X#8)]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[A#25[A#26[(var X#8)]]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[A#23[(letrec {X#1=A#26[(var X#8)]} in A#25[(var X#1)])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[A#25[A#26[(var X#8)]]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[A#25[A#26[(\ X#6.S#10)]]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(letrec {X#1=S#2} in A#25[(app A#26[(var X#8)] T#27[(var X#1)])])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[A#25[(app A#26[(\ X#6.S#10)] T#27[S#2])]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#24,T#4,T#22,A#18,T#15,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#25[(app A#26[(var X#8)] T#27)]),
             (S#2,A#25[(app A#26[(var X#8)] T#27)]),
             (A#25[(app A#26[(var X#8)] T#27[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#25[(app A#26[(var X#8)] T#27[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[A#25[(app A#26[[.]] T#27[S#2])]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21[A#23];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[A#23],
           A#11         |->  A#23[A#25[(app A#26 T#27[S#2])]],
           T#22         |->  A#23,
           T#4          |->  A#25[(app A#26[(var X#8)] T#27)],
           A#24         |->  A#25[(app A#26 T#27[S#2])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[A#25[(app A#26[(var X#8)] T#27[S#2])]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[A#23[(letrec {X#1=S#2} in A#25[(app A#26[(var X#8)] T#27[(var X#1)])])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[A#25[(app A#26[(var X#8)] T#27[S#2])]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[A#25[(app A#26[(\ X#6.S#10)] T#27[S#2])]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(letrec {X#1=A#24[(var X#8)]} in (var X#1))]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[A#24[(\ X#6.S#10)]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#24[(var X#8)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#24[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[A#24[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21[A#23];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[A#23],
           A#11         |->  A#23[A#24],
           T#22         |->  A#23,
           T#4          |->  [.],
           S#2          |->  A#24[(var X#8)]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[A#24[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[A#23[(letrec {X#1=A#24[(var X#8)]} in (var X#1))]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[A#24[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[A#24[(\ X#6.S#10)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[A#23[(app A#24[(var X#8)] T#25[(letrec {X#1=S#2} in T#4[(var X#1)])])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[T#4[S#2]])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[(app A#24[[.]] T#25[T#4[S#2]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[A#23[(app A#24[(var X#8)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#8)] T#25)],
           A#11         |->  A#23[(app A#24 T#25[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[T#4[S#2]])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[(letrec {X#1=S#2} in T#4[(var X#1)])])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[T#4[S#2]])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[T#4[S#2]])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=(var X#8)} in A#23[(var X#1)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(\ X#6.S#10)]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#18,T#15,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[[.]]),
             ((var X#8),A#23[[.]]),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21[[.]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[[.]],
           T#22         |->  [.],
           A#11         |->  A#23,
           T#4          |->  A#23[[.]],
           T#24         |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=(var X#8)} in A#23[(var X#1)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(\ X#6.S#10)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=A#24[(var X#8)]} in A#23[(var X#1)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[A#24[(\ X#6.S#10)]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#18,T#15,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23),
             (A#24[(var X#8)],A#23),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#24[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[A#24[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21[[.]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[[.]],
           T#22         |->  [.],
           A#11         |->  A#23[A#24],
           T#4          |->  A#23,
           S#2          |->  A#24[(var X#8)]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[A#24[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=A#24[(var X#8)]} in A#23[(var X#1)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[A#24[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[A#24[(\ X#6.S#10)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=S#2} in A#23[(app A#24[(var X#8)] T#25[(var X#1)])])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[S#2])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#18,T#15,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[(app A#24[(var X#8)] T#25)]),
             (S#2,A#23[(app A#24[(var X#8)] T#25)]),
             (A#23[(app A#24[(var X#8)] T#25[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[(app A#24[(var X#8)] T#25[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[(app A#24[[.]] T#25[S#2])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21[[.]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[[.]],
           T#22         |->  [.],
           T#4          |->  A#23[(app A#24[(var X#8)] T#25)],
           A#11         |->  A#23[(app A#24 T#25[S#2])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=S#2} in A#23[(app A#24[(var X#8)] T#25[(var X#1)])])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=A#11[(var X#8)]} in (var X#1))]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#11[(\ X#6.S#10)]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#11[(var X#8)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21[[.]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[[.]],
           T#22         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#11[(var X#8)]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#11[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=A#11[(var X#8)]} in (var X#1))];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#11[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#11[(\ X#6.S#10)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=(var X#8)} in A#23[A#25[(var X#1)]])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[A#25[(\ X#6.S#10)]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#24,A#22,T#4,A#18,T#15,T#3,A#11,A#21,A#23,A#25}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[A#25[[.]]]),
             ((var X#8),A#23[A#25[[.]]]),
             (A#23[A#25[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[A#25[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#25[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21;X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[A#23[[.2]]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21[A#23],
           T#15         |->  A#21,
           A#22         |->  A#23,
           T#4          |->  A#23[A#25[[.]]],
           A#11         |->  A#25,
           T#24         |->  A#25[[.]],
           T#26         |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[A#25[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=(var X#8)} in A#23[A#25[(var X#1)]])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[A#25[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[A#25[(\ X#6.S#10)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=A#26[(var X#8)]} in A#23[A#25[(var X#1)]])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[A#25[A#26[(\ X#6.S#10)]]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#24,A#22,T#4,A#18,T#15,T#3,A#11,A#21,A#23,A#25}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[A#25]),
             (A#26[(var X#8)],A#23[A#25]),
             (A#23[A#25[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             (A#26[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[A#25[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#25[A#26[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21;X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[A#23[[.2]]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21[A#23],
           T#15         |->  A#21,
           A#22         |->  A#23,
           T#4          |->  A#23[A#25],
           A#11         |->  A#25[A#26],
           T#24         |->  A#25,
           S#2          |->  A#26[(var X#8)]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[A#25[A#26[(var X#8)]]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=A#26[(var X#8)]} in A#23[A#25[(var X#1)]])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[A#25[A#26[(var X#8)]]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[A#25[A#26[(\ X#6.S#10)]]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=S#2} in A#23[A#25[(app A#26[(var X#8)] T#27[(var X#1)])]])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[A#25[(app A#26[(\ X#6.S#10)] T#27[S#2])]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#24,A#22,T#4,A#18,T#15,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[A#25[(app A#26[(var X#8)] T#27)]]),
             (S#2,A#23[A#25[(app A#26[(var X#8)] T#27)]]),
             (A#23[A#25[(app A#26[(var X#8)] T#27[(dummy3 )])]],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[A#25[(app A#26[(var X#8)] T#27[[.]])]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#25[(app A#26[[.]] T#27[S#2])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21;X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[A#23[[.2]]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21[A#23],
           T#15         |->  A#21,
           A#22         |->  A#23,
           T#4          |->  A#23[A#25[(app A#26[(var X#8)] T#27)]],
           T#24         |->  A#25[(app A#26[(var X#8)] T#27)],
           A#11         |->  A#25[(app A#26 T#27[S#2])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[A#25[(app A#26[(var X#8)] T#27[S#2])]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=S#2} in A#23[A#25[(app A#26[(var X#8)] T#27[(var X#1)])]])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[A#25[(app A#26[(var X#8)] T#27[S#2])]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[A#25[(app A#26[(\ X#6.S#10)] T#27[S#2])]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=A#11[(var X#8)]} in A#23[(var X#1)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[A#11[(\ X#6.S#10)]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,A#18,T#15,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[[.]]),
             (A#11[(var X#8)],A#23[[.]]),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21;X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[A#23[[.2]]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21[A#23],
           T#15         |->  A#21,
           A#22         |->  A#23,
           T#4          |->  A#23[[.]],
           T#24         |->  [.],
           S#2          |->  A#11[(var X#8)]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[A#11[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=A#11[(var X#8)]} in A#23[(var X#1)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[A#11[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[A#11[(\ X#6.S#10)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=A#24[A#11[(var X#8)]]} in A#23[(var X#1)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[A#24[A#11[(\ X#6.S#10)]]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,A#18,T#15,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23),
             (A#24[A#11[(var X#8)]],A#23),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#24[A#11[(var X#8)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21;X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[A#23[A#24[[.2]]]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21[A#23[A#24]],
           T#15         |->  A#21,
           A#22         |->  A#23[A#24],
           T#4          |->  A#23,
           S#2          |->  A#24[A#11[(var X#8)]]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[A#24[A#11[(var X#8)]]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=A#24[A#11[(var X#8)]]} in A#23[(var X#1)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[A#24[A#11[(var X#8)]]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[A#24[A#11[(\ X#6.S#10)]]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=S#2} in A#23[(app A#24[A#11[(var X#8)]] T#25[(var X#1)])])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[A#11[(\ X#6.S#10)]] T#25[S#2])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,A#18,T#15,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[(app A#24[A#11[(var X#8)]] T#25)]),
             (S#2,A#23[(app A#24[A#11[(var X#8)]] T#25)]),
             (A#23[(app A#24[A#11[(var X#8)]] T#25[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[(app A#24[A#11[(var X#8)]] T#25[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21;X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[A#23[(app A#24[[.2]] T#25[S#2])]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21[A#23[(app A#24 T#25[S#2])]],
           T#15         |->  A#21,
           T#4          |->  A#23[(app A#24[A#11[(var X#8)]] T#25)],
           A#22         |->  A#23[(app A#24 T#25[S#2])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[A#11[(var X#8)]] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=S#2} in A#23[(app A#24[A#11[(var X#8)]] T#25[(var X#1)])])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[A#11[(var X#8)]] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(app A#24[A#11[(\ X#6.S#10)]] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=(var X#8)} in A#23[(var X#1)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(\ X#6.S#10)]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#18,T#15,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[[.]]),
             ((var X#8),A#23[[.]]),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21;X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21[[.]],
           T#15         |->  A#21,
           A#22         |->  [.],
           A#11         |->  A#23,
           T#4          |->  A#23[[.]],
           T#24         |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=(var X#8)} in A#23[(var X#1)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(\ X#6.S#10)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=A#24[(var X#8)]} in A#23[(var X#1)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[A#24[(\ X#6.S#10)]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#18,T#15,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23),
             (A#24[(var X#8)],A#23),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#24[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[A#24[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21;X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21[[.]],
           T#15         |->  A#21,
           A#22         |->  [.],
           A#11         |->  A#23[A#24],
           T#4          |->  A#23,
           S#2          |->  A#24[(var X#8)]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[A#24[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=A#24[(var X#8)]} in A#23[(var X#1)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[A#24[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[A#24[(\ X#6.S#10)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=S#2} in A#23[(app A#24[(var X#8)] T#25[(var X#1)])])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[S#2])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#18,T#15,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[(app A#24[(var X#8)] T#25)]),
             (S#2,A#23[(app A#24[(var X#8)] T#25)]),
             (A#23[(app A#24[(var X#8)] T#25[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[(app A#24[(var X#8)] T#25[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[(app A#24[[.]] T#25[S#2])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21;X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21[[.]],
           T#15         |->  A#21,
           A#22         |->  [.],
           T#4          |->  A#23[(app A#24[(var X#8)] T#25)],
           A#11         |->  A#23[(app A#24 T#25[S#2])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=S#2} in A#23[(app A#24[(var X#8)] T#25[(var X#1)])])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=A#22[A#11[(var X#8)]]} in (var X#1))]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#22[A#11[(\ X#6.S#10)]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#22[A#11[(var X#8)]],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#22[A#11[(var X#8)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21;X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[A#22[[.2]]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21[A#22],
           T#15         |->  A#21,
           T#4          |->  [.],
           S#2          |->  A#22[A#11[(var X#8)]]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#22[A#11[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=A#22[A#11[(var X#8)]]} in (var X#1))];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#22[A#11[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#22[A#11[(\ X#6.S#10)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[A#11[(var X#8)]] T#23[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[T#4[S#2]])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[T#4[S#2]])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  A#21[(app A#22[A#11[(var X#8)]] T#23)],
           A#18         |->  A#21[(app A#22 T#23[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[T#4[S#2]])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[(letrec {X#1=S#2} in T#4[(var X#1)])])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[T#4[S#2]])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[T#4[S#2]])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=(var X#8)} in (var X#1))]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[(\ X#6.S#10)]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((var X#8),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21[[.]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           A#11         |->  A#21,
           T#15         |->  A#21[[.]],
           T#22         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#19=A#21[(var X#8)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=(var X#8)} in (var X#1))];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[(var X#8)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(\ X#6.S#10)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=(var X#8)} in A#23[(var X#1)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(\ X#6.S#10)]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,T#15,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[[.]]),
             ((var X#8),A#23[[.]]),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[A#23[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21;X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           A#11         |->  A#21[A#23],
           T#15         |->  A#21,
           A#22         |->  A#23,
           T#4          |->  A#23[[.]],
           T#24         |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=(var X#8)} in A#23[(var X#1)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(\ X#6.S#10)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=A#24[(var X#8)]} in A#23[(var X#1)])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[A#24[(\ X#6.S#10)]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,T#15,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#23),
             (A#24[(var X#8)],A#23),
             (A#23[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#24[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[A#23[A#24[[.]]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21;X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           A#11         |->  A#21[A#23[A#24]],
           T#15         |->  A#21,
           A#22         |->  A#23[A#24],
           T#4          |->  A#23,
           S#2          |->  A#24[(var X#8)]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[A#24[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=A#24[(var X#8)]} in A#23[(var X#1)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[A#24[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[A#24[(\ X#6.S#10)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=S#2} in A#23[(app A#24[(var X#8)] T#25[(var X#1)])])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[S#2])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#22,T#4,T#15,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#23[(app A#24[(var X#8)] T#25)]),
             (S#2,A#23[(app A#24[(var X#8)] T#25)]),
             (A#23[(app A#24[(var X#8)] T#25[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#23[(app A#24[(var X#8)] T#25[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[A#23[(app A#24[[.]] T#25[S#2])]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21;X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           A#11         |->  A#21[A#23[(app A#24 T#25[S#2])]],
           T#15         |->  A#21,
           T#4          |->  A#23[(app A#24[(var X#8)] T#25)],
           A#22         |->  A#23[(app A#24 T#25[S#2])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=S#2} in A#23[(app A#24[(var X#8)] T#25[(var X#1)])])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(letrec {X#1=A#22[(var X#8)]} in (var X#1))]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#22[(\ X#6.S#10)]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#22[(var X#8)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[A#22[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21;X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           A#11         |->  A#21[A#22],
           T#15         |->  A#21,
           T#4          |->  [.],
           S#2          |->  A#22[(var X#8)]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#22[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(letrec {X#1=A#22[(var X#8)]} in (var X#1))];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#22[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#22[(\ X#6.S#10)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(\ X#6.S#10)] T#23[T#4[S#2]])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[T#4[S#2]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           T#15         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[T#4[S#2]])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(letrec {X#1=S#2} in T#4[(var X#1)])])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[T#4[S#2]])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[(\ X#6.S#10)] T#23[T#4[S#2]])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=(var X#8)} in A#21[A#23[(var X#1)]])
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(\ X#6.S#10)]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#18,T#4,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[A#23[[.]]]),
             ((var X#8),A#21[A#23[[.]]]),
             (A#21[A#23[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[A#23[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  A#21,
           T#4          |->  A#21[A#23[[.]]],
           A#11         |->  A#23,
           T#22         |->  A#23[[.]],
           T#24         |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=(var X#8)} in A#21[A#23[(var X#1)]]);X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(\ X#6.S#10)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=A#24[(var X#8)]} in A#21[A#23[(var X#1)]])
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[A#24[(\ X#6.S#10)]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#18,T#4,T#3,A#11,A#21,A#23}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[A#23]),
             (A#24[(var X#8)],A#21[A#23]),
             (A#21[A#23[(dummy3 )]],(letrec {X#1=(dummy3 )} in [.])),
             (A#24[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[A#23[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[A#24[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  A#21,
           T#4          |->  A#21[A#23],
           A#11         |->  A#23[A#24],
           T#22         |->  A#23,
           S#2          |->  A#24[(var X#8)]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[A#24[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=A#24[(var X#8)]} in A#21[A#23[(var X#1)]]);X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[A#24[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[A#24[(\ X#6.S#10)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=S#2} in A#21[A#23[(app A#24[(var X#8)] T#25[(var X#1)])]])
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[S#2])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#18,T#4,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[A#23[(app A#24[(var X#8)] T#25)]]),
             (S#2,A#21[A#23[(app A#24[(var X#8)] T#25)]]),
             (A#21[A#23[(app A#24[(var X#8)] T#25[(dummy3 )])]],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[A#23[(app A#24[(var X#8)] T#25[[.]])]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[(app A#24[[.]] T#25[S#2])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  A#21,
           T#4          |->  A#21[A#23[(app A#24[(var X#8)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#8)] T#25)],
           A#11         |->  A#23[(app A#24 T#25[S#2])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=S#2} in A#21[A#23[(app A#24[(var X#8)] T#25[(var X#1)])]]);X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=A#11[(var X#8)]} in A#21[(var X#1)])
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#11[(\ X#6.S#10)]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[[.]]),
             (A#11[(var X#8)],A#21[[.]]),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  A#21,
           T#4          |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  A#11[(var X#8)]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#11[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=A#11[(var X#8)]} in A#21[(var X#1)]);X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#11[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#11[(\ X#6.S#10)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=A#22[A#11[(var X#8)]]} in A#21[(var X#1)])
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#22[A#11[(\ X#6.S#10)]]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21),
             (A#22[A#11[(var X#8)]],A#21),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[A#11[(var X#8)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[A#22[[.2]]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  A#21[A#22],
           T#4          |->  A#21,
           S#2          |->  A#22[A#11[(var X#8)]]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#22[A#11[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=A#22[A#11[(var X#8)]]} in A#21[(var X#1)]);X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#22[A#11[(var X#8)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#22[A#11[(\ X#6.S#10)]]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=S#2} in A#21[(app A#22[A#11[(var X#8)]] T#23[(var X#1)])])
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[S#2])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#4,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[(app A#22[A#11[(var X#8)]] T#23)]),
             (S#2,A#21[(app A#22[A#11[(var X#8)]] T#23)]),
             (A#21[(app A#22[A#11[(var X#8)]] T#23[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[(app A#22[A#11[(var X#8)]] T#23[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[S#2])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           T#4          |->  A#21[(app A#22[A#11[(var X#8)]] T#23)],
           A#18         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[S#2])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=S#2} in A#21[(app A#22[A#11[(var X#8)]] T#23[(var X#1)])]);X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[S#2])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[S#2])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=(var X#8)} in A#21[(var X#1)])
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[(\ X#6.S#10)]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[[.]]),
             ((var X#8),A#21[[.]]),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#8),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  [.],
           A#11         |->  A#21,
           T#4          |->  A#21[[.]],
           T#22         |->  [.],
           S#2          |->  (var X#8)}

and instantiated rules:

                                  (letrec {X#19=A#21[(var X#8)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=(var X#8)} in A#21[(var X#1)]);X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[(var X#8)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(\ X#6.S#10)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=A#22[(var X#8)]} in A#21[(var X#1)])
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[A#22[(\ X#6.S#10)]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,T#3,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),A#21),
             (A#22[(var X#8)],A#21),
             (A#21[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#22[(var X#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[A#22[[.]]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  [.],
           A#11         |->  A#21[A#22],
           T#4          |->  A#21,
           S#2          |->  A#22[(var X#8)]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#22[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=A#22[(var X#8)]} in A#21[(var X#1)]);X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[A#22[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#22[(\ X#6.S#10)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=S#2} in A#21[(app A#22[(var X#8)] T#23[(var X#1)])])
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(\ X#6.S#10)] T#23[S#2])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),A#21[(app A#22[(var X#8)] T#23)]),
             (S#2,A#21[(app A#22[(var X#8)] T#23)]),
             (A#21[(app A#22[(var X#8)] T#23[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),A#21[(app A#22[(var X#8)] T#23[[.]])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[S#2])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           A#18         |->  [.],
           T#4          |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[S#2])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=S#2} in A#21[(app A#22[(var X#8)] T#23[(var X#1)])]);X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[S#2])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[(\ X#6.S#10)] T#23[S#2])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#19= (letrec {X#1=A#18[A#11[(var X#8)]]} in (var X#1))
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
    ,
     (letrec
        X#19= A#18[A#11[(\ X#6.S#10)]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#3,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             (A#18[A#11[(var X#8)]],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#18[A#11[(var X#8)]],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#19=[.];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#18[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#18[A#11[(var X#8)]]}

and instantiated rules:

                                  (letrec {X#19=A#18[A#11[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#19=(letrec {X#1=A#18[A#11[(var X#8)]]} in (var X#1));X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    ................................................................................
                                  (letrec {X#19=A#18[A#11[(var X#8)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#18[A#11[(\ X#6.S#10)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (\ X#6.S#10)
          ;E#9
          ;EE#13[X#7,A#11[(var X#8)]]
          ;VV#14|X#8,(var X#5)|
        in
           A#16[(app A#17[(var X#7)] T#18[(var X#1)])]
        )
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#16[(app A#17[(var X#7)] T#18[S#2])]
     )
  )

where

   Delta1 = {A#12,T#15,T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18)])),
             (S#2,(letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18)])),
             ((letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[[.]])])),
             ((var X#5),[.]),
             ((var X#7),A#16[(app A#17[[.]] T#18[S#2])]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#16[(app A#17[[.]] T#18[S#2])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18)]),
           T#15  |->  A#16[(app A#17[(var X#7)] T#18)],
           A#12  |->  A#16[(app A#17 T#18[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[S#2])])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[(var X#1)])]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[S#2])])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#16[(app A#17[(var X#7)] T#18[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (\ X#6.S#10)
     in
        (letrec
           X#5= (var X#1)
          ;E#9
          ;EE#13[X#7,A#11[(var X#8)]]
          ;VV#14|X#8,(var X#5)|
        in
           A#12[(var X#7)]
        )
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=[.];E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((\ X#6.S#10),(letrec {X#5=[.];E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((letrec {X#5=(dummy3 );E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             ((\ X#6.S#10),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=[.];E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=[.];E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           X#16  |->  X#5,
           E#17  |->  {E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15  |->  [.],
           S#2   |->  (\ X#6.S#10)}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#1=(\ X#6.S#10)} in (letrec {X#5=(var X#1);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#16= T#15[(var X#1)]
          ;X#5= (\ X#6.S#10)
          ;E#18
          ;EE#13[X#7,A#11[(var X#8)]]
          ;VV#14|X#8,(var X#5)|
        in
           A#12[(var X#7)]
        )
     )
    ,
     (letrec
        X#16= T#15[S#2]
       ;X#5= (\ X#6.S#10)
       ;E#18
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#16=T#15;X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             (S#2,(letrec {X#16=T#15;X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((letrec {X#16=T#15[(dummy3 )];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#16=T#15[[.]];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#16=T#15;X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           E#9   |->  {X#16=T#15[S#2];E#18},
           E#17  |->  {X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|}}

and instantiated rules:

                                  (letrec {X#16=T#15[S#2];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#16=T#15[(var X#1)];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]))
    ................................................................................
                                  (letrec {X#16=T#15[S#2];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#16=T#15[S#2];X#5=(\ X#6.S#10);E#18;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (\ X#6.S#10)
          ;X#7= A#19[A#21[(app A#22[(var X#8)] T#23[(var X#1)])]]
          ;E#9
          ;VV#14|X#8,(var X#5)|
        in
           A#12[(var X#7)]
        )
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[S#2])]]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#20,A#18,T#15,T#4,A#11,A#19}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             (S#2,(letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[(dummy3 )])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[[.]])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[S#2])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23)]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  A#19,
           T#15         |->  A#19[A#21[(app A#22[(var X#8)] T#23)]],
           T#20         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[(var X#1)])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(var X#8)] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[A#21[(app A#22[(\ X#6.S#10)] T#23[S#2])]];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (\ X#6.S#10)
          ;X#7= A#19[(app A#20[A#11[(var X#8)]] T#21[(var X#1)])]
          ;E#9
          ;VV#14|X#8,(var X#5)|
        in
           A#12[(var X#7)]
        )
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[A#11[(\ X#6.S#10)]] T#21[S#2])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             (S#2,(letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[(dummy3 )])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[[.]])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#19[(app A#20[[.2]] T#21[S#2])]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           T#15         |->  A#19[(app A#20[A#11[(var X#8)]] T#21)],
           A#18         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[S#2])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[(var X#1)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(var X#8)]] T#21[S#2])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[A#11[(\ X#6.S#10)]] T#21[S#2])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (\ X#6.S#10)
          ;X#7= A#19[(app A#20[(var X#8)] T#21[(var X#1)])]
          ;E#9
          ;VV#14|X#8,(var X#5)|
        in
           A#12[(var X#7)]
        )
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#19[(app A#20[(\ X#6.S#10)] T#21[S#2])]
       ;E#9
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             (S#2,(letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[(dummy3 )])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[[.]])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#19[(app A#20[[.]] T#21[S#2])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21)];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=[.2]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           T#15         |->  A#19[(app A#20[(var X#8)] T#21)],
           A#11         |->  A#19[(app A#20 T#21[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[S#2])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[(var X#1)])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(var X#8)] T#21[S#2])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#19[(app A#20[(\ X#6.S#10)] T#21[S#2])];E#9;VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (\ X#6.S#10)
          ;X#7= A#21[(app A#22[(var X#19)] T#23[(var X#1)])]
          ;E#9
          ;EE#20[X#19,A#11[(var X#8)]]
          ;VV#14|X#8,(var X#5)|
        in
           A#12[(var X#7)]
        )
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;X#7= A#21[(app A#22[(var X#19)] T#23[S#2])]
       ;E#9
       ;EE#20[X#19,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23)];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             (S#2,(letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23)];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(dummy3 )])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[[.]])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23)];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {[.1]=A#21[(app A#22[(var X#19)] T#23[S#2])];EE#20[X#19,[.2]]},
           X#16         |->  X#7,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  A#21[(app A#22[(var X#19)] T#23)],
           A#18         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[S#2])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[(var X#1)])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[S#2])];E#9;EE#20[X#19,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);X#7=A#21[(app A#22[(var X#19)] T#23[S#2])];E#9;EE#20[X#19,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#19= A#23[(app A#24[(var X#20)] T#25[(var X#1)])]
          ;X#5= (\ X#6.S#10)
          ;E#9
          ;EE#21[X#7,(var X#19)]
          ;EE#22[X#20,A#11[(var X#8)]]
          ;VV#14|X#8,(var X#5)|
        in
           A#12[(var X#7)]
        )
     )
    ,
     (letrec
        X#19= A#23[(app A#24[(var X#20)] T#25[S#2])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#21[X#7,(var X#19)]
       ;EE#22[X#20,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             (S#2,(letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(dummy3 )])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#19=A#23[(app A#24[(var X#20)] T#25[[.]])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25)];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#23[(app A#24[(var X#20)] T#25[S#2])];EE#21[[.1],(var X#19)];EE#22[X#20,[.2]]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|},
           T#15         |->  A#23[(app A#24[(var X#20)] T#25)],
           A#18         |->  A#23[(app A#24 T#25[S#2])]}

and instantiated rules:

                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[S#2])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[(var X#1)])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]))
    ................................................................................
                                  (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[S#2])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#23[(app A#24[(var X#20)] T#25[S#2])];X#5=(\ X#6.S#10);E#9;EE#21[X#7,(var X#19)];EE#22[X#20,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#19= A#21[A#23[(app A#24[(var X#8)] T#25[(var X#1)])]]
          ;X#5= (\ X#6.S#10)
          ;E#9
          ;EE#20[X#7,(var X#19)]
          ;VV#14|X#8,(var X#5)|
        in
           A#12[(var X#7)]
        )
     )
    ,
     (letrec
        X#19= A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[S#2])]]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#22,A#18,T#15,T#4,A#11,A#21}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             (S#2,(letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[(dummy3 )])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[[.]])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#23[(app A#24[[.]] T#25[S#2])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25)]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[[.2]];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  A#21,
           T#15         |->  A#21[A#23[(app A#24[(var X#8)] T#25)]],
           T#22         |->  A#23[(app A#24[(var X#8)] T#25)],
           A#11         |->  A#23[(app A#24 T#25[S#2])]}

and instantiated rules:

                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[(var X#1)])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]))
    ................................................................................
                                  (letrec {X#19=A#21[A#23[(app A#24[(var X#8)] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[A#23[(app A#24[(\ X#6.S#10)] T#25[S#2])]];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#19= A#21[(app A#22[A#11[(var X#8)]] T#23[(var X#1)])]
          ;X#5= (\ X#6.S#10)
          ;E#9
          ;EE#20[X#7,(var X#19)]
          ;VV#14|X#8,(var X#5)|
        in
           A#12[(var X#7)]
        )
     )
    ,
     (letrec
        X#19= A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[S#2])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#18,T#15,T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             (S#2,(letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[(dummy3 )])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[[.]])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=A#21[(app A#22[[.2]] T#23[S#2])];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           T#15         |->  A#21[(app A#22[A#11[(var X#8)]] T#23)],
           A#18         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[S#2])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[(var X#1)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]))
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[A#11[(var X#8)]] T#23[S#2])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[A#11[(\ X#6.S#10)]] T#23[S#2])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#19= A#21[(app A#22[(var X#8)] T#23[(var X#1)])]
          ;X#5= (\ X#6.S#10)
          ;E#9
          ;EE#20[X#7,(var X#19)]
          ;VV#14|X#8,(var X#5)|
        in
           A#12[(var X#7)]
        )
     )
    ,
     (letrec
        X#19= A#21[(app A#22[(\ X#6.S#10)] T#23[S#2])]
       ;X#5= (\ X#6.S#10)
       ;E#9
       ;EE#20[X#7,(var X#19)]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {T#15,T#4,A#11}
   Delta2 = {}
   Delta3 = {((var X#1),(letrec {X#19=A#21[(app A#22[(var X#8)] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             (S#2,(letrec {X#19=A#21[(app A#22[(var X#8)] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(dummy3 )])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),(letrec {X#19=A#21[(app A#22[(var X#8)] T#23[[.]])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#21[(app A#22[[.]] T#23[S#2])]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23)];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),
           EE#13[.1,.2] |-> {X#19=[.2];EE#20[[.1],(var X#19)]},
           X#16         |->  X#19,
           E#17         |->  {X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|},
           A#18         |->  [.],
           T#15         |->  A#21[(app A#22[(var X#8)] T#23)],
           A#11         |->  A#21[(app A#22 T#23[S#2])]}

and instantiated rules:

                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[S#2])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[(var X#1)])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]))
    ................................................................................
                                  (letrec {X#19=A#21[(app A#22[(var X#8)] T#23[S#2])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#19=A#21[(app A#22[(\ X#6.S#10)] T#23[S#2])];X#5=(\ X#6.S#10);E#9;EE#20[X#7,(var X#19)];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec
                X#5= (\ X#6.S#10)
               ;E#9
               ;EE#13[X#7,A#11[(var X#8)]]
               ;VV#14|X#8,(var X#5)|
             in
                A#12[(var X#7)]
             )
     in
        (var X#1)
     )
    ,
     (letrec
        X#5= (\ X#6.S#10)
       ;E#9
       ;EE#13[X#7,A#11[(\ X#6.S#10)]]
       ;VV#14|X#8,(var X#5)|
     in
        A#12[(var X#7)]
     )
  )

where

   Delta1 = {A#11}
   Delta2 = {}
   Delta3 = {((var X#1),[.]),
             ((letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)]),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]]),
             ((var X#8),A#11[[.]]),
             ((var X#5),[.]),
             ((var X#7),A#12[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,cp-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    and constraints: A#11/= [.]

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}
      Delta1=  {A#11}
      Delta2=  {}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#1),T#4[[.]]),((var X#5),[.]),((var X#7),A#12[[.]]),((var X#8),A#11[[.]]),((var X#5),[.]),((var X#7),A#12[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  [.],
           S#2  |->  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])}

and instantiated rules:

                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -ucp3->                       (letrec {X#1=(letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])} in (var X#1))
    ................................................................................
                                  (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(var X#8)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    -SR,cp-e2->                   (letrec {X#5=(\ X#6.S#10);E#9;EE#13[X#7,A#11[(\ X#6.S#10)]];VV#14|X#8,(var X#5)|} in A#12[(var X#7)])
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (letrec {E#6} in T#9[(letrec {X#1=S#2} in T#4[(var X#1)])]))
    ,
     (letrec {E#5;E#6} in T#9[T#4[S#2]])
  )

where

   Delta1 = {T#8,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             [{E#5},(letrec {E#6} in [.])],
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),[{E#5},(letrec {E#6} in [.])],((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  (letrec {E#5} in (letrec {E#6} in T#9)),
           T#8  |->  (letrec {E#6} in T#9),
           S#7  |->  T#9[T#4[S#2]]}

and instantiated rules:

                                  (letrec {E#5} in (letrec {E#6} in T#9[T#4[S#2]]))
    -ucp3->                       (letrec {E#5} in (letrec {E#6} in T#9[(letrec {X#1=S#2} in T#4[(var X#1)])]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in T#9[T#4[S#2]]))
    -SR,llet-in1->                (letrec {E#5;E#6} in T#9[T#4[S#2]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (letrec {X#10=T#9[(letrec {X#1=S#2} in T#4[(var X#1)])];E#12} in S#7)
     )
    ,
     (letrec {X#10=T#9[T#4[S#2]];E#12;E#5} in S#7)
  )

where

   Delta1 = {T#8,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             [{E#5},(letrec {X#10=T#9[T#4[S#2]];E#12} in [.])],
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),[{E#5},(letrec {E#6} in [.])],((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in (letrec {X#10=T#9;E#12} in S#7)),
           T#8   |->  (letrec {X#10=T#9;E#12} in S#7),
           E#6   |->  {X#10=T#9[T#4[S#2]];E#12},
           E#11  |->  {E#12}}

and instantiated rules:

                                  (letrec {E#5} in (letrec {X#10=T#9[T#4[S#2]];E#12} in S#7))
    -ucp3->                       (letrec {E#5} in (letrec {X#10=T#9[(letrec {X#1=S#2} in T#4[(var X#1)])];E#12} in S#7))
    ................................................................................
                                  (letrec {E#5} in (letrec {X#10=T#9[T#4[S#2]];E#12} in S#7))
    -SR,llet-in1->                (letrec {X#10=T#9[T#4[S#2]];E#12;E#5} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (letrec {X#1=S#2} in (letrec {E#6} in T#9[(var X#1)])))
    ,
     (letrec {E#5;E#6} in T#9[S#2])
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#6} in T#9)),
             (S#2,(letrec {E#6} in T#9)),
             ((letrec {E#6} in T#9[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             [{E#5},(letrec {E#6} in [.])],
             ((var X#1),(letrec {E#6} in T#9[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),[{E#5},(letrec {E#6} in [.])],((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  (letrec {E#5} in [.]),
           T#8  |->  [.],
           T#4  |->  (letrec {E#6} in T#9),
           S#7  |->  T#9[S#2]}

and instantiated rules:

                                  (letrec {E#5} in (letrec {E#6} in T#9[S#2]))
    -ucp3->                       (letrec {E#5} in (letrec {X#1=S#2} in (letrec {E#6} in T#9[(var X#1)])))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in T#9[S#2]))
    -SR,llet-in1->                (letrec {E#5;E#6} in T#9[S#2])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (letrec {X#1=S#2} in (letrec {X#10=T#9[(var X#1)];E#12} in S#7))
     )
    ,
     (letrec {X#10=T#9[S#2];E#12;E#5} in S#7)
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {X#10=T#9;E#12} in S#7)),
             (S#2,(letrec {X#10=T#9;E#12} in S#7)),
             ((letrec {X#10=T#9[(dummy3 )];E#12} in S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             [{E#5},(letrec {X#10=T#9[S#2];E#12} in [.])],
             ((var X#1),(letrec {X#10=T#9[[.]];E#12} in S#7))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),[{E#5},(letrec {E#6} in [.])],((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in [.]),
           T#8   |->  [.],
           T#4   |->  (letrec {X#10=T#9;E#12} in S#7),
           E#6   |->  {X#10=T#9[S#2];E#12},
           E#11  |->  {E#12}}

and instantiated rules:

                                  (letrec {E#5} in (letrec {X#10=T#9[S#2];E#12} in S#7))
    -ucp3->                       (letrec {E#5} in (letrec {X#1=S#2} in (letrec {X#10=T#9[(var X#1)];E#12} in S#7)))
    ................................................................................
                                  (letrec {E#5} in (letrec {X#10=T#9[S#2];E#12} in S#7))
    -SR,llet-in1->                (letrec {X#10=T#9[S#2];E#12;E#5} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (letrec {X#1=(letrec {E#6} in S#7)} in (var X#1)))
    ,
     (letrec {E#5;E#6} in S#7)
  )

where

   Delta1 = {T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#6} in S#7),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#6} in S#7),(letrec {X#1=(dummy3 )} in [.])),
             [{E#5},(letrec {E#6} in [.])],
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),[{E#5},(letrec {E#6} in [.])],((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  (letrec {E#5} in [.]),
           T#8  |->  [.],
           T#4  |->  [.],
           S#2  |->  (letrec {E#6} in S#7)}

and instantiated rules:

                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -ucp3->                       (letrec {E#5} in (letrec {X#1=(letrec {E#6} in S#7)} in (var X#1)))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#9= T#8[(letrec {X#1=S#2} in T#4[(var X#1)])]
       ;E#11
     in
        (letrec {E#6} in S#7)
     )
    ,
     (letrec {X#9=T#8[T#4[S#2]];E#11;E#6} in S#7)
  )

where

   Delta1 = {T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             [{X#9=T#8[T#4[S#2]];E#11},(letrec {E#6} in [.])],
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),[{E#5},(letrec {E#6} in [.])],((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#9=T#8;E#11} in (letrec {E#6} in S#7)),
           E#5   |->  {X#9=T#8[T#4[S#2]];E#11},
           E#10  |->  {E#11}}

and instantiated rules:

                                  (letrec {X#9=T#8[T#4[S#2]];E#11} in (letrec {E#6} in S#7))
    -ucp3->                       (letrec {X#9=T#8[(letrec {X#1=S#2} in T#4[(var X#1)])];E#11} in (letrec {E#6} in S#7))
    ................................................................................
                                  (letrec {X#9=T#8[T#4[S#2]];E#11} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {X#9=T#8[T#4[S#2]];E#11;E#6} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#2} in (letrec {E#5} in (letrec {E#6} in T#9[(var X#1)])))
    ,
     (letrec {E#5;E#6} in T#9[S#2])
  )

where

   Delta1 = {T#8,T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#5} in (letrec {E#6} in T#9))),
             (S#2,(letrec {E#5} in (letrec {E#6} in T#9))),
             ((letrec {E#5} in (letrec {E#6} in T#9[(dummy3 )])),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             [{E#5},(letrec {E#6} in [.])],
             ((var X#1),(letrec {E#5} in (letrec {E#6} in T#9[[.]])))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),[{E#5},(letrec {E#6} in [.])],((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  (letrec {E#5} in (letrec {E#6} in T#9)),
           T#8  |->  (letrec {E#6} in T#9),
           S#7  |->  T#9[S#2]}

and instantiated rules:

                                  (letrec {E#5} in (letrec {E#6} in T#9[S#2]))
    -ucp3->                       (letrec {X#1=S#2} in (letrec {E#5} in (letrec {E#6} in T#9[(var X#1)])))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in T#9[S#2]))
    -SR,llet-in1->                (letrec {E#5;E#6} in T#9[S#2])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {E#5} in (letrec {X#10=T#9[(var X#1)];E#12} in S#7))
     )
    ,
     (letrec {X#10=T#9[S#2];E#12;E#5} in S#7)
  )

where

   Delta1 = {T#8,T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#5} in (letrec {X#10=T#9;E#12} in S#7))),
             (S#2,(letrec {E#5} in (letrec {X#10=T#9;E#12} in S#7))),
             ((letrec {E#5} in (letrec {X#10=T#9[(dummy3 )];E#12} in S#7)),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             [{E#5},(letrec {X#10=T#9[S#2];E#12} in [.])],
             ((var X#1),(letrec {E#5} in (letrec {X#10=T#9[[.]];E#12} in S#7)))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),[{E#5},(letrec {E#6} in [.])],((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#5} in (letrec {X#10=T#9;E#12} in S#7)),
           T#8   |->  (letrec {X#10=T#9;E#12} in S#7),
           E#6   |->  {X#10=T#9[S#2];E#12},
           E#11  |->  {E#12}}

and instantiated rules:

                                  (letrec {E#5} in (letrec {X#10=T#9[S#2];E#12} in S#7))
    -ucp3->                       (letrec {X#1=S#2} in (letrec {E#5} in (letrec {X#10=T#9[(var X#1)];E#12} in S#7)))
    ................................................................................
                                  (letrec {E#5} in (letrec {X#10=T#9[S#2];E#12} in S#7))
    -SR,llet-in1->                (letrec {X#10=T#9[S#2];E#12;E#5} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {E#6} in S#7)} in (letrec {E#5} in (var X#1)))
    ,
     (letrec {E#5;E#6} in S#7)
  )

where

   Delta1 = {T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#5} in [.])),
             ((letrec {E#6} in S#7),(letrec {E#5} in [.])),
             ((letrec {E#5} in (dummy3 )),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#6} in S#7),(letrec {X#1=(dummy3 )} in [.])),
             [{E#5},(letrec {E#6} in [.])],
             ((var X#1),(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),[{E#5},(letrec {E#6} in [.])],((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  (letrec {E#5} in [.]),
           T#8  |->  [.],
           S#2  |->  (letrec {E#6} in S#7)}

and instantiated rules:

                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -ucp3->                       (letrec {X#1=(letrec {E#6} in S#7)} in (letrec {E#5} in (var X#1)))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {X#9=T#8[(var X#1)];E#11} in (letrec {E#6} in S#7))
     )
    ,
     (letrec {X#9=T#8[S#2];E#11;E#6} in S#7)
  )

where

   Delta1 = {T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {X#9=T#8;E#11} in (letrec {E#6} in S#7))),
             (S#2,(letrec {X#9=T#8;E#11} in (letrec {E#6} in S#7))),
             ((letrec {X#9=T#8[(dummy3 )];E#11} in (letrec {E#6} in S#7)),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             [{X#9=T#8[S#2];E#11},(letrec {E#6} in [.])],
             ((var X#1),(letrec {X#9=T#8[[.]];E#11} in (letrec {E#6} in S#7)))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),[{E#5},(letrec {E#6} in [.])],((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#9=T#8;E#11} in (letrec {E#6} in S#7)),
           E#5   |->  {X#9=T#8[S#2];E#11},
           E#10  |->  {E#11}}

and instantiated rules:

                                  (letrec {X#9=T#8[S#2];E#11} in (letrec {E#6} in S#7))
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#9=T#8[(var X#1)];E#11} in (letrec {E#6} in S#7)))
    ................................................................................
                                  (letrec {X#9=T#8[S#2];E#11} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {X#9=T#8[S#2];E#11;E#6} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {E#5} in (letrec {E#6} in S#7))} in (var X#1))
    ,
     (letrec {E#5;E#6} in S#7)
  )

where

   Delta1 = {}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#5} in (letrec {E#6} in S#7)),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#5} in (letrec {E#6} in S#7)),(letrec {X#1=(dummy3 )} in [.])),
             [{E#5},(letrec {E#6} in [.])],
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-in1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    and constraints: E#5/= {}, E#6/= {}, ({E#5},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in (letrec {E#6} in S#7))}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),[{E#5},(letrec {E#6} in [.])],((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  [.],
           S#2  |->  (letrec {E#5} in (letrec {E#6} in S#7))}

and instantiated rules:

                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -ucp3->                       (letrec {X#1=(letrec {E#5} in (letrec {E#6} in S#7))} in (var X#1))
    ................................................................................
                                  (letrec {E#5} in (letrec {E#6} in S#7))
    -SR,llet-in1->                (letrec {E#5;E#6} in S#7)
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in S#8)
       ;E#7
     in
        A#11[(letrec {X#1=(var X#5)} in (var X#1))]
     )
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#11[(var X#5)])
  )

where

   Delta1 = {A#9,T#10,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),[.]),
             ((var X#5),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(var X#5)],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),[.]),
             ((var X#5),A#11[[.]]),
             ((var X#5),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[[.]]),
           A#9   |->  A#11,
           T#10  |->  A#11[[.]],
           T#12  |->  [.],
           T#4   |->  [.],
           S#2   |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(letrec {X#1=(var X#5)} in (var X#1))])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#11[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in S#8)
       ;E#7
     in
        A#11[(letrec {X#1=(var X#5)} in A#13[(var X#1)])]
     )
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#11[A#13[(var X#5)]])
  )

where

   Delta1 = {A#12,T#4,A#9,T#10,T#3,A#11,A#13}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#13[[.]]),
             ((var X#5),A#13[[.]]),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             (A#11[A#13[(var X#5)]],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),A#13[[.]]),
             ((var X#5),A#11[A#13[[.]]]),
             ((var X#5),A#11[A#13[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11),
           A#9   |->  A#11[A#13],
           T#10  |->  A#11,
           A#12  |->  A#13,
           T#4   |->  A#13[[.]],
           T#14  |->  [.],
           S#2   |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[A#13[(var X#5)]])
    -ucp3->                       (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(letrec {X#1=(var X#5)} in A#13[(var X#1)])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[A#13[(var X#5)]])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#11[A#13[(var X#5)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in S#8)
       ;E#7
     in
        A#11[(letrec {X#1=A#14[(var X#5)]} in A#13[(var X#1)])]
     )
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#11[A#13[A#14[(var X#5)]]])
  )

where

   Delta1 = {A#12,T#4,A#9,T#10,T#3,A#11,A#13}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#13),
             (A#14[(var X#5)],A#13),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             (A#11[A#13[A#14[(var X#5)]]],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),A#13[[.]]),
             ((var X#5),A#11[A#13[A#14[[.]]]]),
             ((var X#5),A#11[A#13[A#14[[.]]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11),
           A#9   |->  A#11[A#13[A#14]],
           T#10  |->  A#11,
           A#12  |->  A#13[A#14],
           T#4   |->  A#13,
           S#2   |->  A#14[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[A#13[A#14[(var X#5)]]])
    -ucp3->                       (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(letrec {X#1=A#14[(var X#5)]} in A#13[(var X#1)])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[A#13[A#14[(var X#5)]]])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#11[A#13[A#14[(var X#5)]]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in S#8)
       ;E#7
     in
        A#11[(letrec {X#1=S#2} in A#13[(app A#14[(var X#5)] T#15[(var X#1)])])]
     )
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#11[A#13[(app A#14[(var X#5)] T#15[S#2])]])
  )

where

   Delta1 = {A#12,T#4,A#9,T#10,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#13[(app A#14[(var X#5)] T#15)]),
             (S#2,A#13[(app A#14[(var X#5)] T#15)]),
             (A#13[(app A#14[(var X#5)] T#15[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (A#11[A#13[(app A#14[(var X#5)] T#15[S#2])]],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),A#13[(app A#14[(var X#5)] T#15[[.]])]),
             ((var X#5),A#11[A#13[(app A#14[[.]] T#15[S#2])]]),
             ((var X#5),A#11[A#13[(app A#14[[.]] T#15[S#2])]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11),
           A#9   |->  A#11[A#13[(app A#14 T#15[S#2])]],
           T#10  |->  A#11,
           T#4   |->  A#13[(app A#14[(var X#5)] T#15)],
           A#12  |->  A#13[(app A#14 T#15[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[A#13[(app A#14[(var X#5)] T#15[S#2])]])
    -ucp3->                       (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(letrec {X#1=S#2} in A#13[(app A#14[(var X#5)] T#15[(var X#1)])])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[A#13[(app A#14[(var X#5)] T#15[S#2])]])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#11[A#13[(app A#14[(var X#5)] T#15[S#2])]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in S#8)
       ;E#7
     in
        A#11[(letrec {X#1=A#12[(var X#5)]} in (var X#1))]
     )
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#11[A#12[(var X#5)]])
  )

where

   Delta1 = {A#9,T#10,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),[.]),
             (A#12[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             (A#11[A#12[(var X#5)]],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),[.]),
             ((var X#5),A#11[A#12[[.]]]),
             ((var X#5),A#11[A#12[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11),
           A#9   |->  A#11[A#12],
           T#10  |->  A#11,
           T#4   |->  [.],
           S#2   |->  A#12[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[A#12[(var X#5)]])
    -ucp3->                       (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(letrec {X#1=A#12[(var X#5)]} in (var X#1))])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[A#12[(var X#5)]])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#11[A#12[(var X#5)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in S#8)
       ;E#7
     in
        A#11[(app A#12[(var X#5)] T#13[(letrec {X#1=S#2} in T#4[(var X#1)])])]
     )
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#11[(app A#12[(var X#5)] T#13[T#4[S#2]])])
  )

where

   Delta1 = {A#9,T#10,T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(app A#12[(var X#5)] T#13[T#4[S#2]])],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),T#4[[.]]),
             ((var X#5),A#11[(app A#12[[.]] T#13[T#4[S#2]])]),
             ((var X#5),A#11[(app A#12[[.]] T#13[T#4[S#2]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)]),
           T#10  |->  A#11[(app A#12[(var X#5)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[T#4[S#2]])])
    -ucp3->                       (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(letrec {X#1=S#2} in T#4[(var X#1)])])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[T#4[S#2]])])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#11[(app A#12[(var X#5)] T#13[T#4[S#2]])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in S#8)
       ;E#7
     in
        (letrec {X#1=(var X#5)} in A#11[(var X#1)])
     )
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#11[(var X#5)])
  )

where

   Delta1 = {A#9,T#4,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#11[[.]]),
             ((var X#5),A#11[[.]]),
             (A#11[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(var X#5)],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),A#11[[.]]),
             ((var X#5),A#11[[.]]),
             ((var X#5),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in [.]),
           T#10  |->  [.],
           A#9   |->  A#11,
           T#4   |->  A#11[[.]],
           T#12  |->  [.],
           S#2   |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {E#6} in S#8);E#7} in (letrec {X#1=(var X#5)} in A#11[(var X#1)]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#11[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in S#8)
       ;E#7
     in
        (letrec {X#1=A#12[(var X#5)]} in A#11[(var X#1)])
     )
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#11[A#12[(var X#5)]])
  )

where

   Delta1 = {A#9,T#4,T#3,A#11}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#11),
             (A#12[(var X#5)],A#11),
             (A#11[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             (A#11[A#12[(var X#5)]],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),A#11[[.]]),
             ((var X#5),A#11[A#12[[.]]]),
             ((var X#5),A#11[A#12[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in [.]),
           T#10  |->  [.],
           A#9   |->  A#11[A#12],
           T#4   |->  A#11,
           S#2   |->  A#12[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[A#12[(var X#5)]])
    -ucp3->                       (letrec {X#5=(letrec {E#6} in S#8);E#7} in (letrec {X#1=A#12[(var X#5)]} in A#11[(var X#1)]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[A#12[(var X#5)]])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#11[A#12[(var X#5)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in S#8)
       ;E#7
     in
        (letrec {X#1=S#2} in A#11[(app A#12[(var X#5)] T#13[(var X#1)])])
     )
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#11[(app A#12[(var X#5)] T#13[S#2])])
  )

where

   Delta1 = {A#9,T#4,T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),A#11[(app A#12[(var X#5)] T#13)]),
             (S#2,A#11[(app A#12[(var X#5)] T#13)]),
             (A#11[(app A#12[(var X#5)] T#13[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(app A#12[(var X#5)] T#13[S#2])],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),A#11[(app A#12[(var X#5)] T#13[[.]])]),
             ((var X#5),A#11[(app A#12[[.]] T#13[S#2])]),
             ((var X#5),A#11[(app A#12[[.]] T#13[S#2])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in [.]),
           T#10  |->  [.],
           T#4   |->  A#11[(app A#12[(var X#5)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[S#2])])
    -ucp3->                       (letrec {X#5=(letrec {E#6} in S#8);E#7} in (letrec {X#1=S#2} in A#11[(app A#12[(var X#5)] T#13[(var X#1)])]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[S#2])])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#11[(app A#12[(var X#5)] T#13[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in S#8)
       ;E#7
     in
        (letrec {X#1=A#9[(var X#5)]} in (var X#1))
     )
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),[.]),
             (A#9[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in [.]),
           T#10  |->  [.],
           T#4   |->  [.],
           S#2   |->  A#9[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {E#6} in S#8);E#7} in (letrec {X#1=A#9[(var X#5)]} in (var X#1)))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#6} in T#13[(letrec {X#1=S#2} in T#4[(var X#1)])])
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#5=T#13[T#4[S#2]];E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#10,T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),T#4[[.]]),
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#6} in T#13);E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  (letrec {E#6} in T#13),
           S#8   |->  T#13[T#4[S#2]]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in T#13[T#4[S#2]]);E#7} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {E#6} in T#13[(letrec {X#1=S#2} in T#4[(var X#1)])]);E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in T#13[T#4[S#2]]);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=T#13[T#4[S#2]];E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#14=T#13[(letrec {X#1=S#2} in T#4[(var X#1)])];E#16} in S#8)
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#14=T#13[T#4[S#2]];X#5=S#8;E#16;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#10,T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(var X#5)],(letrec {X#14=T#13[T#4[S#2]];E#16} in [.])),
             [{E#7},(letrec {X#14=T#13[T#4[S#2]];E#16} in [.])],
             ((var X#1),T#4[[.]]),
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {X#14=T#13;E#16} in S#8);E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  (letrec {X#14=T#13;E#16} in S#8),
           E#6   |->  {X#14=T#13[T#4[S#2]];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#14=T#13[T#4[S#2]];E#16} in S#8);E#7} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#14=T#13[(letrec {X#1=S#2} in T#4[(var X#1)])];E#16} in S#8);E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {X#14=T#13[T#4[S#2]];E#16} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#14=T#13[T#4[S#2]];X#5=S#8;E#16;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=S#2} in (letrec {E#6} in T#13[(var X#1)]))
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#5=T#13[S#2];E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {E#6} in T#13)),
             (S#2,(letrec {E#6} in T#13)),
             ((letrec {E#6} in T#13[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),(letrec {E#6} in T#13[[.]])),
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=[.];E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  [.],
           T#4   |->  (letrec {E#6} in T#13),
           S#8   |->  T#13[S#2]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in T#13[S#2]);E#7} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in (letrec {E#6} in T#13[(var X#1)]));E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in T#13[S#2]);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=T#13[S#2];E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=S#2} in (letrec {X#14=T#13[(var X#1)];E#16} in S#8))
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#14=T#13[S#2];X#5=S#8;E#16;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {X#14=T#13;E#16} in S#8)),
             (S#2,(letrec {X#14=T#13;E#16} in S#8)),
             ((letrec {X#14=T#13[(dummy3 )];E#16} in S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(var X#5)],(letrec {X#14=T#13[S#2];E#16} in [.])),
             [{E#7},(letrec {X#14=T#13[S#2];E#16} in [.])],
             ((var X#1),(letrec {X#14=T#13[[.]];E#16} in S#8)),
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=[.];E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  [.],
           T#4   |->  (letrec {X#14=T#13;E#16} in S#8),
           E#6   |->  {X#14=T#13[S#2];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#14=T#13[S#2];E#16} in S#8);E#7} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in (letrec {X#14=T#13[(var X#1)];E#16} in S#8));E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {X#14=T#13[S#2];E#16} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#14=T#13[S#2];X#5=S#8;E#16;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=(letrec {E#6} in S#8)} in (var X#1))
       ;E#7
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#6} in S#8),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#6} in S#8),(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=[.];E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  [.],
           T#4   |->  [.],
           S#2   |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=(letrec {E#6} in S#8)} in (var X#1));E#7} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(letrec {X#1=S#2} in T#4[(var X#1)])]
       ;X#5= (letrec {E#6} in S#8)
       ;E#13
     in
        A#9[(var X#5)]
     )
    ,
     (letrec {X#11=T#10[T#4[S#2]];X#5=S#8;E#13;E#6} in A#9[(var X#5)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#11=T#10[T#4[S#2]];E#13},(letrec {E#6} in [.])],
             ((var X#1),T#4[[.]]),
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#11=T#10;X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)]),
           E#7   |->  {X#11=T#10[T#4[S#2]];E#13},
           E#12  |->  {X#5=(letrec {E#6} in S#8);E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[T#4[S#2]];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#11=T#10[(letrec {X#1=S#2} in T#4[(var X#1)])];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    ................................................................................
                                  (letrec {X#11=T#10[T#4[S#2]];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#11=T#10[T#4[S#2]];X#5=S#8;E#13;E#6} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (letrec {E#6} in S#8)
          ;E#7
        in
           A#11[(app A#12[(var X#5)] T#13[(var X#1)])]
        )
     )
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#11[(app A#12[(var X#5)] T#13[S#2])])
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)])),
             (S#2,(letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)])),
             ((letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (A#11[(app A#12[(var X#5)] T#13[S#2])],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),(letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[[.]])])),
             ((var X#5),A#11[(app A#12[[.]] T#13[S#2])]),
             ((var X#5),A#11[(app A#12[[.]] T#13[S#2])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13)]),
           T#10  |->  A#11[(app A#12[(var X#5)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[S#2])])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[(var X#1)])]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#11[(app A#12[(var X#5)] T#13[S#2])])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#11[(app A#12[(var X#5)] T#13[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {X#5=(letrec {E#6} in T#13[(var X#1)]);E#7} in A#9[(var X#5)])
     )
    ,
     (letrec {X#5=T#13[S#2];E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {X#5=(letrec {E#6} in T#13);E#7} in A#9[(var X#5)])),
             (S#2,(letrec {X#5=(letrec {E#6} in T#13);E#7} in A#9[(var X#5)])),
             ((letrec {X#5=(letrec {E#6} in T#13[(dummy3 )]);E#7} in A#9[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),(letrec {X#5=(letrec {E#6} in T#13[[.]]);E#7} in A#9[(var X#5)])),
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=(letrec {E#6} in T#13);E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  (letrec {E#6} in T#13),
           S#8   |->  T#13[S#2]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in T#13[S#2]);E#7} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(letrec {E#6} in T#13[(var X#1)]);E#7} in A#9[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in T#13[S#2]);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=T#13[S#2];E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {X#5=(letrec {X#14=T#13[(var X#1)];E#16} in S#8);E#7} in A#9[(var X#5)])
     )
    ,
     (letrec {X#14=T#13[S#2];X#5=S#8;E#16;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {X#5=(letrec {X#14=T#13;E#16} in S#8);E#7} in A#9[(var X#5)])),
             (S#2,(letrec {X#5=(letrec {X#14=T#13;E#16} in S#8);E#7} in A#9[(var X#5)])),
             ((letrec {X#5=(letrec {X#14=T#13[(dummy3 )];E#16} in S#8);E#7} in A#9[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(var X#5)],(letrec {X#14=T#13[S#2];E#16} in [.])),
             [{E#7},(letrec {X#14=T#13[S#2];E#16} in [.])],
             ((var X#1),(letrec {X#5=(letrec {X#14=T#13[[.]];E#16} in S#8);E#7} in A#9[(var X#5)])),
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=(letrec {X#14=T#13;E#16} in S#8);E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  (letrec {X#14=T#13;E#16} in S#8),
           E#6   |->  {X#14=T#13[S#2];E#16},
           E#15  |->  {E#16}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#14=T#13[S#2];E#16} in S#8);E#7} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(letrec {X#14=T#13[(var X#1)];E#16} in S#8);E#7} in A#9[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=(letrec {X#14=T#13[S#2];E#16} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#14=T#13[S#2];X#5=S#8;E#16;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#6} in S#8)
     in
        (letrec {X#5=(var X#1);E#7} in A#9[(var X#5)])
     )
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {X#5=[.];E#7} in A#9[(var X#5)])),
             ((letrec {E#6} in S#8),(letrec {X#5=[.];E#7} in A#9[(var X#5)])),
             ((letrec {X#5=(dummy3 );E#7} in A#9[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#6} in S#8),(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),(letrec {X#5=[.];E#7} in A#9[(var X#5)])),
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=[.];E#7} in A#9[(var X#5)]),
           X#11  |->  X#5,
           E#12  |->  {E#7},
           T#10  |->  [.],
           S#2   |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#1=(letrec {E#6} in S#8)} in (letrec {X#5=(var X#1);E#7} in A#9[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {X#11=T#10[(var X#1)];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
     )
    ,
     (letrec {X#11=T#10[S#2];X#5=S#8;E#13;E#6} in A#9[(var X#5)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#6}
   Delta3 = {((var X#1),(letrec {X#11=T#10;X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])),
             (S#2,(letrec {X#11=T#10;X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])),
             ((letrec {X#11=T#10[(dummy3 )];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{X#11=T#10[S#2];E#13},(letrec {E#6} in [.])],
             ((var X#1),(letrec {X#11=T#10[[.]];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])),
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#11=T#10;X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)]),
           E#7   |->  {X#11=T#10[S#2];E#13},
           E#12  |->  {X#5=(letrec {E#6} in S#8);E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[S#2];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#11=T#10[(var X#1)];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)]))
    ................................................................................
                                  (letrec {X#11=T#10[S#2];X#5=(letrec {E#6} in S#8);E#13} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#11=T#10[S#2];X#5=S#8;E#13;E#6} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
     in
        (var X#1)
     )
    ,
     (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
  )

where

   Delta1 = {}
   Delta2 = {E#6}
   Delta3 = {((var X#1),[.]),
             ((letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)]),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(var X#5)],(letrec {E#6} in [.])),
             [{E#7},(letrec {E#6} in [.])],
             ((var X#1),[.]),
             ((var X#5),A#9[[.]]),
             ((var X#5),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    and constraints: E#6/= {}, (A#9[(var X#5)],(letrec {E#6} in [.])), ({E#7},(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(A#9[(var X#5)],(letrec {E#6} in [.])),[{E#7},(letrec {E#6} in [.])],((var X#1),T#4[[.]]),((var X#5),A#9[[.]]),((var X#5),A#9[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  [.],
           S#2  |->  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -ucp3->                       (letrec {X#1=(letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])} in (var X#1))
    ................................................................................
                                  (letrec {X#5=(letrec {E#6} in S#8);E#7} in A#9[(var X#5)])
    -SR,llet-e1->                 (letrec {X#5=S#8;E#6;E#7} in A#9[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(letrec {X#1=(var X#6)} in (var X#1))]
     )
    ,
     (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[(var X#6)])
  )

where

   Delta1 = {A#10,T#12,T#3,A#13}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((var X#6),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#13[(var X#6)],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#13[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[[.]]),
           A#10  |->  A#13,
           T#12  |->  A#13[[.]],
           T#14  |->  [.],
           T#4   |->  [.],
           S#2   |->  (var X#6)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(letrec {X#1=(var X#6)} in (var X#1))])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(letrec {X#1=(var X#6)} in A#15[(var X#1)])]
     )
    ,
     (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[A#15[(var X#6)]])
  )

where

   Delta1 = {A#14,T#4,A#10,T#12,T#3,A#13,A#15}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#15[[.]]),
             ((var X#6),A#15[[.]]),
             (A#15[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#13[A#15[(var X#6)]],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#15[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#13[A#15[[.]]]),
             ((var X#5),[.]),
             ((var X#6),A#13[A#15[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13),
           A#10  |->  A#13[A#15],
           T#12  |->  A#13,
           A#14  |->  A#15,
           T#4   |->  A#15[[.]],
           T#16  |->  [.],
           S#2   |->  (var X#6)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[A#15[(var X#6)]])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(letrec {X#1=(var X#6)} in A#15[(var X#1)])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[A#15[(var X#6)]])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[A#15[(var X#6)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(letrec {X#1=A#16[(var X#6)]} in A#15[(var X#1)])]
     )
    ,
     (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[A#15[A#16[(var X#6)]]])
  )

where

   Delta1 = {A#14,T#4,A#10,T#12,T#3,A#13,A#15}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#15),
             (A#16[(var X#6)],A#15),
             (A#15[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#16[(var X#6)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#13[A#15[A#16[(var X#6)]]],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#15[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#13[A#15[A#16[[.]]]]),
             ((var X#5),[.]),
             ((var X#6),A#13[A#15[A#16[[.]]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13),
           A#10  |->  A#13[A#15[A#16]],
           T#12  |->  A#13,
           A#14  |->  A#15[A#16],
           T#4   |->  A#15,
           S#2   |->  A#16[(var X#6)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[A#15[A#16[(var X#6)]]])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(letrec {X#1=A#16[(var X#6)]} in A#15[(var X#1)])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[A#15[A#16[(var X#6)]]])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[A#15[A#16[(var X#6)]]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(letrec {X#1=S#2} in A#15[(app A#16[(var X#6)] T#17[(var X#1)])])]
     )
    ,
     (letrec
        X#5= S#9
       ;E#7
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[A#15[(app A#16[(var X#6)] T#17[S#2])]]
     )
  )

where

   Delta1 = {A#14,T#4,A#10,T#12,T#3,A#13}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#15[(app A#16[(var X#6)] T#17)]),
             (S#2,A#15[(app A#16[(var X#6)] T#17)]),
             (A#15[(app A#16[(var X#6)] T#17[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#13[A#15[(app A#16[(var X#6)] T#17[S#2])]],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#15[(app A#16[(var X#6)] T#17[[.]])]),
             ((var X#5),[.]),
             ((var X#6),A#13[A#15[(app A#16[[.]] T#17[S#2])]]),
             ((var X#5),[.]),
             ((var X#6),A#13[A#15[(app A#16[[.]] T#17[S#2])]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13),
           A#10  |->  A#13[A#15[(app A#16 T#17[S#2])]],
           T#12  |->  A#13,
           T#4   |->  A#15[(app A#16[(var X#6)] T#17)],
           A#14  |->  A#15[(app A#16 T#17[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[A#15[(app A#16[(var X#6)] T#17[S#2])]])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(letrec {X#1=S#2} in A#15[(app A#16[(var X#6)] T#17[(var X#1)])])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[A#15[(app A#16[(var X#6)] T#17[S#2])]])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[A#15[(app A#16[(var X#6)] T#17[S#2])]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(letrec {X#1=A#14[(var X#6)]} in (var X#1))]
     )
    ,
     (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[A#14[(var X#6)]])
  )

where

   Delta1 = {A#10,T#12,T#3,A#13}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#14[(var X#6)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(var X#6)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#13[A#14[(var X#6)]],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#13[A#14[[.]]]),
             ((var X#5),[.]),
             ((var X#6),A#13[A#14[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13),
           A#10  |->  A#13[A#14],
           T#12  |->  A#13,
           T#4   |->  [.],
           S#2   |->  A#14[(var X#6)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[A#14[(var X#6)]])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(letrec {X#1=A#14[(var X#6)]} in (var X#1))])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[A#14[(var X#6)]])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[A#14[(var X#6)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(app A#14[(var X#6)] T#15[(letrec {X#1=S#2} in T#4[(var X#1)])])]
     )
    ,
     (letrec
        X#5= S#9
       ;E#7
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(app A#14[(var X#6)] T#15[T#4[S#2]])]
     )
  )

where

   Delta1 = {A#10,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#13[(app A#14[(var X#6)] T#15[T#4[S#2]])],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#13[(app A#14[[.]] T#15[T#4[S#2]])]),
             ((var X#5),[.]),
             ((var X#6),A#13[(app A#14[[.]] T#15[T#4[S#2]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#6)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[T#4[S#2]])])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(letrec {X#1=S#2} in T#4[(var X#1)])])])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[T#4[S#2]])])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[T#4[S#2]])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        (letrec {X#1=(var X#6)} in A#13[(var X#1)])
     )
    ,
     (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[(var X#6)])
  )

where

   Delta1 = {A#10,T#4,T#3,A#13}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#13[[.]]),
             ((var X#6),A#13[[.]]),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#6),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#13[(var X#6)],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#13[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#13[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in [.]),
           T#12  |->  [.],
           A#10  |->  A#13,
           T#4   |->  A#13[[.]],
           T#14  |->  [.],
           S#2   |->  (var X#6)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in (letrec {X#1=(var X#6)} in A#13[(var X#1)]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        (letrec {X#1=A#14[(var X#6)]} in A#13[(var X#1)])
     )
    ,
     (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[A#14[(var X#6)]])
  )

where

   Delta1 = {A#10,T#4,T#3,A#13}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#13),
             (A#14[(var X#6)],A#13),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(var X#6)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#13[A#14[(var X#6)]],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#13[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#13[A#14[[.]]]),
             ((var X#5),[.]),
             ((var X#6),A#13[A#14[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in [.]),
           T#12  |->  [.],
           A#10  |->  A#13[A#14],
           T#4   |->  A#13,
           S#2   |->  A#14[(var X#6)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[A#14[(var X#6)]])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in (letrec {X#1=A#14[(var X#6)]} in A#13[(var X#1)]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[A#14[(var X#6)]])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[A#14[(var X#6)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        (letrec {X#1=S#2} in A#13[(app A#14[(var X#6)] T#15[(var X#1)])])
     )
    ,
     (letrec
        X#5= S#9
       ;E#7
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(app A#14[(var X#6)] T#15[S#2])]
     )
  )

where

   Delta1 = {A#10,T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#13[(app A#14[(var X#6)] T#15)]),
             (S#2,A#13[(app A#14[(var X#6)] T#15)]),
             (A#13[(app A#14[(var X#6)] T#15[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#13[(app A#14[(var X#6)] T#15[S#2])],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#13[(app A#14[(var X#6)] T#15[[.]])]),
             ((var X#5),[.]),
             ((var X#6),A#13[(app A#14[[.]] T#15[S#2])]),
             ((var X#5),[.]),
             ((var X#6),A#13[(app A#14[[.]] T#15[S#2])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in [.]),
           T#12  |->  [.],
           T#4   |->  A#13[(app A#14[(var X#6)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[S#2])])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in (letrec {X#1=S#2} in A#13[(app A#14[(var X#6)] T#15[(var X#1)])]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[S#2])])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        (letrec {X#1=A#10[(var X#6)]} in (var X#1))
     )
    ,
     (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#10[(var X#6)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#6)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in [.]),
           T#12  |->  [.],
           T#4   |->  [.],
           S#2   |->  A#10[(var X#6)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in (letrec {X#1=A#10[(var X#6)]} in (var X#1)))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in T#15[(letrec {X#1=S#2} in T#4[(var X#1)])])
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#5=T#15[T#4[S#2]];E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
  )

where

   Delta1 = {T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {E#7} in T#15);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  (letrec {E#7} in T#15),
           S#9   |->  T#15[T#4[S#2]]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in T#15[T#4[S#2]]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in T#15[(letrec {X#1=S#2} in T#4[(var X#1)])]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in T#15[T#4[S#2]]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=T#15[T#4[S#2]];E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#16=T#15[(letrec {X#1=S#2} in T#4[(var X#1)])];E#18} in S#9)
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= T#15[T#4[S#2]]
       ;X#5= S#9
       ;E#18
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=T#15[T#4[S#2]];E#18;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {X#16=T#15[T#4[S#2]];E#18} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {X#16=T#15[T#4[S#2]];E#18} in [.])],
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=(letrec {X#16=T#15;E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  (letrec {X#16=T#15;E#18} in S#9),
           E#7   |->  {X#16=T#15[T#4[S#2]];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#16=T#15[T#4[S#2]];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {X#16=T#15[(letrec {X#1=S#2} in T#4[(var X#1)])];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {X#16=T#15[T#4[S#2]];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=T#15[T#4[S#2]];X#5=S#9;E#18;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=S#2} in (letrec {E#7} in T#15[(var X#1)]))
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#5=T#15[S#2];E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {E#7} in T#15)),
             (S#2,(letrec {E#7} in T#15)),
             ((letrec {E#7} in T#15[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),(letrec {E#7} in T#15[[.]])),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=[.];E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  [.],
           T#4   |->  (letrec {E#7} in T#15),
           S#9   |->  T#15[S#2]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in T#15[S#2]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in (letrec {E#7} in T#15[(var X#1)]));E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in T#15[S#2]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=T#15[S#2];E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=S#2} in (letrec {X#16=T#15[(var X#1)];E#18} in S#9))
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= T#15[S#2]
       ;X#5= S#9
       ;E#18
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=T#15;E#18} in S#9)),
             (S#2,(letrec {X#16=T#15;E#18} in S#9)),
             ((letrec {X#16=T#15[(dummy3 )];E#18} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=T#15[S#2];E#18;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {X#16=T#15[S#2];E#18} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {X#16=T#15[S#2];E#18} in [.])],
             ((var X#1),(letrec {X#16=T#15[[.]];E#18} in S#9)),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=[.];E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  [.],
           T#4   |->  (letrec {X#16=T#15;E#18} in S#9),
           E#7   |->  {X#16=T#15[S#2];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#16=T#15[S#2];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in (letrec {X#16=T#15[(var X#1)];E#18} in S#9));E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {X#16=T#15[S#2];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=T#15[S#2];X#5=S#9;E#18;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=(letrec {E#7} in S#9)} in (var X#1))
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#7} in S#9),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#5=[.];E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  [.],
           T#4   |->  [.],
           S#2   |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=(letrec {E#7} in S#9)} in (var X#1));E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=S#2} in T#4[(var X#1)])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#15
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#13= T#12[T#4[S#2]]
       ;X#5= S#9
       ;E#15
       ;E#7
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#13=T#12[T#4[S#2]];E#15;E#7;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#13=T#12[T#4[S#2]];E#15;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#13=T#12;X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           E#8   |->  {X#13=T#12[T#4[S#2]];E#15},
           E#14  |->  {X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[T#4[S#2]];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#13=T#12[(letrec {X#1=S#2} in T#4[(var X#1)])];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#13=T#12[T#4[S#2]];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#13=T#12[T#4[S#2]];X#5=S#9;E#15;E#7;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#16[(letrec {X#1=(var X#5)} in (var X#1))]
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#5=S#9;X#6=A#16[(var X#5)];E#7;E#8} in A#10[(var X#6)])
  )

where

   Delta1 = {A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((var X#5),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#16[(var X#5)];E#7;E#8} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#16[(var X#5)];E#8},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[[.]];E#8} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8},
           A#15         |->  A#16,
           T#12         |->  A#16[[.]],
           T#17         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(var X#5)];E#8} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(letrec {X#1=(var X#5)} in (var X#1))];E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(var X#5)];E#8} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#16[(var X#5)];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#16[(letrec {X#1=(var X#5)} in A#18[(var X#1)])]
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#5=S#9;X#6=A#16[A#18[(var X#5)]];E#7;E#8} in A#10[(var X#6)])
  )

where

   Delta1 = {A#17,T#4,A#15,T#12,T#3,A#16,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[[.]]),
             ((var X#5),A#18[[.]]),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#16[A#18[(var X#5)]];E#7;E#8} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#16[A#18[(var X#5)]];E#8},(letrec {E#7} in [.])],
             ((var X#1),A#18[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16;E#8} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#18[[.2]]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8},
           A#15         |->  A#16[A#18],
           T#12         |->  A#16,
           A#17         |->  A#18,
           T#4          |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[A#18[(var X#5)]];E#8} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(letrec {X#1=(var X#5)} in A#18[(var X#1)])];E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[A#18[(var X#5)]];E#8} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#16[A#18[(var X#5)]];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#16[(letrec {X#1=A#19[(var X#5)]} in A#18[(var X#1)])]
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#5=S#9;X#6=A#16[A#18[A#19[(var X#5)]]];E#7;E#8} in A#10[(var X#6)])
  )

where

   Delta1 = {A#17,T#4,A#15,T#12,T#3,A#16,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18),
             (A#19[(var X#5)],A#18),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#16[A#18[A#19[(var X#5)]]];E#7;E#8} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#16[A#18[A#19[(var X#5)]]];E#8},(letrec {E#7} in [.])],
             ((var X#1),A#18[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16;E#8} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#18[A#19[[.2]]]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8},
           A#15         |->  A#16[A#18[A#19]],
           T#12         |->  A#16,
           A#17         |->  A#18[A#19],
           T#4          |->  A#18,
           S#2          |->  A#19[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[A#18[A#19[(var X#5)]]];E#8} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(letrec {X#1=A#19[(var X#5)]} in A#18[(var X#1)])];E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[A#18[A#19[(var X#5)]]];E#8} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#16[A#18[A#19[(var X#5)]]];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#16[(letrec {X#1=S#2} in A#18[(app A#19[(var X#5)] T#20[(var X#1)])])]
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#16[A#18[(app A#19[(var X#5)] T#20[S#2])]]
       ;E#7
       ;E#8
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#17,T#4,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[(app A#19[(var X#5)] T#20)]),
             (S#2,A#18[(app A#19[(var X#5)] T#20)]),
             (A#18[(app A#19[(var X#5)] T#20[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#16[A#18[(app A#19[(var X#5)] T#20[S#2])]];E#7;E#8} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#16[A#18[(app A#19[(var X#5)] T#20[S#2])]];E#8},(letrec {E#7} in [.])],
             ((var X#1),A#18[(app A#19[(var X#5)] T#20[[.]])]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16;E#8} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#18[(app A#19[[.2]] T#20[S#2])]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8},
           A#15         |->  A#16[A#18[(app A#19 T#20[S#2])]],
           T#12         |->  A#16,
           T#4          |->  A#18[(app A#19[(var X#5)] T#20)],
           A#17         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[A#18[(app A#19[(var X#5)] T#20[S#2])]];E#8} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(letrec {X#1=S#2} in A#18[(app A#19[(var X#5)] T#20[(var X#1)])])];E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[A#18[(app A#19[(var X#5)] T#20[S#2])]];E#8} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#16[A#18[(app A#19[(var X#5)] T#20[S#2])]];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#16[(letrec {X#1=A#17[(var X#5)]} in (var X#1))]
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#5=S#9;X#6=A#16[A#17[(var X#5)]];E#7;E#8} in A#10[(var X#6)])
  )

where

   Delta1 = {A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#17[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#17[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#16[A#17[(var X#5)]];E#7;E#8} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#16[A#17[(var X#5)]];E#8},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16;E#8} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#17[[.2]]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8},
           A#15         |->  A#16[A#17],
           T#12         |->  A#16,
           T#4          |->  [.],
           S#2          |->  A#17[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[A#17[(var X#5)]];E#8} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(letrec {X#1=A#17[(var X#5)]} in (var X#1))];E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[A#17[(var X#5)]];E#8} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#16[A#17[(var X#5)]];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#16[(app A#17[(var X#5)] T#18[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#16[(app A#17[(var X#5)] T#18[T#4[S#2]])]
       ;E#7
       ;E#8
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#16[(app A#17[(var X#5)] T#18[T#4[S#2]])];E#7;E#8} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#16[(app A#17[(var X#5)] T#18[T#4[S#2]])];E#8},(letrec {E#7} in [.])],
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18)];E#8} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[T#4[S#2]])]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8},
           T#12         |->  A#16[(app A#17[(var X#5)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[T#4[S#2]])];E#8} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[T#4[S#2]])];E#8} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#16[(app A#17[(var X#5)] T#18[T#4[S#2]])];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= (letrec {X#1=(var X#5)} in A#16[(var X#1)])
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#5=S#9;X#6=A#16[(var X#5)];E#7;E#8} in A#10[(var X#6)])
  )

where

   Delta1 = {A#15,T#4,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#16[[.]]),
             ((var X#5),A#16[[.]]),
             (A#16[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#16[(var X#5)];E#7;E#8} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#16[(var X#5)];E#8},(letrec {E#7} in [.])],
             ((var X#1),A#16[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=[.];E#8} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8},
           T#12         |->  [.],
           A#15         |->  A#16,
           T#4          |->  A#16[[.]],
           T#17         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(var X#5)];E#8} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=(letrec {X#1=(var X#5)} in A#16[(var X#1)]);E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(var X#5)];E#8} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#16[(var X#5)];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= (letrec {X#1=A#17[(var X#5)]} in A#16[(var X#1)])
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#5=S#9;X#6=A#16[A#17[(var X#5)]];E#7;E#8} in A#10[(var X#6)])
  )

where

   Delta1 = {A#15,T#4,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#16),
             (A#17[(var X#5)],A#16),
             (A#16[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#17[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#16[A#17[(var X#5)]];E#7;E#8} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#16[A#17[(var X#5)]];E#8},(letrec {E#7} in [.])],
             ((var X#1),A#16[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=[.];E#8} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#17[[.2]]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8},
           T#12         |->  [.],
           A#15         |->  A#16[A#17],
           T#4          |->  A#16,
           S#2          |->  A#17[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[A#17[(var X#5)]];E#8} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=(letrec {X#1=A#17[(var X#5)]} in A#16[(var X#1)]);E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[A#17[(var X#5)]];E#8} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#16[A#17[(var X#5)]];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= (letrec {X#1=S#2} in A#16[(app A#17[(var X#5)] T#18[(var X#1)])])
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#16[(app A#17[(var X#5)] T#18[S#2])]
       ;E#7
       ;E#8
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#16[(app A#17[(var X#5)] T#18)]),
             (S#2,A#16[(app A#17[(var X#5)] T#18)]),
             (A#16[(app A#17[(var X#5)] T#18[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#16[(app A#17[(var X#5)] T#18[S#2])];E#7;E#8} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#16[(app A#17[(var X#5)] T#18[S#2])];E#8},(letrec {E#7} in [.])],
             ((var X#1),A#16[(app A#17[(var X#5)] T#18[[.]])]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=[.];E#8} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[S#2])]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8},
           T#12         |->  [.],
           T#4          |->  A#16[(app A#17[(var X#5)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[S#2])];E#8} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=(letrec {X#1=S#2} in A#16[(app A#17[(var X#5)] T#18[(var X#1)])]);E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[S#2])];E#8} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#16[(app A#17[(var X#5)] T#18[S#2])];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= (letrec {X#1=A#15[(var X#5)]} in (var X#1))
       ;E#8
     in
        A#10[(var X#6)]
     )
    ,
     (letrec {X#5=S#9;X#6=A#15[(var X#5)];E#7;E#8} in A#10[(var X#6)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#15[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#15[(var X#5)];E#7;E#8} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#15[(var X#5)];E#8},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=[.];E#8} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#15[(var X#5)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#15[(var X#5)];E#8} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=(letrec {X#1=A#15[(var X#5)]} in (var X#1));E#8} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#15[(var X#5)];E#8} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#15[(var X#5)];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#18[(letrec {X#1=(var X#16)} in (var X#1))]
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#18[(var X#16)]
       ;E#7
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((var X#16),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#16),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#18[(var X#16)];E#7;E#8;EE#17[X#16,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#18[(var X#16)];E#8;EE#17[X#16,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[[.]];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(var X#16)];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#16,(var X#5)]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(var X#16)];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(letrec {X#1=(var X#16)} in (var X#1))];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(var X#16)];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#18[(var X#16)];E#7;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#18[(letrec {X#1=(var X#16)} in A#20[(var X#1)])]
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#18[A#20[(var X#16)]]
       ;E#7
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[[.]]),
             ((var X#16),A#20[[.]]),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#16),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#18[A#20[(var X#16)]];E#7;E#8;EE#17[X#16,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#18[A#20[(var X#16)]];E#8;EE#17[X#16,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#20[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#20[(var X#16)]];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#16,(var X#5)]},
           A#15         |->  A#18[A#20],
           T#12         |->  A#18,
           A#19         |->  A#20,
           T#4          |->  A#20[[.]],
           T#21         |->  [.],
           S#2          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[A#20[(var X#16)]];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(letrec {X#1=(var X#16)} in A#20[(var X#1)])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[A#20[(var X#16)]];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#18[A#20[(var X#16)]];E#7;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#18[(letrec {X#1=A#21[(var X#16)]} in A#20[(var X#1)])]
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#18[A#20[A#21[(var X#16)]]]
       ;E#7
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20),
             (A#21[(var X#16)],A#20),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#21[(var X#16)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#18[A#20[A#21[(var X#16)]]];E#7;E#8;EE#17[X#16,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#18[A#20[A#21[(var X#16)]]];E#8;EE#17[X#16,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#20[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#20[A#21[(var X#16)]]];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#16,(var X#5)]},
           A#15         |->  A#18[A#20[A#21]],
           T#12         |->  A#18,
           A#19         |->  A#20[A#21],
           T#4          |->  A#20,
           S#2          |->  A#21[(var X#16)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[A#20[A#21[(var X#16)]]];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(letrec {X#1=A#21[(var X#16)]} in A#20[(var X#1)])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[A#20[A#21[(var X#16)]]];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#18[A#20[A#21[(var X#16)]]];E#7;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#18[(letrec {X#1=S#2} in A#20[(app A#21[(var X#16)] T#22[(var X#1)])])]
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]]
       ;E#7
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[(app A#21[(var X#16)] T#22)]),
             (S#2,A#20[(app A#21[(var X#16)] T#22)]),
             (A#20[(app A#21[(var X#16)] T#22[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]];E#7;E#8;EE#17[X#16,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]];E#8;EE#17[X#16,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#20[(app A#21[(var X#16)] T#22[[.]])]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#16,(var X#5)]},
           A#15         |->  A#18[A#20[(app A#21 T#22[S#2])]],
           T#12         |->  A#18,
           T#4          |->  A#20[(app A#21[(var X#16)] T#22)],
           A#19         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(letrec {X#1=S#2} in A#20[(app A#21[(var X#16)] T#22[(var X#1)])])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]];E#7;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#18[(letrec {X#1=A#19[(var X#16)]} in (var X#1))]
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#18[A#19[(var X#16)]]
       ;E#7
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#19[(var X#16)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(var X#16)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#18[A#19[(var X#16)]];E#7;E#8;EE#17[X#16,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#18[A#19[(var X#16)]];E#8;EE#17[X#16,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#19[(var X#16)]];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#16,(var X#5)]},
           A#15         |->  A#18[A#19],
           T#12         |->  A#18,
           T#4          |->  [.],
           S#2          |->  A#19[(var X#16)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[A#19[(var X#16)]];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(letrec {X#1=A#19[(var X#16)]} in (var X#1))];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[A#19[(var X#16)]];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#18[A#19[(var X#16)]];E#7;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])]
       ;E#7
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])];E#7;E#8;EE#17[X#16,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])];E#8;EE#17[X#16,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20)];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#16,(var X#5)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])];E#7;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= (letrec {X#1=(var X#16)} in A#18[(var X#1)])
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#18[(var X#16)]
       ;E#7
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[[.]]),
             ((var X#16),A#18[[.]]),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#16),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#18[(var X#16)];E#7;E#8;EE#17[X#16,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#18[(var X#16)];E#8;EE#17[X#16,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#18[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=[.];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(var X#16)];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#16,(var X#5)]},
           T#12         |->  [.],
           A#15         |->  A#18,
           T#4          |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(var X#16)];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=(letrec {X#1=(var X#16)} in A#18[(var X#1)]);E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(var X#16)];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#18[(var X#16)];E#7;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= (letrec {X#1=A#19[(var X#16)]} in A#18[(var X#1)])
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#18[A#19[(var X#16)]]
       ;E#7
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18),
             (A#19[(var X#16)],A#18),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(var X#16)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#18[A#19[(var X#16)]];E#7;E#8;EE#17[X#16,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#18[A#19[(var X#16)]];E#8;EE#17[X#16,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#18[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=[.];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#19[(var X#16)]];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#16,(var X#5)]},
           T#12         |->  [.],
           A#15         |->  A#18[A#19],
           T#4          |->  A#18,
           S#2          |->  A#19[(var X#16)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[A#19[(var X#16)]];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=(letrec {X#1=A#19[(var X#16)]} in A#18[(var X#1)]);E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[A#19[(var X#16)]];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#18[A#19[(var X#16)]];E#7;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= (letrec {X#1=S#2} in A#18[(app A#19[(var X#16)] T#20[(var X#1)])])
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#18[(app A#19[(var X#16)] T#20[S#2])]
       ;E#7
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[(app A#19[(var X#16)] T#20)]),
             (S#2,A#18[(app A#19[(var X#16)] T#20)]),
             (A#18[(app A#19[(var X#16)] T#20[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#18[(app A#19[(var X#16)] T#20[S#2])];E#7;E#8;EE#17[X#16,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#18[(app A#19[(var X#16)] T#20[S#2])];E#8;EE#17[X#16,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#18[(app A#19[(var X#16)] T#20[[.]])]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=[.];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[S#2])];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#16,(var X#5)]},
           T#12         |->  [.],
           T#4          |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[S#2])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=(letrec {X#1=S#2} in A#18[(app A#19[(var X#16)] T#20[(var X#1)])]);E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[S#2])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#18[(app A#19[(var X#16)] T#20[S#2])];E#7;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {E#7} in S#9)
       ;X#6= (letrec {X#1=A#15[(var X#16)]} in (var X#1))
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#15[(var X#16)]
       ;E#7
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#15[(var X#16)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(var X#16)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#15[(var X#16)];E#7;E#8;EE#17[X#16,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#15[(var X#16)];E#8;EE#17[X#16,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=[.];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#15[(var X#16)];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#16,(var X#5)]},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#15[(var X#16)]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#15[(var X#16)];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#5=(letrec {E#7} in S#9);X#6=(letrec {X#1=A#15[(var X#16)]} in (var X#1));E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#15[(var X#16)];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#15[(var X#16)];E#7;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {X#1=(var X#17)} in (var X#1))]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[(var X#17)]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((var X#17),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#20[(var X#17)];E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#20[(var X#17)];E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20[[.]];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},
           A#15         |->  A#20,
           T#12         |->  A#20[[.]],
           T#21         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#16=A#20[(var X#17)];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=A#20[(letrec {X#1=(var X#17)} in (var X#1))];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[(var X#17)];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#20[(var X#17)];X#5=S#9;E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {X#1=(var X#17)} in A#22[(var X#1)])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[A#22[(var X#17)]]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#21,T#4,A#15,T#12,T#3,A#20,A#22}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#22[[.]]),
             ((var X#17),A#22[[.]]),
             (A#22[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#20[A#22[(var X#17)]];E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#20[A#22[(var X#17)]];E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#22[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20;X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#22[(var X#17)]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},
           A#15         |->  A#20[A#22],
           T#12         |->  A#20,
           A#21         |->  A#22,
           T#4          |->  A#22[[.]],
           T#23         |->  [.],
           S#2          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#16=A#20[A#22[(var X#17)]];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=A#20[(letrec {X#1=(var X#17)} in A#22[(var X#1)])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[A#22[(var X#17)]];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#20[A#22[(var X#17)]];X#5=S#9;E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {X#1=A#23[(var X#17)]} in A#22[(var X#1)])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[A#22[A#23[(var X#17)]]]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#21,T#4,A#15,T#12,T#3,A#20,A#22}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#22),
             (A#23[(var X#17)],A#22),
             (A#22[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#23[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#20[A#22[A#23[(var X#17)]]];E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#20[A#22[A#23[(var X#17)]]];E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#22[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20;X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#22[A#23[(var X#17)]]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},
           A#15         |->  A#20[A#22[A#23]],
           T#12         |->  A#20,
           A#21         |->  A#22[A#23],
           T#4          |->  A#22,
           S#2          |->  A#23[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#22[A#23[(var X#17)]]];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=A#20[(letrec {X#1=A#23[(var X#17)]} in A#22[(var X#1)])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[A#22[A#23[(var X#17)]]];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#20[A#22[A#23[(var X#17)]]];X#5=S#9;E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {X#1=S#2} in A#22[(app A#23[(var X#17)] T#24[(var X#1)])])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#21,T#4,A#15,T#12,T#3,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#22[(app A#23[(var X#17)] T#24)]),
             (S#2,A#22[(app A#23[(var X#17)] T#24)]),
             (A#22[(app A#23[(var X#17)] T#24[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]];E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]];E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#22[(app A#23[(var X#17)] T#24[[.]])]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20;X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},
           A#15         |->  A#20[A#22[(app A#23 T#24[S#2])]],
           T#12         |->  A#20,
           T#4          |->  A#22[(app A#23[(var X#17)] T#24)],
           A#21         |->  A#22[(app A#23 T#24[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=A#20[(letrec {X#1=S#2} in A#22[(app A#23[(var X#17)] T#24[(var X#1)])])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]];X#5=S#9;E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {X#1=A#21[(var X#17)]} in (var X#1))]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[A#21[(var X#17)]]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#21[(var X#17)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#21[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#20[A#21[(var X#17)]];E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#20[A#21[(var X#17)]];E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20;X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#21[(var X#17)]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},
           A#15         |->  A#20[A#21],
           T#12         |->  A#20,
           T#4          |->  [.],
           S#2          |->  A#21[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#21[(var X#17)]];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=A#20[(letrec {X#1=A#21[(var X#17)]} in (var X#1))];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[A#21[(var X#17)]];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#20[A#21[(var X#17)]];X#5=S#9;E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])];E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])];E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in T#4[(var X#1)])])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])];X#5=S#9;E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=(var X#17)} in A#20[(var X#1)])
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[(var X#17)]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[[.]]),
             ((var X#17),A#20[[.]]),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#20[(var X#17)];E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#20[(var X#17)];E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#20[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},
           T#12         |->  [.],
           A#15         |->  A#20,
           T#4          |->  A#20[[.]],
           T#21         |->  [.],
           S#2          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#16=A#20[(var X#17)];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=(var X#17)} in A#20[(var X#1)]);X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[(var X#17)];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#20[(var X#17)];X#5=S#9;E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=A#21[(var X#17)]} in A#20[(var X#1)])
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[A#21[(var X#17)]]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20),
             (A#21[(var X#17)],A#20),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#21[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#20[A#21[(var X#17)]];E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#20[A#21[(var X#17)]];E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#20[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#21[(var X#17)]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},
           T#12         |->  [.],
           A#15         |->  A#20[A#21],
           T#4          |->  A#20,
           S#2          |->  A#21[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#21[(var X#17)]];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=A#21[(var X#17)]} in A#20[(var X#1)]);X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[A#21[(var X#17)]];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#20[A#21[(var X#17)]];X#5=S#9;E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=S#2} in A#20[(app A#21[(var X#17)] T#22[(var X#1)])])
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[S#2])]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[(app A#21[(var X#17)] T#22)]),
             (S#2,A#20[(app A#21[(var X#17)] T#22)]),
             (A#20[(app A#21[(var X#17)] T#22[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),A#20[(app A#21[(var X#17)] T#22[[.]])]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},
           T#12         |->  [.],
           T#4          |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=S#2} in A#20[(app A#21[(var X#17)] T#22[(var X#1)])]);X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];X#5=S#9;E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=A#15[(var X#17)]} in (var X#1))
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#15[(var X#17)]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#15[(var X#17)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#15[(var X#17)];E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#15[(var X#17)];E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#15[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#15[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#15[(var X#17)];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=A#15[(var X#17)]} in (var X#1));X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#15[(var X#17)];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#15[(var X#17)];X#5=S#9;E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=(var X#5)} in (var X#1))]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[(var X#5)]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((var X#5),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#18[(var X#5)];E#7;E#8;EE#17[X#6,(var X#16)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#18[(var X#5)];E#8;EE#17[X#6,(var X#16)]},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[[.]];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#16=A#18[(var X#5)];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=(var X#5)} in (var X#1))];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[(var X#5)];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#18[(var X#5)];X#5=S#9;E#7;E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=(var X#5)} in A#20[(var X#1)])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[A#20[(var X#5)]]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[[.]]),
             ((var X#5),A#20[[.]]),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#18[A#20[(var X#5)]];E#7;E#8;EE#17[X#6,(var X#16)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#18[A#20[(var X#5)]];E#8;EE#17[X#6,(var X#16)]},(letrec {E#7} in [.])],
             ((var X#1),A#20[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#20[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]},
           A#15         |->  A#18[A#20],
           T#12         |->  A#18,
           A#19         |->  A#20,
           T#4          |->  A#20[[.]],
           T#21         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[(var X#5)]];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=(var X#5)} in A#20[(var X#1)])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[(var X#5)]];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#18[A#20[(var X#5)]];X#5=S#9;E#7;E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=A#21[(var X#5)]} in A#20[(var X#1)])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[A#20[A#21[(var X#5)]]]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20),
             (A#21[(var X#5)],A#20),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#21[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#18[A#20[A#21[(var X#5)]]];E#7;E#8;EE#17[X#6,(var X#16)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#18[A#20[A#21[(var X#5)]]];E#8;EE#17[X#6,(var X#16)]},(letrec {E#7} in [.])],
             ((var X#1),A#20[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#20[A#21[[.2]]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]},
           A#15         |->  A#18[A#20[A#21]],
           T#12         |->  A#18,
           A#19         |->  A#20[A#21],
           T#4          |->  A#20,
           S#2          |->  A#21[(var X#5)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[A#21[(var X#5)]]];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=A#21[(var X#5)]} in A#20[(var X#1)])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[A#21[(var X#5)]]];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#18[A#20[A#21[(var X#5)]]];X#5=S#9;E#7;E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=S#2} in A#20[(app A#21[(var X#5)] T#22[(var X#1)])])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[A#20[(app A#21[(var X#5)] T#22[S#2])]]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[(app A#21[(var X#5)] T#22)]),
             (S#2,A#20[(app A#21[(var X#5)] T#22)]),
             (A#20[(app A#21[(var X#5)] T#22[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#18[A#20[(app A#21[(var X#5)] T#22[S#2])]];E#7;E#8;EE#17[X#6,(var X#16)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#18[A#20[(app A#21[(var X#5)] T#22[S#2])]];E#8;EE#17[X#6,(var X#16)]},(letrec {E#7} in [.])],
             ((var X#1),A#20[(app A#21[(var X#5)] T#22[[.]])]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#20[(app A#21[[.2]] T#22[S#2])]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]},
           A#15         |->  A#18[A#20[(app A#21 T#22[S#2])]],
           T#12         |->  A#18,
           T#4          |->  A#20[(app A#21[(var X#5)] T#22)],
           A#19         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[(app A#21[(var X#5)] T#22[S#2])]];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=S#2} in A#20[(app A#21[(var X#5)] T#22[(var X#1)])])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[(app A#21[(var X#5)] T#22[S#2])]];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#18[A#20[(app A#21[(var X#5)] T#22[S#2])]];X#5=S#9;E#7;E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=A#19[(var X#5)]} in (var X#1))]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[A#19[(var X#5)]]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#19[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#18[A#19[(var X#5)]];E#7;E#8;EE#17[X#6,(var X#16)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#18[A#19[(var X#5)]];E#8;EE#17[X#6,(var X#16)]},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#19[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]},
           A#15         |->  A#18[A#19],
           T#12         |->  A#18,
           T#4          |->  [.],
           S#2          |->  A#19[(var X#5)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#19[(var X#5)]];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=A#19[(var X#5)]} in (var X#1))];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[A#19[(var X#5)]];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#18[A#19[(var X#5)]];X#5=S#9;E#7;E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(var X#5)] T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(var X#5)] T#20[T#4[S#2]])]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#18[(app A#19[(var X#5)] T#20[T#4[S#2]])];E#7;E#8;EE#17[X#6,(var X#16)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#18[(app A#19[(var X#5)] T#20[T#4[S#2]])];E#8;EE#17[X#6,(var X#16)]},(letrec {E#7} in [.])],
             ((var X#1),T#4[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20)];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[T#4[S#2]])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]},
           T#12         |->  A#18[(app A#19[(var X#5)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[T#4[S#2]])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[T#4[S#2]])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[T#4[S#2]])];X#5=S#9;E#7;E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=(var X#5)} in A#18[(var X#1)])
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[(var X#5)]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[[.]]),
             ((var X#5),A#18[[.]]),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#18[(var X#5)];E#7;E#8;EE#17[X#6,(var X#16)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#18[(var X#5)];E#8;EE#17[X#6,(var X#16)]},(letrec {E#7} in [.])],
             ((var X#1),A#18[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  A#18,
           T#4          |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  (var X#5)}

and instantiated rules:

                                  (letrec {X#16=A#18[(var X#5)];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=(var X#5)} in A#18[(var X#1)]);X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[(var X#5)];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#18[(var X#5)];X#5=S#9;E#7;E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=A#19[(var X#5)]} in A#18[(var X#1)])
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[A#19[(var X#5)]]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18),
             (A#19[(var X#5)],A#18),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#18[A#19[(var X#5)]];E#7;E#8;EE#17[X#6,(var X#16)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#18[A#19[(var X#5)]];E#8;EE#17[X#6,(var X#16)]},(letrec {E#7} in [.])],
             ((var X#1),A#18[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#19[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  A#18[A#19],
           T#4          |->  A#18,
           S#2          |->  A#19[(var X#5)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#19[(var X#5)]];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=A#19[(var X#5)]} in A#18[(var X#1)]);X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[A#19[(var X#5)]];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#18[A#19[(var X#5)]];X#5=S#9;E#7;E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=S#2} in A#18[(app A#19[(var X#5)] T#20[(var X#1)])])
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(var X#5)] T#20[S#2])]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[(app A#19[(var X#5)] T#20)]),
             (S#2,A#18[(app A#19[(var X#5)] T#20)]),
             (A#18[(app A#19[(var X#5)] T#20[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#18[(app A#19[(var X#5)] T#20[S#2])];E#7;E#8;EE#17[X#6,(var X#16)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#18[(app A#19[(var X#5)] T#20[S#2])];E#8;EE#17[X#6,(var X#16)]},(letrec {E#7} in [.])],
             ((var X#1),A#18[(app A#19[(var X#5)] T#20[[.]])]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[S#2])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]},
           T#12         |->  [.],
           T#4          |->  A#18[(app A#19[(var X#5)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[S#2])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=S#2} in A#18[(app A#19[(var X#5)] T#20[(var X#1)])]);X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[S#2])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[S#2])];X#5=S#9;E#7;E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=A#15[(var X#5)]} in (var X#1))
       ;X#5= (letrec {E#7} in S#9)
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
    ,
     (letrec
        X#16= A#15[(var X#5)]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#15[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#15[(var X#5)];E#7;E#8;EE#17[X#6,(var X#16)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#15[(var X#5)];E#8;EE#17[X#6,(var X#16)]},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#15[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#15[(var X#5)]}

and instantiated rules:

                                  (letrec {X#16=A#15[(var X#5)];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=A#15[(var X#5)]} in (var X#1));X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    ................................................................................
                                  (letrec {X#16=A#15[(var X#5)];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#15[(var X#5)];X#5=S#9;E#7;E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (letrec {E#7} in S#9)
          ;E#8
          ;EE#11[X#6,(var X#5)]
        in
           A#13[(app A#14[(var X#6)] T#15[(var X#1)])]
        )
     )
    ,
     (letrec
        X#5= S#9
       ;E#7
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#13[(app A#14[(var X#6)] T#15[S#2])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15)])),
             (S#2,(letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15)])),
             ((letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#13[(app A#14[(var X#6)] T#15[S#2])],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),(letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[[.]])])),
             ((var X#5),[.]),
             ((var X#6),A#13[(app A#14[[.]] T#15[S#2])]),
             ((var X#5),[.]),
             ((var X#6),A#13[(app A#14[[.]] T#15[S#2])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#6)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[S#2])])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[(var X#1)])]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[S#2])])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#13[(app A#14[(var X#6)] T#15[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (letrec {E#7} in T#15[(var X#1)])
          ;E#8
          ;EE#11[X#6,(var X#5)]
        in
           A#10[(var X#6)]
        )
     )
    ,
     (letrec {X#5=T#15[S#2];E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=(letrec {E#7} in T#15);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])),
             (S#2,(letrec {X#5=(letrec {E#7} in T#15);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])),
             ((letrec {X#5=(letrec {E#7} in T#15[(dummy3 )]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),(letrec {X#5=(letrec {E#7} in T#15[[.]]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=(letrec {E#7} in T#15);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  (letrec {E#7} in T#15),
           S#9   |->  T#15[S#2]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in T#15[S#2]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(letrec {E#7} in T#15[(var X#1)]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in T#15[S#2]);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=T#15[S#2];E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (letrec {X#16=T#15[(var X#1)];E#18} in S#9)
          ;E#8
          ;EE#11[X#6,(var X#5)]
        in
           A#10[(var X#6)]
        )
     )
    ,
     (letrec
        X#16= T#15[S#2]
       ;X#5= S#9
       ;E#18
       ;E#8
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=(letrec {X#16=T#15;E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])),
             (S#2,(letrec {X#5=(letrec {X#16=T#15;E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])),
             ((letrec {X#5=(letrec {X#16=T#15[(dummy3 )];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=T#15[S#2];E#18;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {X#16=T#15[S#2];E#18} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {X#16=T#15[S#2];E#18} in [.])],
             ((var X#1),(letrec {X#5=(letrec {X#16=T#15[[.]];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=(letrec {X#16=T#15;E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  (letrec {X#16=T#15;E#18} in S#9),
           E#7   |->  {X#16=T#15[S#2];E#18},
           E#17  |->  {E#18}}

and instantiated rules:

                                  (letrec {X#5=(letrec {X#16=T#15[S#2];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(letrec {X#16=T#15[(var X#1)];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]))
    ................................................................................
                                  (letrec {X#5=(letrec {X#16=T#15[S#2];E#18} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=T#15[S#2];X#5=S#9;E#18;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#7} in S#9)
     in
        (letrec {X#5=(var X#1);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
     )
    ,
     (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=[.];E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])),
             ((letrec {E#7} in S#9),(letrec {X#5=[.];E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])),
             ((letrec {X#5=(dummy3 );E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),(letrec {X#5=[.];E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#5=[.];E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           X#13  |->  X#5,
           E#14  |->  {E#8;EE#11[X#6,(var X#5)]},
           T#12  |->  [.],
           S#2   |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#1=(letrec {E#7} in S#9)} in (letrec {X#5=(var X#1);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#13= T#12[(var X#1)]
          ;X#5= (letrec {E#7} in S#9)
          ;E#15
          ;EE#11[X#6,(var X#5)]
        in
           A#10[(var X#6)]
        )
     )
    ,
     (letrec
        X#13= T#12[S#2]
       ;X#5= S#9
       ;E#15
       ;E#7
       ;EE#11[X#6,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#13=T#12;X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])),
             (S#2,(letrec {X#13=T#12;X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])),
             ((letrec {X#13=T#12[(dummy3 )];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#13=T#12[S#2];E#15;E#7;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#13=T#12[S#2];E#15;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),(letrec {X#13=T#12[[.]];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#13=T#12;X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),
           E#8   |->  {X#13=T#12[S#2];E#15},
           E#14  |->  {X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[S#2];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#13=T#12[(var X#1)];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]))
    ................................................................................
                                  (letrec {X#13=T#12[S#2];X#5=(letrec {E#7} in S#9);E#15;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#13=T#12[S#2];X#5=S#9;E#15;E#7;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (letrec {E#7} in S#9)
          ;X#6= A#16[(app A#17[(var X#5)] T#18[(var X#1)])]
          ;E#8
        in
           A#10[(var X#6)]
        )
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#16[(app A#17[(var X#5)] T#18[S#2])]
       ;E#7
       ;E#8
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18)];E#8} in A#10[(var X#6)])),
             (S#2,(letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18)];E#8} in A#10[(var X#6)])),
             ((letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[(dummy3 )])];E#8} in A#10[(var X#6)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#16[(app A#17[(var X#5)] T#18[S#2])];E#7;E#8} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#16[(app A#17[(var X#5)] T#18[S#2])];E#8},(letrec {E#7} in [.])],
             ((var X#1),(letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[[.]])];E#8} in A#10[(var X#6)])),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18)];E#8} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[S#2])]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8},
           T#12         |->  A#16[(app A#17[(var X#5)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[S#2])];E#8} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[(var X#1)])];E#8} in A#10[(var X#6)]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#16[(app A#17[(var X#5)] T#18[S#2])];E#8} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#16[(app A#17[(var X#5)] T#18[S#2])];E#7;E#8} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (letrec {E#7} in S#9)
          ;X#6= A#18[(app A#19[(var X#16)] T#20[(var X#1)])]
          ;E#8
          ;EE#17[X#16,(var X#5)]
        in
           A#10[(var X#6)]
        )
     )
    ,
     (letrec
        X#5= S#9
       ;X#6= A#18[(app A#19[(var X#16)] T#20[S#2])]
       ;E#7
       ;E#8
       ;EE#17[X#16,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20)];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])),
             (S#2,(letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20)];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])),
             ((letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[(dummy3 )])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#6=A#18[(app A#19[(var X#16)] T#20[S#2])];E#7;E#8;EE#17[X#16,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#6=A#18[(app A#19[(var X#16)] T#20[S#2])];E#8;EE#17[X#16,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),(letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[[.]])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20)];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[S#2])];EE#17[X#16,[.2]]},
           X#13         |->  X#6,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#16,(var X#5)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[S#2])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[(var X#1)])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);X#6=A#18[(app A#19[(var X#16)] T#20[S#2])];E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;X#6=A#18[(app A#19[(var X#16)] T#20[S#2])];E#7;E#8;EE#17[X#16,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#16= A#20[(app A#21[(var X#17)] T#22[(var X#1)])]
          ;X#5= (letrec {E#7} in S#9)
          ;E#8
          ;EE#18[X#6,(var X#16)]
          ;EE#19[X#17,(var X#5)]
        in
           A#10[(var X#6)]
        )
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[S#2])]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#18[X#6,(var X#16)]
       ;EE#19[X#17,(var X#5)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])),
             (S#2,(letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])),
             ((letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(dummy3 )])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),(letrec {X#16=A#20[(app A#21[(var X#17)] T#22[[.]])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(var X#1)])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)]))
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];X#5=(letrec {E#7} in S#9);E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];X#5=S#9;E#7;E#8;EE#18[X#6,(var X#16)];EE#19[X#17,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#16= A#18[(app A#19[(var X#5)] T#20[(var X#1)])]
          ;X#5= (letrec {E#7} in S#9)
          ;E#8
          ;EE#17[X#6,(var X#16)]
        in
           A#10[(var X#6)]
        )
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(var X#5)] T#20[S#2])]
       ;X#5= S#9
       ;E#7
       ;E#8
       ;EE#17[X#6,(var X#16)]
     in
        A#10[(var X#6)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=A#18[(app A#19[(var X#5)] T#20)];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])),
             (S#2,(letrec {X#16=A#18[(app A#19[(var X#5)] T#20)];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])),
             ((letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(dummy3 )])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#16=A#18[(app A#19[(var X#5)] T#20[S#2])];E#7;E#8;EE#17[X#6,(var X#16)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{X#16=A#18[(app A#19[(var X#5)] T#20[S#2])];E#8;EE#17[X#6,(var X#16)]},(letrec {E#7} in [.])],
             ((var X#1),(letrec {X#16=A#18[(app A#19[(var X#5)] T#20[[.]])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20)];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[S#2])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]},
           T#12         |->  A#18[(app A#19[(var X#5)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[S#2])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[(var X#1)])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)]))
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[S#2])];X#5=(letrec {E#7} in S#9);E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#16=A#18[(app A#19[(var X#5)] T#20[S#2])];X#5=S#9;E#7;E#8;EE#17[X#6,(var X#16)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
     in
        (var X#1)
     )
    ,
     (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
  )

where

   Delta1 = {}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)]),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),
             (A#10[(var X#6)],(letrec {E#7} in [.])),
             [{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],
             ((var X#1),[.]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]]),
             ((var X#5),[.]),
             ((var X#6),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,llet-e2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    and constraints: E#7/= {}, ((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])), (A#10[(var X#6)],(letrec {E#7} in [.])), ({E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),((var X#5),(letrec {E#7;E#8;EE#11[X#6,(var X#5)]} in [.])),(A#10[(var X#6)],(letrec {E#7} in [.])),[{E#8;EE#11[X#6,(var X#5)]},(letrec {E#7} in [.])],((var X#1),T#4[[.]]),((var X#5),[.]),((var X#6),A#10[[.]]),((var X#5),[.]),((var X#6),A#10[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  [.],
           S#2  |->  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])}

and instantiated rules:

                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -ucp3->                       (letrec {X#1=(letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])} in (var X#1))
    ................................................................................
                                  (letrec {X#5=(letrec {E#7} in S#9);E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    -SR,llet-e2->                 (letrec {X#5=S#9;E#7;E#8;EE#11[X#6,(var X#5)]} in A#10[(var X#6)])
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {E#5} in T#12[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#6)]
    ,
     A#9[(letrec {E#5} in (app T#12[T#4[S#2]] S#6))]
  )

where

   Delta1 = {T#11,T#10,A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[(app (letrec {E#5} in T#12) S#6)],
           T#10  |->  (app (letrec {E#5} in T#12) S#6),
           T#11  |->  (letrec {E#5} in T#12),
           S#7   |->  T#12[T#4[S#2]]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in T#12[T#4[S#2]]) S#6)]
    -ucp3->                       A#9[(app (letrec {E#5} in T#12[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#6)]
    ................................................................................
                                  A#9[(app (letrec {E#5} in T#12[T#4[S#2]]) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app T#12[T#4[S#2]] S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {X#13=T#12[(letrec {X#1=S#2} in T#4[(var X#1)])];E#15} in S#7) S#6)]
    ,
     A#9[(letrec {X#13=T#12[T#4[S#2]];E#15} in (app S#7 S#6))]
  )

where

   Delta1 = {T#11,T#10,A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {X#13=T#12[T#4[S#2]];E#15} in [.])),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[(app (letrec {X#13=T#12;E#15} in S#7) S#6)],
           T#10  |->  (app (letrec {X#13=T#12;E#15} in S#7) S#6),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#7),
           E#5   |->  {X#13=T#12[T#4[S#2]];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  A#9[(app (letrec {X#13=T#12[T#4[S#2]];E#15} in S#7) S#6)]
    -ucp3->                       A#9[(app (letrec {X#13=T#12[(letrec {X#1=S#2} in T#4[(var X#1)])];E#15} in S#7) S#6)]
    ................................................................................
                                  A#9[(app (letrec {X#13=T#12[T#4[S#2]];E#15} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {X#13=T#12[T#4[S#2]];E#15} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {X#1=S#2} in (letrec {E#5} in T#12[(var X#1)])) S#6)]
    ,
     A#9[(letrec {E#5} in (app T#12[S#2] S#6))]
  )

where

   Delta1 = {T#4,T#10,A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(letrec {E#5} in T#12)),
             (S#2,(letrec {E#5} in T#12)),
             ((letrec {E#5} in T#12[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),(letrec {E#5} in T#12[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[(app [.] S#6)],
           T#10  |->  (app [.] S#6),
           T#11  |->  [.],
           T#4   |->  (letrec {E#5} in T#12),
           S#7   |->  T#12[S#2]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in T#12[S#2]) S#6)]
    -ucp3->                       A#9[(app (letrec {X#1=S#2} in (letrec {E#5} in T#12[(var X#1)])) S#6)]
    ................................................................................
                                  A#9[(app (letrec {E#5} in T#12[S#2]) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app T#12[S#2] S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {X#1=S#2} in (letrec {X#13=T#12[(var X#1)];E#15} in S#7)) S#6)]
    ,
     A#9[(letrec {X#13=T#12[S#2];E#15} in (app S#7 S#6))]
  )

where

   Delta1 = {T#4,T#10,A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(letrec {X#13=T#12;E#15} in S#7)),
             (S#2,(letrec {X#13=T#12;E#15} in S#7)),
             ((letrec {X#13=T#12[(dummy3 )];E#15} in S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {X#13=T#12[S#2];E#15} in [.])),
             ((var X#1),(letrec {X#13=T#12[[.]];E#15} in S#7))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[(app [.] S#6)],
           T#10  |->  (app [.] S#6),
           T#11  |->  [.],
           T#4   |->  (letrec {X#13=T#12;E#15} in S#7),
           E#5   |->  {X#13=T#12[S#2];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  A#9[(app (letrec {X#13=T#12[S#2];E#15} in S#7) S#6)]
    -ucp3->                       A#9[(app (letrec {X#1=S#2} in (letrec {X#13=T#12[(var X#1)];E#15} in S#7)) S#6)]
    ................................................................................
                                  A#9[(app (letrec {X#13=T#12[S#2];E#15} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {X#13=T#12[S#2];E#15} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {X#1=(letrec {E#5} in S#7)} in (var X#1)) S#6)]
    ,
     A#9[(letrec {E#5} in (app S#7 S#6))]
  )

where

   Delta1 = {T#10,A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#5} in S#7),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#5} in S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[(app [.] S#6)],
           T#10  |->  (app [.] S#6),
           T#11  |->  [.],
           T#4   |->  [.],
           S#2   |->  (letrec {E#5} in S#7)}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in S#7) S#6)]
    -ucp3->                       A#9[(app (letrec {X#1=(letrec {E#5} in S#7)} in (var X#1)) S#6)]
    ................................................................................
                                  A#9[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(app (letrec {E#5} in S#7) T#11[(letrec {X#1=S#2} in T#4[(var X#1)])])]
    ,
     A#9[(letrec {E#5} in (app S#7 T#11[T#4[S#2]]))]
  )

where

   Delta1 = {T#10,A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[T#4[S#2]],(letrec {E#5} in [.])),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[(app (letrec {E#5} in S#7) T#11)],
           T#10  |->  (app (letrec {E#5} in S#7) T#11),
           S#6   |->  T#11[T#4[S#2]]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in S#7) T#11[T#4[S#2]])]
    -ucp3->                       A#9[(app (letrec {E#5} in S#7) T#11[(letrec {X#1=S#2} in T#4[(var X#1)])])]
    ................................................................................
                                  A#9[(app (letrec {E#5} in S#7) T#11[T#4[S#2]])]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app S#7 T#11[T#4[S#2]]))]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=S#2} in (app (letrec {E#5} in T#12[(var X#1)]) S#6))]
    ,
     A#9[(letrec {E#5} in (app T#12[S#2] S#6))]
  )

where

   Delta1 = {T#11,T#4,A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(app (letrec {E#5} in T#12) S#6)),
             (S#2,(app (letrec {E#5} in T#12) S#6)),
             ((app (letrec {E#5} in T#12[(dummy3 )]) S#6),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),(app (letrec {E#5} in T#12[[.]]) S#6))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[[.]],
           T#10  |->  [.],
           T#4   |->  (app (letrec {E#5} in T#12) S#6),
           T#11  |->  (letrec {E#5} in T#12),
           S#7   |->  T#12[S#2]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in T#12[S#2]) S#6)]
    -ucp3->                       A#9[(letrec {X#1=S#2} in (app (letrec {E#5} in T#12[(var X#1)]) S#6))]
    ................................................................................
                                  A#9[(app (letrec {E#5} in T#12[S#2]) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app T#12[S#2] S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=S#2} in (app (letrec {X#13=T#12[(var X#1)];E#15} in S#7) S#6))]
    ,
     A#9[(letrec {X#13=T#12[S#2];E#15} in (app S#7 S#6))]
  )

where

   Delta1 = {T#11,T#4,A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(app (letrec {X#13=T#12;E#15} in S#7) S#6)),
             (S#2,(app (letrec {X#13=T#12;E#15} in S#7) S#6)),
             ((app (letrec {X#13=T#12[(dummy3 )];E#15} in S#7) S#6),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {X#13=T#12[S#2];E#15} in [.])),
             ((var X#1),(app (letrec {X#13=T#12[[.]];E#15} in S#7) S#6))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[[.]],
           T#10  |->  [.],
           T#4   |->  (app (letrec {X#13=T#12;E#15} in S#7) S#6),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#7),
           E#5   |->  {X#13=T#12[S#2];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  A#9[(app (letrec {X#13=T#12[S#2];E#15} in S#7) S#6)]
    -ucp3->                       A#9[(letrec {X#1=S#2} in (app (letrec {X#13=T#12[(var X#1)];E#15} in S#7) S#6))]
    ................................................................................
                                  A#9[(app (letrec {X#13=T#12[S#2];E#15} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {X#13=T#12[S#2];E#15} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=(letrec {E#5} in S#7)} in (app (var X#1) S#6))]
    ,
     A#9[(letrec {E#5} in (app S#7 S#6))]
  )

where

   Delta1 = {T#4,A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(app [.] S#6)),
             ((letrec {E#5} in S#7),(app [.] S#6)),
             ((app (dummy3 ) S#6),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#5} in S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),(app [.] S#6))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[[.]],
           T#10  |->  [.],
           T#4   |->  (app [.] S#6),
           T#11  |->  [.],
           S#2   |->  (letrec {E#5} in S#7)}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in S#7) S#6)]
    -ucp3->                       A#9[(letrec {X#1=(letrec {E#5} in S#7)} in (app (var X#1) S#6))]
    ................................................................................
                                  A#9[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=S#2} in (app (letrec {E#5} in S#7) T#11[(var X#1)]))]
    ,
     A#9[(letrec {E#5} in (app S#7 T#11[S#2]))]
  )

where

   Delta1 = {T#4,A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(app (letrec {E#5} in S#7) T#11)),
             (S#2,(app (letrec {E#5} in S#7) T#11)),
             ((app (letrec {E#5} in S#7) T#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[S#2],(letrec {E#5} in [.])),
             ((var X#1),(app (letrec {E#5} in S#7) T#11[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[[.]],
           T#10  |->  [.],
           T#4   |->  (app (letrec {E#5} in S#7) T#11),
           S#6   |->  T#11[S#2]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in S#7) T#11[S#2])]
    -ucp3->                       A#9[(letrec {X#1=S#2} in (app (letrec {E#5} in S#7) T#11[(var X#1)]))]
    ................................................................................
                                  A#9[(app (letrec {E#5} in S#7) T#11[S#2])]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app S#7 T#11[S#2]))]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=(app (letrec {E#5} in S#7) S#6)} in (var X#1))]
    ,
     A#9[(letrec {E#5} in (app S#7 S#6))]
  )

where

   Delta1 = {A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),[.]),
             ((app (letrec {E#5} in S#7) S#6),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#5} in S#7) S#6),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9,
           T#3   |->  A#9[[.]],
           T#10  |->  [.],
           T#4   |->  [.],
           S#2   |->  (app (letrec {E#5} in S#7) S#6)}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in S#7) S#6)]
    -ucp3->                       A#9[(letrec {X#1=(app (letrec {E#5} in S#7) S#6)} in (var X#1))]
    ................................................................................
                                  A#9[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=S#2} in A#11[(app (letrec {E#5} in T#14[(var X#1)]) S#6)])]
    ,
     A#9[A#11[(letrec {E#5} in (app T#14[S#2] S#6))]]
  )

where

   Delta1 = {T#13,T#12,A#10,T#4,A#8,T#3,A#9,A#11}
   Delta2 = {E#5}
   Delta3 = {((var X#1),A#11[(app (letrec {E#5} in T#14) S#6)]),
             (S#2,A#11[(app (letrec {E#5} in T#14) S#6)]),
             (A#11[(app (letrec {E#5} in T#14[(dummy3 )]) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),A#11[(app (letrec {E#5} in T#14[[.]]) S#6)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[A#11],
           T#3   |->  A#9,
           A#10  |->  A#11,
           T#4   |->  A#11[(app (letrec {E#5} in T#14) S#6)],
           T#12  |->  (app (letrec {E#5} in T#14) S#6),
           T#13  |->  (letrec {E#5} in T#14),
           S#7   |->  T#14[S#2]}

and instantiated rules:

                                  A#9[A#11[(app (letrec {E#5} in T#14[S#2]) S#6)]]
    -ucp3->                       A#9[(letrec {X#1=S#2} in A#11[(app (letrec {E#5} in T#14[(var X#1)]) S#6)])]
    ................................................................................
                                  A#9[A#11[(app (letrec {E#5} in T#14[S#2]) S#6)]]
    -SR,lapp1->                   A#9[A#11[(letrec {E#5} in (app T#14[S#2] S#6))]]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec
             X#1= S#2
          in
             A#11[(app (letrec {X#15=T#14[(var X#1)];E#17} in S#7) S#6)]
          )]
    ,
     A#9[A#11[(letrec {X#15=T#14[S#2];E#17} in (app S#7 S#6))]]
  )

where

   Delta1 = {T#13,T#12,A#10,T#4,A#8,T#3,A#9,A#11}
   Delta2 = {E#5}
   Delta3 = {((var X#1),A#11[(app (letrec {X#15=T#14;E#17} in S#7) S#6)]),
             (S#2,A#11[(app (letrec {X#15=T#14;E#17} in S#7) S#6)]),
             (A#11[(app (letrec {X#15=T#14[(dummy3 )];E#17} in S#7) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {X#15=T#14[S#2];E#17} in [.])),
             ((var X#1),A#11[(app (letrec {X#15=T#14[[.]];E#17} in S#7) S#6)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[A#11],
           T#3   |->  A#9,
           A#10  |->  A#11,
           T#4   |->  A#11[(app (letrec {X#15=T#14;E#17} in S#7) S#6)],
           T#12  |->  (app (letrec {X#15=T#14;E#17} in S#7) S#6),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#7),
           E#5   |->  {X#15=T#14[S#2];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  A#9[A#11[(app (letrec {X#15=T#14[S#2];E#17} in S#7) S#6)]]
    -ucp3->                       A#9[(letrec {X#1=S#2} in A#11[(app (letrec {X#15=T#14[(var X#1)];E#17} in S#7) S#6)])]
    ................................................................................
                                  A#9[A#11[(app (letrec {X#15=T#14[S#2];E#17} in S#7) S#6)]]
    -SR,lapp1->                   A#9[A#11[(letrec {X#15=T#14[S#2];E#17} in (app S#7 S#6))]]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=(letrec {E#5} in S#7)} in A#11[(app (var X#1) S#6)])]
    ,
     A#9[A#11[(letrec {E#5} in (app S#7 S#6))]]
  )

where

   Delta1 = {T#12,A#10,T#4,A#8,T#3,A#9,A#11}
   Delta2 = {E#5}
   Delta3 = {((var X#1),A#11[(app [.] S#6)]),
             ((letrec {E#5} in S#7),A#11[(app [.] S#6)]),
             (A#11[(app (dummy3 ) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#5} in S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),A#11[(app [.] S#6)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[A#11],
           T#3   |->  A#9,
           A#10  |->  A#11,
           T#4   |->  A#11[(app [.] S#6)],
           T#12  |->  (app [.] S#6),
           T#13  |->  [.],
           S#2   |->  (letrec {E#5} in S#7)}

and instantiated rules:

                                  A#9[A#11[(app (letrec {E#5} in S#7) S#6)]]
    -ucp3->                       A#9[(letrec {X#1=(letrec {E#5} in S#7)} in A#11[(app (var X#1) S#6)])]
    ................................................................................
                                  A#9[A#11[(app (letrec {E#5} in S#7) S#6)]]
    -SR,lapp1->                   A#9[A#11[(letrec {E#5} in (app S#7 S#6))]]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=S#2} in A#11[(app (letrec {E#5} in S#7) T#13[(var X#1)])])]
    ,
     A#9[A#11[(letrec {E#5} in (app S#7 T#13[S#2]))]]
  )

where

   Delta1 = {T#12,A#10,T#4,A#8,T#3,A#9,A#11}
   Delta2 = {E#5}
   Delta3 = {((var X#1),A#11[(app (letrec {E#5} in S#7) T#13)]),
             (S#2,A#11[(app (letrec {E#5} in S#7) T#13)]),
             (A#11[(app (letrec {E#5} in S#7) T#13[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#13[S#2],(letrec {E#5} in [.])),
             ((var X#1),A#11[(app (letrec {E#5} in S#7) T#13[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[A#11],
           T#3   |->  A#9,
           A#10  |->  A#11,
           T#4   |->  A#11[(app (letrec {E#5} in S#7) T#13)],
           T#12  |->  (app (letrec {E#5} in S#7) T#13),
           S#6   |->  T#13[S#2]}

and instantiated rules:

                                  A#9[A#11[(app (letrec {E#5} in S#7) T#13[S#2])]]
    -ucp3->                       A#9[(letrec {X#1=S#2} in A#11[(app (letrec {E#5} in S#7) T#13[(var X#1)])])]
    ................................................................................
                                  A#9[A#11[(app (letrec {E#5} in S#7) T#13[S#2])]]
    -SR,lapp1->                   A#9[A#11[(letrec {E#5} in (app S#7 T#13[S#2]))]]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=(app (letrec {E#5} in S#7) S#6)} in A#11[(var X#1)])]
    ,
     A#9[A#11[(letrec {E#5} in (app S#7 S#6))]]
  )

where

   Delta1 = {A#10,T#4,A#8,T#3,A#9,A#11}
   Delta2 = {E#5}
   Delta3 = {((var X#1),A#11[[.]]),
             ((app (letrec {E#5} in S#7) S#6),A#11[[.]]),
             (A#11[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#5} in S#7) S#6),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[A#11],
           T#3   |->  A#9,
           A#10  |->  A#11,
           T#4   |->  A#11[[.]],
           T#12  |->  [.],
           S#2   |->  (app (letrec {E#5} in S#7) S#6)}

and instantiated rules:

                                  A#9[A#11[(app (letrec {E#5} in S#7) S#6)]]
    -ucp3->                       A#9[(letrec {X#1=(app (letrec {E#5} in S#7) S#6)} in A#11[(var X#1)])]
    ................................................................................
                                  A#9[A#11[(app (letrec {E#5} in S#7) S#6)]]
    -SR,lapp1->                   A#9[A#11[(letrec {E#5} in (app S#7 S#6))]]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=A#12[(app (letrec {E#5} in S#7) S#6)]} in A#11[(var X#1)])]
    ,
     A#9[A#11[A#12[(letrec {E#5} in (app S#7 S#6))]]]
  )

where

   Delta1 = {A#10,T#4,A#8,T#3,A#9,A#11}
   Delta2 = {E#5}
   Delta3 = {((var X#1),A#11),
             (A#12[(app (letrec {E#5} in S#7) S#6)],A#11),
             (A#11[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(app (letrec {E#5} in S#7) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[A#11[A#12]],
           T#3   |->  A#9,
           A#10  |->  A#11[A#12],
           T#4   |->  A#11,
           S#2   |->  A#12[(app (letrec {E#5} in S#7) S#6)]}

and instantiated rules:

                                  A#9[A#11[A#12[(app (letrec {E#5} in S#7) S#6)]]]
    -ucp3->                       A#9[(letrec {X#1=A#12[(app (letrec {E#5} in S#7) S#6)]} in A#11[(var X#1)])]
    ................................................................................
                                  A#9[A#11[A#12[(app (letrec {E#5} in S#7) S#6)]]]
    -SR,lapp1->                   A#9[A#11[A#12[(letrec {E#5} in (app S#7 S#6))]]]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec
             X#1= S#2
          in
             A#11[(app A#12[(app (letrec {E#5} in S#7) S#6)] T#13[(var X#1)])]
          )]
    ,
     A#9[A#11[(app A#12[(letrec {E#5} in (app S#7 S#6))] T#13[S#2])]]
  )

where

   Delta1 = {A#10,T#4,A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),A#11[(app A#12[(app (letrec {E#5} in S#7) S#6)] T#13)]),
             (S#2,A#11[(app A#12[(app (letrec {E#5} in S#7) S#6)] T#13)]),
             (A#11[(app A#12[(app (letrec {E#5} in S#7) S#6)] T#13[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),A#11[(app A#12[(app (letrec {E#5} in S#7) S#6)] T#13[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[A#11[(app A#12 T#13[S#2])]],
           T#3   |->  A#9,
           T#4   |->  A#11[(app A#12[(app (letrec {E#5} in S#7) S#6)] T#13)],
           A#10  |->  A#11[(app A#12 T#13[S#2])]}

and instantiated rules:

                                  A#9[A#11[(app A#12[(app (letrec {E#5} in S#7) S#6)] T#13[S#2])]]
    -ucp3->                       A#9[(letrec {X#1=S#2} in A#11[(app A#12[(app (letrec {E#5} in S#7) S#6)] T#13[(var X#1)])])]
    ................................................................................
                                  A#9[A#11[(app A#12[(app (letrec {E#5} in S#7) S#6)] T#13[S#2])]]
    -SR,lapp1->                   A#9[A#11[(app A#12[(letrec {E#5} in (app S#7 S#6))] T#13[S#2])]]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=S#2} in (app (letrec {E#5} in T#12[(var X#1)]) S#6))]
    ,
     A#9[(letrec {E#5} in (app T#12[S#2] S#6))]
  )

where

   Delta1 = {T#11,T#4,A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(app (letrec {E#5} in T#12) S#6)),
             (S#2,(app (letrec {E#5} in T#12) S#6)),
             ((app (letrec {E#5} in T#12[(dummy3 )]) S#6),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),(app (letrec {E#5} in T#12[[.]]) S#6))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[[.]],
           T#3   |->  A#9,
           A#10  |->  [.],
           T#4   |->  (app (letrec {E#5} in T#12) S#6),
           T#11  |->  (letrec {E#5} in T#12),
           S#7   |->  T#12[S#2]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in T#12[S#2]) S#6)]
    -ucp3->                       A#9[(letrec {X#1=S#2} in (app (letrec {E#5} in T#12[(var X#1)]) S#6))]
    ................................................................................
                                  A#9[(app (letrec {E#5} in T#12[S#2]) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app T#12[S#2] S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=S#2} in (app (letrec {X#13=T#12[(var X#1)];E#15} in S#7) S#6))]
    ,
     A#9[(letrec {X#13=T#12[S#2];E#15} in (app S#7 S#6))]
  )

where

   Delta1 = {T#11,T#4,A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(app (letrec {X#13=T#12;E#15} in S#7) S#6)),
             (S#2,(app (letrec {X#13=T#12;E#15} in S#7) S#6)),
             ((app (letrec {X#13=T#12[(dummy3 )];E#15} in S#7) S#6),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {X#13=T#12[S#2];E#15} in [.])),
             ((var X#1),(app (letrec {X#13=T#12[[.]];E#15} in S#7) S#6))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[[.]],
           T#3   |->  A#9,
           A#10  |->  [.],
           T#4   |->  (app (letrec {X#13=T#12;E#15} in S#7) S#6),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#7),
           E#5   |->  {X#13=T#12[S#2];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  A#9[(app (letrec {X#13=T#12[S#2];E#15} in S#7) S#6)]
    -ucp3->                       A#9[(letrec {X#1=S#2} in (app (letrec {X#13=T#12[(var X#1)];E#15} in S#7) S#6))]
    ................................................................................
                                  A#9[(app (letrec {X#13=T#12[S#2];E#15} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {X#13=T#12[S#2];E#15} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=(letrec {E#5} in S#7)} in (app (var X#1) S#6))]
    ,
     A#9[(letrec {E#5} in (app S#7 S#6))]
  )

where

   Delta1 = {T#4,A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(app [.] S#6)),
             ((letrec {E#5} in S#7),(app [.] S#6)),
             ((app (dummy3 ) S#6),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#5} in S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),(app [.] S#6))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[[.]],
           T#3   |->  A#9,
           A#10  |->  [.],
           T#4   |->  (app [.] S#6),
           T#11  |->  [.],
           S#2   |->  (letrec {E#5} in S#7)}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in S#7) S#6)]
    -ucp3->                       A#9[(letrec {X#1=(letrec {E#5} in S#7)} in (app (var X#1) S#6))]
    ................................................................................
                                  A#9[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=S#2} in (app (letrec {E#5} in S#7) T#11[(var X#1)]))]
    ,
     A#9[(letrec {E#5} in (app S#7 T#11[S#2]))]
  )

where

   Delta1 = {T#4,A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(app (letrec {E#5} in S#7) T#11)),
             (S#2,(app (letrec {E#5} in S#7) T#11)),
             ((app (letrec {E#5} in S#7) T#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[S#2],(letrec {E#5} in [.])),
             ((var X#1),(app (letrec {E#5} in S#7) T#11[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  A#9[[.]],
           T#3   |->  A#9,
           A#10  |->  [.],
           T#4   |->  (app (letrec {E#5} in S#7) T#11),
           S#6   |->  T#11[S#2]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in S#7) T#11[S#2])]
    -ucp3->                       A#9[(letrec {X#1=S#2} in (app (letrec {E#5} in S#7) T#11[(var X#1)]))]
    ................................................................................
                                  A#9[(app (letrec {E#5} in S#7) T#11[S#2])]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app S#7 T#11[S#2]))]
    

================================================================================
Critical Pair:

  (
     A#9[(letrec {X#1=A#10[(app (letrec {E#5} in S#7) S#6)]} in (var X#1))]
    ,
     A#9[A#10[(letrec {E#5} in (app S#7 S#6))]]
  )

where

   Delta1 = {A#8,T#3,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),[.]),
             (A#10[(app (letrec {E#5} in S#7) S#6)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(app (letrec {E#5} in S#7) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8  |->  A#9[A#10],
           T#3  |->  A#9,
           T#4  |->  [.],
           S#2  |->  A#10[(app (letrec {E#5} in S#7) S#6)]}

and instantiated rules:

                                  A#9[A#10[(app (letrec {E#5} in S#7) S#6)]]
    -ucp3->                       A#9[(letrec {X#1=A#10[(app (letrec {E#5} in S#7) S#6)]} in (var X#1))]
    ................................................................................
                                  A#9[A#10[(app (letrec {E#5} in S#7) S#6)]]
    -SR,lapp1->                   A#9[A#10[(letrec {E#5} in (app S#7 S#6))]]
    

================================================================================
Critical Pair:

  (
     A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(letrec {X#1=S#2} in T#4[(var X#1)])])]
    ,
     A#9[(app A#10[(letrec {E#5} in (app S#7 S#6))] T#11[T#4[S#2]])]
  )

where

   Delta1 = {A#8,T#3}
   Delta2 = {E#5}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11)],
           A#8  |->  A#9[(app A#10 T#11[T#4[S#2]])]}

and instantiated rules:

                                  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[T#4[S#2]])]
    -ucp3->                       A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(letrec {X#1=S#2} in T#4[(var X#1)])])]
    ................................................................................
                                  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[T#4[S#2]])]
    -SR,lapp1->                   A#9[(app A#10[(letrec {E#5} in (app S#7 S#6))] T#11[T#4[S#2]])]
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#5} in T#10[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#6)
    ,
     (letrec {E#5} in (app T#10[T#4[S#2]] S#6))
  )

where

   Delta1 = {T#9,T#3}
   Delta2 = {E#5}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8  |->  [.],
           T#3  |->  (app (letrec {E#5} in T#10) S#6),
           T#9  |->  (letrec {E#5} in T#10),
           S#7  |->  T#10[T#4[S#2]]}

and instantiated rules:

                                  (app (letrec {E#5} in T#10[T#4[S#2]]) S#6)
    -ucp3->                       (app (letrec {E#5} in T#10[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#6)
    ................................................................................
                                  (app (letrec {E#5} in T#10[T#4[S#2]]) S#6)
    -SR,lapp1->                   (letrec {E#5} in (app T#10[T#4[S#2]] S#6))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#11=T#10[(letrec {X#1=S#2} in T#4[(var X#1)])];E#13} in S#7) S#6)
    ,
     (letrec {X#11=T#10[T#4[S#2]];E#13} in (app S#7 S#6))
  )

where

   Delta1 = {T#9,T#3}
   Delta2 = {E#5}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {X#11=T#10[T#4[S#2]];E#13} in [.])),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  [.],
           T#3   |->  (app (letrec {X#11=T#10;E#13} in S#7) S#6),
           T#9   |->  (letrec {X#11=T#10;E#13} in S#7),
           E#5   |->  {X#11=T#10[T#4[S#2]];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (app (letrec {X#11=T#10[T#4[S#2]];E#13} in S#7) S#6)
    -ucp3->                       (app (letrec {X#11=T#10[(letrec {X#1=S#2} in T#4[(var X#1)])];E#13} in S#7) S#6)
    ................................................................................
                                  (app (letrec {X#11=T#10[T#4[S#2]];E#13} in S#7) S#6)
    -SR,lapp1->                   (letrec {X#11=T#10[T#4[S#2]];E#13} in (app S#7 S#6))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#1=S#2} in (letrec {E#5} in T#10[(var X#1)])) S#6)
    ,
     (letrec {E#5} in (app T#10[S#2] S#6))
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(letrec {E#5} in T#10)),
             (S#2,(letrec {E#5} in T#10)),
             ((letrec {E#5} in T#10[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),(letrec {E#5} in T#10[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8  |->  [.],
           T#3  |->  (app [.] S#6),
           T#9  |->  [.],
           T#4  |->  (letrec {E#5} in T#10),
           S#7  |->  T#10[S#2]}

and instantiated rules:

                                  (app (letrec {E#5} in T#10[S#2]) S#6)
    -ucp3->                       (app (letrec {X#1=S#2} in (letrec {E#5} in T#10[(var X#1)])) S#6)
    ................................................................................
                                  (app (letrec {E#5} in T#10[S#2]) S#6)
    -SR,lapp1->                   (letrec {E#5} in (app T#10[S#2] S#6))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#1=S#2} in (letrec {X#11=T#10[(var X#1)];E#13} in S#7)) S#6)
    ,
     (letrec {X#11=T#10[S#2];E#13} in (app S#7 S#6))
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(letrec {X#11=T#10;E#13} in S#7)),
             (S#2,(letrec {X#11=T#10;E#13} in S#7)),
             ((letrec {X#11=T#10[(dummy3 )];E#13} in S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {X#11=T#10[S#2];E#13} in [.])),
             ((var X#1),(letrec {X#11=T#10[[.]];E#13} in S#7))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8   |->  [.],
           T#3   |->  (app [.] S#6),
           T#9   |->  [.],
           T#4   |->  (letrec {X#11=T#10;E#13} in S#7),
           E#5   |->  {X#11=T#10[S#2];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (app (letrec {X#11=T#10[S#2];E#13} in S#7) S#6)
    -ucp3->                       (app (letrec {X#1=S#2} in (letrec {X#11=T#10[(var X#1)];E#13} in S#7)) S#6)
    ................................................................................
                                  (app (letrec {X#11=T#10[S#2];E#13} in S#7) S#6)
    -SR,lapp1->                   (letrec {X#11=T#10[S#2];E#13} in (app S#7 S#6))
    

================================================================================
Critical Pair:

  (
     (app (letrec {X#1=(letrec {E#5} in S#7)} in (var X#1)) S#6)
    ,
     (letrec {E#5} in (app S#7 S#6))
  )

where

   Delta1 = {T#3}
   Delta2 = {E#5}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#5} in S#7),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#5} in S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8  |->  [.],
           T#3  |->  (app [.] S#6),
           T#9  |->  [.],
           T#4  |->  [.],
           S#2  |->  (letrec {E#5} in S#7)}

and instantiated rules:

                                  (app (letrec {E#5} in S#7) S#6)
    -ucp3->                       (app (letrec {X#1=(letrec {E#5} in S#7)} in (var X#1)) S#6)
    ................................................................................
                                  (app (letrec {E#5} in S#7) S#6)
    -SR,lapp1->                   (letrec {E#5} in (app S#7 S#6))
    

================================================================================
Critical Pair:

  (
     (app (letrec {E#5} in S#7) T#9[(letrec {X#1=S#2} in T#4[(var X#1)])])
    ,
     (letrec {E#5} in (app S#7 T#9[T#4[S#2]]))
  )

where

   Delta1 = {T#3}
   Delta2 = {E#5}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#9[T#4[S#2]],(letrec {E#5} in [.])),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {A#8  |->  [.],
           T#3  |->  (app (letrec {E#5} in S#7) T#9),
           S#6  |->  T#9[T#4[S#2]]}

and instantiated rules:

                                  (app (letrec {E#5} in S#7) T#9[T#4[S#2]])
    -ucp3->                       (app (letrec {E#5} in S#7) T#9[(letrec {X#1=S#2} in T#4[(var X#1)])])
    ................................................................................
                                  (app (letrec {E#5} in S#7) T#9[T#4[S#2]])
    -SR,lapp1->                   (letrec {E#5} in (app S#7 T#9[T#4[S#2]]))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#2} in A#9[(app (letrec {E#5} in T#12[(var X#1)]) S#6)])
    ,
     A#9[(letrec {E#5} in (app T#12[S#2] S#6))]
  )

where

   Delta1 = {T#11,T#10,A#8,T#4,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),A#9[(app (letrec {E#5} in T#12) S#6)]),
             (S#2,A#9[(app (letrec {E#5} in T#12) S#6)]),
             (A#9[(app (letrec {E#5} in T#12[(dummy3 )]) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),A#9[(app (letrec {E#5} in T#12[[.]]) S#6)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           A#8   |->  A#9,
           T#4   |->  A#9[(app (letrec {E#5} in T#12) S#6)],
           T#10  |->  (app (letrec {E#5} in T#12) S#6),
           T#11  |->  (letrec {E#5} in T#12),
           S#7   |->  T#12[S#2]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in T#12[S#2]) S#6)]
    -ucp3->                       (letrec {X#1=S#2} in A#9[(app (letrec {E#5} in T#12[(var X#1)]) S#6)])
    ................................................................................
                                  A#9[(app (letrec {E#5} in T#12[S#2]) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app T#12[S#2] S#6))]
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#2} in A#9[(app (letrec {X#13=T#12[(var X#1)];E#15} in S#7) S#6)])
    ,
     A#9[(letrec {X#13=T#12[S#2];E#15} in (app S#7 S#6))]
  )

where

   Delta1 = {T#11,T#10,A#8,T#4,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),A#9[(app (letrec {X#13=T#12;E#15} in S#7) S#6)]),
             (S#2,A#9[(app (letrec {X#13=T#12;E#15} in S#7) S#6)]),
             (A#9[(app (letrec {X#13=T#12[(dummy3 )];E#15} in S#7) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {X#13=T#12[S#2];E#15} in [.])),
             ((var X#1),A#9[(app (letrec {X#13=T#12[[.]];E#15} in S#7) S#6)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           A#8   |->  A#9,
           T#4   |->  A#9[(app (letrec {X#13=T#12;E#15} in S#7) S#6)],
           T#10  |->  (app (letrec {X#13=T#12;E#15} in S#7) S#6),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#7),
           E#5   |->  {X#13=T#12[S#2];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  A#9[(app (letrec {X#13=T#12[S#2];E#15} in S#7) S#6)]
    -ucp3->                       (letrec {X#1=S#2} in A#9[(app (letrec {X#13=T#12[(var X#1)];E#15} in S#7) S#6)])
    ................................................................................
                                  A#9[(app (letrec {X#13=T#12[S#2];E#15} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {X#13=T#12[S#2];E#15} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {E#5} in S#7)} in A#9[(app (var X#1) S#6)])
    ,
     A#9[(letrec {E#5} in (app S#7 S#6))]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),A#9[(app [.] S#6)]),
             ((letrec {E#5} in S#7),A#9[(app [.] S#6)]),
             (A#9[(app (dummy3 ) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#5} in S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),A#9[(app [.] S#6)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           A#8   |->  A#9,
           T#4   |->  A#9[(app [.] S#6)],
           T#10  |->  (app [.] S#6),
           T#11  |->  [.],
           S#2   |->  (letrec {E#5} in S#7)}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in S#7) S#6)]
    -ucp3->                       (letrec {X#1=(letrec {E#5} in S#7)} in A#9[(app (var X#1) S#6)])
    ................................................................................
                                  A#9[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#2} in A#9[(app (letrec {E#5} in S#7) T#11[(var X#1)])])
    ,
     A#9[(letrec {E#5} in (app S#7 T#11[S#2]))]
  )

where

   Delta1 = {T#10,A#8,T#4,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),A#9[(app (letrec {E#5} in S#7) T#11)]),
             (S#2,A#9[(app (letrec {E#5} in S#7) T#11)]),
             (A#9[(app (letrec {E#5} in S#7) T#11[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[S#2],(letrec {E#5} in [.])),
             ((var X#1),A#9[(app (letrec {E#5} in S#7) T#11[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           A#8   |->  A#9,
           T#4   |->  A#9[(app (letrec {E#5} in S#7) T#11)],
           T#10  |->  (app (letrec {E#5} in S#7) T#11),
           S#6   |->  T#11[S#2]}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in S#7) T#11[S#2])]
    -ucp3->                       (letrec {X#1=S#2} in A#9[(app (letrec {E#5} in S#7) T#11[(var X#1)])])
    ................................................................................
                                  A#9[(app (letrec {E#5} in S#7) T#11[S#2])]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app S#7 T#11[S#2]))]
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(app (letrec {E#5} in S#7) S#6)} in A#9[(var X#1)])
    ,
     A#9[(letrec {E#5} in (app S#7 S#6))]
  )

where

   Delta1 = {A#8,T#4,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),A#9[[.]]),
             ((app (letrec {E#5} in S#7) S#6),A#9[[.]]),
             (A#9[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#5} in S#7) S#6),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           A#8   |->  A#9,
           T#4   |->  A#9[[.]],
           T#10  |->  [.],
           S#2   |->  (app (letrec {E#5} in S#7) S#6)}

and instantiated rules:

                                  A#9[(app (letrec {E#5} in S#7) S#6)]
    -ucp3->                       (letrec {X#1=(app (letrec {E#5} in S#7) S#6)} in A#9[(var X#1)])
    ................................................................................
                                  A#9[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#9[(letrec {E#5} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=A#10[(app (letrec {E#5} in S#7) S#6)]} in A#9[(var X#1)])
    ,
     A#9[A#10[(letrec {E#5} in (app S#7 S#6))]]
  )

where

   Delta1 = {A#8,T#4,A#9}
   Delta2 = {E#5}
   Delta3 = {((var X#1),A#9),
             (A#10[(app (letrec {E#5} in S#7) S#6)],A#9),
             (A#9[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(app (letrec {E#5} in S#7) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),A#9[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           A#8  |->  A#9[A#10],
           T#4  |->  A#9,
           S#2  |->  A#10[(app (letrec {E#5} in S#7) S#6)]}

and instantiated rules:

                                  A#9[A#10[(app (letrec {E#5} in S#7) S#6)]]
    -ucp3->                       (letrec {X#1=A#10[(app (letrec {E#5} in S#7) S#6)]} in A#9[(var X#1)])
    ................................................................................
                                  A#9[A#10[(app (letrec {E#5} in S#7) S#6)]]
    -SR,lapp1->                   A#9[A#10[(letrec {E#5} in (app S#7 S#6))]]
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(var X#1)])]
     )
    ,
     A#9[(app A#10[(letrec {E#5} in (app S#7 S#6))] T#11[S#2])]
  )

where

   Delta1 = {A#8,T#4}
   Delta2 = {E#5}
   Delta3 = {((var X#1),A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11)]),
             (S#2,A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11)]),
             (A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11)],
           A#8  |->  A#9[(app A#10 T#11[S#2])]}

and instantiated rules:

                                  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[S#2])]
    -ucp3->                       (letrec {X#1=S#2} in A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[(var X#1)])])
    ................................................................................
                                  A#9[(app A#10[(app (letrec {E#5} in S#7) S#6)] T#11[S#2])]
    -SR,lapp1->                   A#9[(app A#10[(letrec {E#5} in (app S#7 S#6))] T#11[S#2])]
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#2} in (app (letrec {E#5} in T#10[(var X#1)]) S#6))
    ,
     (letrec {E#5} in (app T#10[S#2] S#6))
  )

where

   Delta1 = {T#9,T#4}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(app (letrec {E#5} in T#10) S#6)),
             (S#2,(app (letrec {E#5} in T#10) S#6)),
             ((app (letrec {E#5} in T#10[(dummy3 )]) S#6),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),(app (letrec {E#5} in T#10[[.]]) S#6))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           A#8  |->  [.],
           T#4  |->  (app (letrec {E#5} in T#10) S#6),
           T#9  |->  (letrec {E#5} in T#10),
           S#7  |->  T#10[S#2]}

and instantiated rules:

                                  (app (letrec {E#5} in T#10[S#2]) S#6)
    -ucp3->                       (letrec {X#1=S#2} in (app (letrec {E#5} in T#10[(var X#1)]) S#6))
    ................................................................................
                                  (app (letrec {E#5} in T#10[S#2]) S#6)
    -SR,lapp1->                   (letrec {E#5} in (app T#10[S#2] S#6))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#2} in (app (letrec {X#11=T#10[(var X#1)];E#13} in S#7) S#6))
    ,
     (letrec {X#11=T#10[S#2];E#13} in (app S#7 S#6))
  )

where

   Delta1 = {T#9,T#4}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(app (letrec {X#11=T#10;E#13} in S#7) S#6)),
             (S#2,(app (letrec {X#11=T#10;E#13} in S#7) S#6)),
             ((app (letrec {X#11=T#10[(dummy3 )];E#13} in S#7) S#6),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {X#11=T#10[S#2];E#13} in [.])),
             ((var X#1),(app (letrec {X#11=T#10[[.]];E#13} in S#7) S#6))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           A#8   |->  [.],
           T#4   |->  (app (letrec {X#11=T#10;E#13} in S#7) S#6),
           T#9   |->  (letrec {X#11=T#10;E#13} in S#7),
           E#5   |->  {X#11=T#10[S#2];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (app (letrec {X#11=T#10[S#2];E#13} in S#7) S#6)
    -ucp3->                       (letrec {X#1=S#2} in (app (letrec {X#11=T#10[(var X#1)];E#13} in S#7) S#6))
    ................................................................................
                                  (app (letrec {X#11=T#10[S#2];E#13} in S#7) S#6)
    -SR,lapp1->                   (letrec {X#11=T#10[S#2];E#13} in (app S#7 S#6))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {E#5} in S#7)} in (app (var X#1) S#6))
    ,
     (letrec {E#5} in (app S#7 S#6))
  )

where

   Delta1 = {T#4}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(app [.] S#6)),
             ((letrec {E#5} in S#7),(app [.] S#6)),
             ((app (dummy3 ) S#6),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#5} in S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),(app [.] S#6))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           A#8  |->  [.],
           T#4  |->  (app [.] S#6),
           T#9  |->  [.],
           S#2  |->  (letrec {E#5} in S#7)}

and instantiated rules:

                                  (app (letrec {E#5} in S#7) S#6)
    -ucp3->                       (letrec {X#1=(letrec {E#5} in S#7)} in (app (var X#1) S#6))
    ................................................................................
                                  (app (letrec {E#5} in S#7) S#6)
    -SR,lapp1->                   (letrec {E#5} in (app S#7 S#6))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=S#2} in (app (letrec {E#5} in S#7) T#9[(var X#1)]))
    ,
     (letrec {E#5} in (app S#7 T#9[S#2]))
  )

where

   Delta1 = {T#4}
   Delta2 = {E#5}
   Delta3 = {((var X#1),(app (letrec {E#5} in S#7) T#9)),
             (S#2,(app (letrec {E#5} in S#7) T#9)),
             ((app (letrec {E#5} in S#7) T#9[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#9[S#2],(letrec {E#5} in [.])),
             ((var X#1),(app (letrec {E#5} in S#7) T#9[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           A#8  |->  [.],
           T#4  |->  (app (letrec {E#5} in S#7) T#9),
           S#6  |->  T#9[S#2]}

and instantiated rules:

                                  (app (letrec {E#5} in S#7) T#9[S#2])
    -ucp3->                       (letrec {X#1=S#2} in (app (letrec {E#5} in S#7) T#9[(var X#1)]))
    ................................................................................
                                  (app (letrec {E#5} in S#7) T#9[S#2])
    -SR,lapp1->                   (letrec {E#5} in (app S#7 T#9[S#2]))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=A#8[(app (letrec {E#5} in S#7) S#6)]} in (var X#1))
    ,
     A#8[(letrec {E#5} in (app S#7 S#6))]
  )

where

   Delta1 = {}
   Delta2 = {E#5}
   Delta3 = {((var X#1),[.]),
             (A#8[(app (letrec {E#5} in S#7) S#6)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#8[(app (letrec {E#5} in S#7) S#6)],(letrec {X#1=(dummy3 )} in [.])),
             (S#6,(letrec {E#5} in [.])),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp1-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    and constraints: E#5/= {}, (S#6,(letrec {E#5} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= A#8[(app (letrec {E#5} in S#7) S#6)]}
      Delta1=  {}
      Delta2=  {E#5}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#6,(letrec {E#5} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  [.],
           S#2  |->  A#8[(app (letrec {E#5} in S#7) S#6)]}

and instantiated rules:

                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -ucp3->                       (letrec {X#1=A#8[(app (letrec {E#5} in S#7) S#6)]} in (var X#1))
    ................................................................................
                                  A#8[(app (letrec {E#5} in S#7) S#6)]
    -SR,lapp1->                   A#8[(letrec {E#5} in (app S#7 S#6))]
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {E#6} in T#14[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#7)]
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[T#4[S#2]] S#7))])
  )

where

   Delta1 = {T#13,T#12,A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14) S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {E#6} in T#14) S#7)],
           T#12  |->  (app (letrec {E#6} in T#14) S#7),
           T#13  |->  (letrec {E#6} in T#14),
           S#8   |->  T#14[T#4[S#2]]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[T#4[S#2]]) S#7)])
    -ucp3->                       (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[T#4[S#2]]) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[T#4[S#2]] S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {X#15=T#14[(letrec {X#1=S#2} in T#4[(var X#1)])];E#17} in S#8) S#7)]
     )
    ,
     (letrec {E#5} in A#11[(letrec {X#15=T#14[T#4[S#2]];E#17} in (app S#8 S#7))])
  )

where

   Delta1 = {T#13,T#12,A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {X#15=T#14[T#4[S#2]];E#17} in [.])),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)],
           T#12  |->  (app (letrec {X#15=T#14;E#17} in S#8) S#7),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#8),
           E#6   |->  {X#15=T#14[T#4[S#2]];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[T#4[S#2]];E#17} in S#8) S#7)])
    -ucp3->                       (letrec {E#5} in A#11[(app (letrec {X#15=T#14[(letrec {X#1=S#2} in T#4[(var X#1)])];E#17} in S#8) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[T#4[S#2]];E#17} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {X#15=T#14[T#4[S#2]];E#17} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {X#1=S#2} in (letrec {E#6} in T#14[(var X#1)])) S#7)]
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[S#2] S#7))])
  )

where

   Delta1 = {T#4,T#12,A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#6} in T#14)),
             (S#2,(letrec {E#6} in T#14)),
             ((letrec {E#6} in T#14[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(letrec {E#6} in T#14[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11[(app [.] S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app [.] S#7)],
           T#12  |->  (app [.] S#7),
           T#13  |->  [.],
           T#4   |->  (letrec {E#6} in T#14),
           S#8   |->  T#14[S#2]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[S#2]) S#7)])
    -ucp3->                       (letrec {E#5} in A#11[(app (letrec {X#1=S#2} in (letrec {E#6} in T#14[(var X#1)])) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[S#2]) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[S#2] S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {X#1=S#2} in (letrec {X#15=T#14[(var X#1)];E#17} in S#8)) S#7)]
     )
    ,
     (letrec {E#5} in A#11[(letrec {X#15=T#14[S#2];E#17} in (app S#8 S#7))])
  )

where

   Delta1 = {T#4,T#12,A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {X#15=T#14;E#17} in S#8)),
             (S#2,(letrec {X#15=T#14;E#17} in S#8)),
             ((letrec {X#15=T#14[(dummy3 )];E#17} in S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {X#15=T#14[S#2];E#17} in [.])),
             ((var X#1),(letrec {X#15=T#14[[.]];E#17} in S#8))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11[(app [.] S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app [.] S#7)],
           T#12  |->  (app [.] S#7),
           T#13  |->  [.],
           T#4   |->  (letrec {X#15=T#14;E#17} in S#8),
           E#6   |->  {X#15=T#14[S#2];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[S#2];E#17} in S#8) S#7)])
    -ucp3->                       (letrec {E#5} in A#11[(app (letrec {X#1=S#2} in (letrec {X#15=T#14[(var X#1)];E#17} in S#8)) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[S#2];E#17} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {X#15=T#14[S#2];E#17} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {X#1=(letrec {E#6} in S#8)} in (var X#1)) S#7)]
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {T#12,A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#6} in S#8),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#6} in S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11[(app [.] S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app [.] S#7)],
           T#12  |->  (app [.] S#7),
           T#13  |->  [.],
           T#4   |->  [.],
           S#2   |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -ucp3->                       (letrec {E#5} in A#11[(app (letrec {X#1=(letrec {E#6} in S#8)} in (var X#1)) S#7)])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app (letrec {E#6} in S#8) T#13[(letrec {X#1=S#2} in T#4[(var X#1)])])]
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 T#13[T#4[S#2]]))])
  )

where

   Delta1 = {T#12,A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#13[T#4[S#2]],(letrec {E#6} in [.])),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {E#6} in S#8) T#13)],
           T#12  |->  (app (letrec {E#6} in S#8) T#13),
           S#7   |->  T#13[T#4[S#2]]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[T#4[S#2]])])
    -ucp3->                       (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(letrec {X#1=S#2} in T#4[(var X#1)])])])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[T#4[S#2]])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 T#13[T#4[S#2]]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec {X#1=S#2} in (app (letrec {E#6} in T#14[(var X#1)]) S#7))]
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[S#2] S#7))])
  )

where

   Delta1 = {T#13,T#4,A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(app (letrec {E#6} in T#14) S#7)),
             (S#2,(app (letrec {E#6} in T#14) S#7)),
             ((app (letrec {E#6} in T#14[(dummy3 )]) S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(app (letrec {E#6} in T#14[[.]]) S#7))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11[[.]]),
           A#9   |->  A#11,
           T#10  |->  A#11[[.]],
           T#12  |->  [.],
           T#4   |->  (app (letrec {E#6} in T#14) S#7),
           T#13  |->  (letrec {E#6} in T#14),
           S#8   |->  T#14[S#2]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[S#2]) S#7)])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=S#2} in (app (letrec {E#6} in T#14[(var X#1)]) S#7))])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[S#2]) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[S#2] S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec {X#1=S#2} in (app (letrec {X#15=T#14[(var X#1)];E#17} in S#8) S#7))]
     )
    ,
     (letrec {E#5} in A#11[(letrec {X#15=T#14[S#2];E#17} in (app S#8 S#7))])
  )

where

   Delta1 = {T#13,T#4,A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(app (letrec {X#15=T#14;E#17} in S#8) S#7)),
             (S#2,(app (letrec {X#15=T#14;E#17} in S#8) S#7)),
             ((app (letrec {X#15=T#14[(dummy3 )];E#17} in S#8) S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {X#15=T#14[S#2];E#17} in [.])),
             ((var X#1),(app (letrec {X#15=T#14[[.]];E#17} in S#8) S#7))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11[[.]]),
           A#9   |->  A#11,
           T#10  |->  A#11[[.]],
           T#12  |->  [.],
           T#4   |->  (app (letrec {X#15=T#14;E#17} in S#8) S#7),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#8),
           E#6   |->  {X#15=T#14[S#2];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[S#2];E#17} in S#8) S#7)])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=S#2} in (app (letrec {X#15=T#14[(var X#1)];E#17} in S#8) S#7))])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[S#2];E#17} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {X#15=T#14[S#2];E#17} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec {X#1=(letrec {E#6} in S#8)} in (app (var X#1) S#7))]
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {T#4,A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(app [.] S#7)),
             ((letrec {E#6} in S#8),(app [.] S#7)),
             ((app (dummy3 ) S#7),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#6} in S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(app [.] S#7))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11[[.]]),
           A#9   |->  A#11,
           T#10  |->  A#11[[.]],
           T#12  |->  [.],
           T#4   |->  (app [.] S#7),
           T#13  |->  [.],
           S#2   |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=(letrec {E#6} in S#8)} in (app (var X#1) S#7))])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec {X#1=S#2} in (app (letrec {E#6} in S#8) T#13[(var X#1)]))]
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 T#13[S#2]))])
  )

where

   Delta1 = {T#4,A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(app (letrec {E#6} in S#8) T#13)),
             (S#2,(app (letrec {E#6} in S#8) T#13)),
             ((app (letrec {E#6} in S#8) T#13[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#13[S#2],(letrec {E#6} in [.])),
             ((var X#1),(app (letrec {E#6} in S#8) T#13[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11[[.]]),
           A#9   |->  A#11,
           T#10  |->  A#11[[.]],
           T#12  |->  [.],
           T#4   |->  (app (letrec {E#6} in S#8) T#13),
           S#7   |->  T#13[S#2]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[S#2])])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=S#2} in (app (letrec {E#6} in S#8) T#13[(var X#1)]))])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[S#2])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 T#13[S#2]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec {X#1=(app (letrec {E#6} in S#8) S#7)} in (var X#1))]
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),[.]),
             ((app (letrec {E#6} in S#8) S#7),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#6} in S#8) S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11[[.]]),
           A#9   |->  A#11,
           T#10  |->  A#11[[.]],
           T#12  |->  [.],
           T#4   |->  [.],
           S#2   |->  (app (letrec {E#6} in S#8) S#7)}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=(app (letrec {E#6} in S#8) S#7)} in (var X#1))])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec {X#1=S#2} in A#13[(app (letrec {E#6} in T#16[(var X#1)]) S#7)])]
     )
    ,
     (letrec {E#5} in A#11[A#13[(letrec {E#6} in (app T#16[S#2] S#7))]])
  )

where

   Delta1 = {T#15,T#14,A#12,T#4,A#9,T#10,T#3,A#11,A#13}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),A#13[(app (letrec {E#6} in T#16) S#7)]),
             (S#2,A#13[(app (letrec {E#6} in T#16) S#7)]),
             (A#13[(app (letrec {E#6} in T#16[(dummy3 )]) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),A#13[(app (letrec {E#6} in T#16[[.]]) S#7)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11),
           A#9   |->  A#11[A#13],
           T#10  |->  A#11,
           A#12  |->  A#13,
           T#4   |->  A#13[(app (letrec {E#6} in T#16) S#7)],
           T#14  |->  (app (letrec {E#6} in T#16) S#7),
           T#15  |->  (letrec {E#6} in T#16),
           S#8   |->  T#16[S#2]}

and instantiated rules:

                                  (letrec {E#5} in A#11[A#13[(app (letrec {E#6} in T#16[S#2]) S#7)]])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=S#2} in A#13[(app (letrec {E#6} in T#16[(var X#1)]) S#7)])])
    ................................................................................
                                  (letrec {E#5} in A#11[A#13[(app (letrec {E#6} in T#16[S#2]) S#7)]])
    -SR,lapp2->                   (letrec {E#5} in A#11[A#13[(letrec {E#6} in (app T#16[S#2] S#7))]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec
                 X#1= S#2
              in
                 A#13[(app (letrec {X#17=T#16[(var X#1)];E#19} in S#8) S#7)]
              )]
     )
    ,
     (letrec {E#5} in A#11[A#13[(letrec {X#17=T#16[S#2];E#19} in (app S#8 S#7))]])
  )

where

   Delta1 = {T#15,T#14,A#12,T#4,A#9,T#10,T#3,A#11,A#13}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),A#13[(app (letrec {X#17=T#16;E#19} in S#8) S#7)]),
             (S#2,A#13[(app (letrec {X#17=T#16;E#19} in S#8) S#7)]),
             (A#13[(app (letrec {X#17=T#16[(dummy3 )];E#19} in S#8) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {X#17=T#16[S#2];E#19} in [.])),
             ((var X#1),A#13[(app (letrec {X#17=T#16[[.]];E#19} in S#8) S#7)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11),
           A#9   |->  A#11[A#13],
           T#10  |->  A#11,
           A#12  |->  A#13,
           T#4   |->  A#13[(app (letrec {X#17=T#16;E#19} in S#8) S#7)],
           T#14  |->  (app (letrec {X#17=T#16;E#19} in S#8) S#7),
           T#15  |->  (letrec {X#17=T#16;E#19} in S#8),
           E#6   |->  {X#17=T#16[S#2];E#19},
           E#18  |->  {E#19}}

and instantiated rules:

                                  (letrec {E#5} in A#11[A#13[(app (letrec {X#17=T#16[S#2];E#19} in S#8) S#7)]])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=S#2} in A#13[(app (letrec {X#17=T#16[(var X#1)];E#19} in S#8) S#7)])])
    ................................................................................
                                  (letrec {E#5} in A#11[A#13[(app (letrec {X#17=T#16[S#2];E#19} in S#8) S#7)]])
    -SR,lapp2->                   (letrec {E#5} in A#11[A#13[(letrec {X#17=T#16[S#2];E#19} in (app S#8 S#7))]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec {X#1=(letrec {E#6} in S#8)} in A#13[(app (var X#1) S#7)])]
     )
    ,
     (letrec {E#5} in A#11[A#13[(letrec {E#6} in (app S#8 S#7))]])
  )

where

   Delta1 = {T#14,A#12,T#4,A#9,T#10,T#3,A#11,A#13}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),A#13[(app [.] S#7)]),
             ((letrec {E#6} in S#8),A#13[(app [.] S#7)]),
             (A#13[(app (dummy3 ) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#6} in S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),A#13[(app [.] S#7)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11),
           A#9   |->  A#11[A#13],
           T#10  |->  A#11,
           A#12  |->  A#13,
           T#4   |->  A#13[(app [.] S#7)],
           T#14  |->  (app [.] S#7),
           T#15  |->  [.],
           S#2   |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {E#5} in A#11[A#13[(app (letrec {E#6} in S#8) S#7)]])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=(letrec {E#6} in S#8)} in A#13[(app (var X#1) S#7)])])
    ................................................................................
                                  (letrec {E#5} in A#11[A#13[(app (letrec {E#6} in S#8) S#7)]])
    -SR,lapp2->                   (letrec {E#5} in A#11[A#13[(letrec {E#6} in (app S#8 S#7))]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec {X#1=S#2} in A#13[(app (letrec {E#6} in S#8) T#15[(var X#1)])])]
     )
    ,
     (letrec {E#5} in A#11[A#13[(letrec {E#6} in (app S#8 T#15[S#2]))]])
  )

where

   Delta1 = {T#14,A#12,T#4,A#9,T#10,T#3,A#11,A#13}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),A#13[(app (letrec {E#6} in S#8) T#15)]),
             (S#2,A#13[(app (letrec {E#6} in S#8) T#15)]),
             (A#13[(app (letrec {E#6} in S#8) T#15[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#15[S#2],(letrec {E#6} in [.])),
             ((var X#1),A#13[(app (letrec {E#6} in S#8) T#15[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11),
           A#9   |->  A#11[A#13],
           T#10  |->  A#11,
           A#12  |->  A#13,
           T#4   |->  A#13[(app (letrec {E#6} in S#8) T#15)],
           T#14  |->  (app (letrec {E#6} in S#8) T#15),
           S#7   |->  T#15[S#2]}

and instantiated rules:

                                  (letrec {E#5} in A#11[A#13[(app (letrec {E#6} in S#8) T#15[S#2])]])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=S#2} in A#13[(app (letrec {E#6} in S#8) T#15[(var X#1)])])])
    ................................................................................
                                  (letrec {E#5} in A#11[A#13[(app (letrec {E#6} in S#8) T#15[S#2])]])
    -SR,lapp2->                   (letrec {E#5} in A#11[A#13[(letrec {E#6} in (app S#8 T#15[S#2]))]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec {X#1=(app (letrec {E#6} in S#8) S#7)} in A#13[(var X#1)])]
     )
    ,
     (letrec {E#5} in A#11[A#13[(letrec {E#6} in (app S#8 S#7))]])
  )

where

   Delta1 = {A#12,T#4,A#9,T#10,T#3,A#11,A#13}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),A#13[[.]]),
             ((app (letrec {E#6} in S#8) S#7),A#13[[.]]),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#6} in S#8) S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11),
           A#9   |->  A#11[A#13],
           T#10  |->  A#11,
           A#12  |->  A#13,
           T#4   |->  A#13[[.]],
           T#14  |->  [.],
           S#2   |->  (app (letrec {E#6} in S#8) S#7)}

and instantiated rules:

                                  (letrec {E#5} in A#11[A#13[(app (letrec {E#6} in S#8) S#7)]])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=(app (letrec {E#6} in S#8) S#7)} in A#13[(var X#1)])])
    ................................................................................
                                  (letrec {E#5} in A#11[A#13[(app (letrec {E#6} in S#8) S#7)]])
    -SR,lapp2->                   (letrec {E#5} in A#11[A#13[(letrec {E#6} in (app S#8 S#7))]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec {X#1=A#14[(app (letrec {E#6} in S#8) S#7)]} in A#13[(var X#1)])]
     )
    ,
     (letrec {E#5} in A#11[A#13[A#14[(letrec {E#6} in (app S#8 S#7))]]])
  )

where

   Delta1 = {A#12,T#4,A#9,T#10,T#3,A#11,A#13}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),A#13),
             (A#14[(app (letrec {E#6} in S#8) S#7)],A#13),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(app (letrec {E#6} in S#8) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11),
           A#9   |->  A#11[A#13[A#14]],
           T#10  |->  A#11,
           A#12  |->  A#13[A#14],
           T#4   |->  A#13,
           S#2   |->  A#14[(app (letrec {E#6} in S#8) S#7)]}

and instantiated rules:

                                  (letrec {E#5} in A#11[A#13[A#14[(app (letrec {E#6} in S#8) S#7)]]])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=A#14[(app (letrec {E#6} in S#8) S#7)]} in A#13[(var X#1)])])
    ................................................................................
                                  (letrec {E#5} in A#11[A#13[A#14[(app (letrec {E#6} in S#8) S#7)]]])
    -SR,lapp2->                   (letrec {E#5} in A#11[A#13[A#14[(letrec {E#6} in (app S#8 S#7))]]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec
                 X#1= S#2
              in
                 A#13[(app A#14[(app (letrec {E#6} in S#8) S#7)] T#15[(var X#1)])]
              )]
     )
    ,
     (letrec
        E#5
     in
        A#11[A#13[(app A#14[(letrec {E#6} in (app S#8 S#7))] T#15[S#2])]]
     )
  )

where

   Delta1 = {A#12,T#4,A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),A#13[(app A#14[(app (letrec {E#6} in S#8) S#7)] T#15)]),
             (S#2,A#13[(app A#14[(app (letrec {E#6} in S#8) S#7)] T#15)]),
             (A#13[(app A#14[(app (letrec {E#6} in S#8) S#7)] T#15[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),A#13[(app A#14[(app (letrec {E#6} in S#8) S#7)] T#15[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11),
           A#9   |->  A#11[A#13[(app A#14 T#15[S#2])]],
           T#10  |->  A#11,
           T#4   |->  A#13[(app A#14[(app (letrec {E#6} in S#8) S#7)] T#15)],
           A#12  |->  A#13[(app A#14 T#15[S#2])]}

and instantiated rules:

                                  (letrec {E#5} in A#11[A#13[(app A#14[(app (letrec {E#6} in S#8) S#7)] T#15[S#2])]])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=S#2} in A#13[(app A#14[(app (letrec {E#6} in S#8) S#7)] T#15[(var X#1)])])])
    ................................................................................
                                  (letrec {E#5} in A#11[A#13[(app A#14[(app (letrec {E#6} in S#8) S#7)] T#15[S#2])]])
    -SR,lapp2->                   (letrec {E#5} in A#11[A#13[(app A#14[(letrec {E#6} in (app S#8 S#7))] T#15[S#2])]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec {X#1=S#2} in (app (letrec {E#6} in T#14[(var X#1)]) S#7))]
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[S#2] S#7))])
  )

where

   Delta1 = {T#13,T#4,A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(app (letrec {E#6} in T#14) S#7)),
             (S#2,(app (letrec {E#6} in T#14) S#7)),
             ((app (letrec {E#6} in T#14[(dummy3 )]) S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(app (letrec {E#6} in T#14[[.]]) S#7))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11),
           A#9   |->  A#11[[.]],
           T#10  |->  A#11,
           A#12  |->  [.],
           T#4   |->  (app (letrec {E#6} in T#14) S#7),
           T#13  |->  (letrec {E#6} in T#14),
           S#8   |->  T#14[S#2]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[S#2]) S#7)])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=S#2} in (app (letrec {E#6} in T#14[(var X#1)]) S#7))])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[S#2]) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[S#2] S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec {X#1=S#2} in (app (letrec {X#15=T#14[(var X#1)];E#17} in S#8) S#7))]
     )
    ,
     (letrec {E#5} in A#11[(letrec {X#15=T#14[S#2];E#17} in (app S#8 S#7))])
  )

where

   Delta1 = {T#13,T#4,A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(app (letrec {X#15=T#14;E#17} in S#8) S#7)),
             (S#2,(app (letrec {X#15=T#14;E#17} in S#8) S#7)),
             ((app (letrec {X#15=T#14[(dummy3 )];E#17} in S#8) S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {X#15=T#14[S#2];E#17} in [.])),
             ((var X#1),(app (letrec {X#15=T#14[[.]];E#17} in S#8) S#7))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11),
           A#9   |->  A#11[[.]],
           T#10  |->  A#11,
           A#12  |->  [.],
           T#4   |->  (app (letrec {X#15=T#14;E#17} in S#8) S#7),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#8),
           E#6   |->  {X#15=T#14[S#2];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[S#2];E#17} in S#8) S#7)])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=S#2} in (app (letrec {X#15=T#14[(var X#1)];E#17} in S#8) S#7))])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[S#2];E#17} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {X#15=T#14[S#2];E#17} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec {X#1=(letrec {E#6} in S#8)} in (app (var X#1) S#7))]
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {T#4,A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(app [.] S#7)),
             ((letrec {E#6} in S#8),(app [.] S#7)),
             ((app (dummy3 ) S#7),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#6} in S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(app [.] S#7))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11),
           A#9   |->  A#11[[.]],
           T#10  |->  A#11,
           A#12  |->  [.],
           T#4   |->  (app [.] S#7),
           T#13  |->  [.],
           S#2   |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=(letrec {E#6} in S#8)} in (app (var X#1) S#7))])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec {X#1=S#2} in (app (letrec {E#6} in S#8) T#13[(var X#1)]))]
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 T#13[S#2]))])
  )

where

   Delta1 = {T#4,A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(app (letrec {E#6} in S#8) T#13)),
             (S#2,(app (letrec {E#6} in S#8) T#13)),
             ((app (letrec {E#6} in S#8) T#13[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#13[S#2],(letrec {E#6} in [.])),
             ((var X#1),(app (letrec {E#6} in S#8) T#13[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11),
           A#9   |->  A#11[[.]],
           T#10  |->  A#11,
           A#12  |->  [.],
           T#4   |->  (app (letrec {E#6} in S#8) T#13),
           S#7   |->  T#13[S#2]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[S#2])])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=S#2} in (app (letrec {E#6} in S#8) T#13[(var X#1)]))])
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[S#2])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 T#13[S#2]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(letrec {X#1=A#12[(app (letrec {E#6} in S#8) S#7)]} in (var X#1))]
     )
    ,
     (letrec {E#5} in A#11[A#12[(letrec {E#6} in (app S#8 S#7))]])
  )

where

   Delta1 = {A#9,T#10,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),[.]),
             (A#12[(app (letrec {E#6} in S#8) S#7)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(app (letrec {E#6} in S#8) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11),
           A#9   |->  A#11[A#12],
           T#10  |->  A#11,
           T#4   |->  [.],
           S#2   |->  A#12[(app (letrec {E#6} in S#8) S#7)]}

and instantiated rules:

                                  (letrec {E#5} in A#11[A#12[(app (letrec {E#6} in S#8) S#7)]])
    -ucp3->                       (letrec {E#5} in A#11[(letrec {X#1=A#12[(app (letrec {E#6} in S#8) S#7)]} in (var X#1))])
    ................................................................................
                                  (letrec {E#5} in A#11[A#12[(app (letrec {E#6} in S#8) S#7)]])
    -SR,lapp2->                   (letrec {E#5} in A#11[A#12[(letrec {E#6} in (app S#8 S#7))]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(letrec {X#1=S#2} in T#4[(var X#1)])])]
     )
    ,
     (letrec
        E#5
     in
        A#11[(app A#12[(letrec {E#6} in (app S#8 S#7))] T#13[T#4[S#2]])]
     )
  )

where

   Delta1 = {A#9,T#10,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)]),
           T#10  |->  A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[T#4[S#2]])])
    -ucp3->                       (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(letrec {X#1=S#2} in T#4[(var X#1)])])])
    ................................................................................
                                  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[T#4[S#2]])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(app A#12[(letrec {E#6} in (app S#8 S#7))] T#13[T#4[S#2]])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (app (letrec {E#6} in T#12[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#7)
     )
    ,
     (letrec {E#5} in (letrec {E#6} in (app T#12[T#4[S#2]] S#7)))
  )

where

   Delta1 = {T#11,T#10,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in (app (letrec {E#6} in T#12) S#7)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {E#6} in T#12) S#7),
           T#11  |->  (letrec {E#6} in T#12),
           S#8   |->  T#12[T#4[S#2]]}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in T#12[T#4[S#2]]) S#7))
    -ucp3->                       (letrec {E#5} in (app (letrec {E#6} in T#12[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in T#12[T#4[S#2]]) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app T#12[T#4[S#2]] S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (app (letrec {X#13=T#12[(letrec {X#1=S#2} in T#4[(var X#1)])];E#15} in S#8) S#7)
     )
    ,
     (letrec {E#5} in (letrec {X#13=T#12[T#4[S#2]];E#15} in (app S#8 S#7)))
  )

where

   Delta1 = {T#11,T#10,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {X#13=T#12[T#4[S#2]];E#15} in [.])),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in (app (letrec {X#13=T#12;E#15} in S#8) S#7)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {X#13=T#12;E#15} in S#8) S#7),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#8),
           E#6   |->  {X#13=T#12[T#4[S#2]];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {X#13=T#12[T#4[S#2]];E#15} in S#8) S#7))
    -ucp3->                       (letrec {E#5} in (app (letrec {X#13=T#12[(letrec {X#1=S#2} in T#4[(var X#1)])];E#15} in S#8) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {X#13=T#12[T#4[S#2]];E#15} in S#8) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {X#13=T#12[T#4[S#2]];E#15} in (app S#8 S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (app (letrec {X#1=S#2} in (letrec {E#6} in T#12[(var X#1)])) S#7)
     )
    ,
     (letrec {E#5} in (letrec {E#6} in (app T#12[S#2] S#7)))
  )

where

   Delta1 = {T#4,T#10,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#6} in T#12)),
             (S#2,(letrec {E#6} in T#12)),
             ((letrec {E#6} in T#12[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(letrec {E#6} in T#12[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in (app [.] S#7)),
           A#9   |->  [.],
           T#10  |->  (app [.] S#7),
           T#11  |->  [.],
           T#4   |->  (letrec {E#6} in T#12),
           S#8   |->  T#12[S#2]}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in T#12[S#2]) S#7))
    -ucp3->                       (letrec {E#5} in (app (letrec {X#1=S#2} in (letrec {E#6} in T#12[(var X#1)])) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in T#12[S#2]) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app T#12[S#2] S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (app (letrec {X#1=S#2} in (letrec {X#13=T#12[(var X#1)];E#15} in S#8)) S#7)
     )
    ,
     (letrec {E#5} in (letrec {X#13=T#12[S#2];E#15} in (app S#8 S#7)))
  )

where

   Delta1 = {T#4,T#10,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {X#13=T#12;E#15} in S#8)),
             (S#2,(letrec {X#13=T#12;E#15} in S#8)),
             ((letrec {X#13=T#12[(dummy3 )];E#15} in S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {X#13=T#12[S#2];E#15} in [.])),
             ((var X#1),(letrec {X#13=T#12[[.]];E#15} in S#8))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in (app [.] S#7)),
           A#9   |->  [.],
           T#10  |->  (app [.] S#7),
           T#11  |->  [.],
           T#4   |->  (letrec {X#13=T#12;E#15} in S#8),
           E#6   |->  {X#13=T#12[S#2];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {X#13=T#12[S#2];E#15} in S#8) S#7))
    -ucp3->                       (letrec {E#5} in (app (letrec {X#1=S#2} in (letrec {X#13=T#12[(var X#1)];E#15} in S#8)) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {X#13=T#12[S#2];E#15} in S#8) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {X#13=T#12[S#2];E#15} in (app S#8 S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (app (letrec {X#1=(letrec {E#6} in S#8)} in (var X#1)) S#7))
    ,
     (letrec {E#5} in (letrec {E#6} in (app S#8 S#7)))
  )

where

   Delta1 = {T#10,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#6} in S#8),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#6} in S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in (app [.] S#7)),
           A#9   |->  [.],
           T#10  |->  (app [.] S#7),
           T#11  |->  [.],
           T#4   |->  [.],
           S#2   |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in S#8) S#7))
    -ucp3->                       (letrec {E#5} in (app (letrec {X#1=(letrec {E#6} in S#8)} in (var X#1)) S#7))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in S#8) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app S#8 S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (app (letrec {E#6} in S#8) T#11[(letrec {X#1=S#2} in T#4[(var X#1)])])
     )
    ,
     (letrec {E#5} in (letrec {E#6} in (app S#8 T#11[T#4[S#2]])))
  )

where

   Delta1 = {T#10,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[T#4[S#2]],(letrec {E#6} in [.])),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {E#6} in S#8) T#11),
           S#7   |->  T#11[T#4[S#2]]}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[T#4[S#2]]))
    -ucp3->                       (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(letrec {X#1=S#2} in T#4[(var X#1)])]))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[T#4[S#2]]))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app S#8 T#11[T#4[S#2]])))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (letrec {X#1=S#2} in A#11[(app (letrec {E#6} in T#14[(var X#1)]) S#7)])
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[S#2] S#7))])
  )

where

   Delta1 = {T#13,T#12,A#9,T#4,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),A#11[(app (letrec {E#6} in T#14) S#7)]),
             (S#2,A#11[(app (letrec {E#6} in T#14) S#7)]),
             (A#11[(app (letrec {E#6} in T#14[(dummy3 )]) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),A#11[(app (letrec {E#6} in T#14[[.]]) S#7)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in [.]),
           T#10  |->  [.],
           A#9   |->  A#11,
           T#4   |->  A#11[(app (letrec {E#6} in T#14) S#7)],
           T#12  |->  (app (letrec {E#6} in T#14) S#7),
           T#13  |->  (letrec {E#6} in T#14),
           S#8   |->  T#14[S#2]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[S#2]) S#7)])
    -ucp3->                       (letrec {E#5} in (letrec {X#1=S#2} in A#11[(app (letrec {E#6} in T#14[(var X#1)]) S#7)]))
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[S#2]) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[S#2] S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (letrec
           X#1= S#2
        in
           A#11[(app (letrec {X#15=T#14[(var X#1)];E#17} in S#8) S#7)]
        )
     )
    ,
     (letrec {E#5} in A#11[(letrec {X#15=T#14[S#2];E#17} in (app S#8 S#7))])
  )

where

   Delta1 = {T#13,T#12,A#9,T#4,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)]),
             (S#2,A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)]),
             (A#11[(app (letrec {X#15=T#14[(dummy3 )];E#17} in S#8) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {X#15=T#14[S#2];E#17} in [.])),
             ((var X#1),A#11[(app (letrec {X#15=T#14[[.]];E#17} in S#8) S#7)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in [.]),
           T#10  |->  [.],
           A#9   |->  A#11,
           T#4   |->  A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)],
           T#12  |->  (app (letrec {X#15=T#14;E#17} in S#8) S#7),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#8),
           E#6   |->  {X#15=T#14[S#2];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[S#2];E#17} in S#8) S#7)])
    -ucp3->                       (letrec {E#5} in (letrec {X#1=S#2} in A#11[(app (letrec {X#15=T#14[(var X#1)];E#17} in S#8) S#7)]))
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[S#2];E#17} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {X#15=T#14[S#2];E#17} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (letrec {X#1=(letrec {E#6} in S#8)} in A#11[(app (var X#1) S#7)])
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {T#12,A#9,T#4,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),A#11[(app [.] S#7)]),
             ((letrec {E#6} in S#8),A#11[(app [.] S#7)]),
             (A#11[(app (dummy3 ) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#6} in S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),A#11[(app [.] S#7)])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in [.]),
           T#10  |->  [.],
           A#9   |->  A#11,
           T#4   |->  A#11[(app [.] S#7)],
           T#12  |->  (app [.] S#7),
           T#13  |->  [.],
           S#2   |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -ucp3->                       (letrec {E#5} in (letrec {X#1=(letrec {E#6} in S#8)} in A#11[(app (var X#1) S#7)]))
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (letrec {X#1=S#2} in A#11[(app (letrec {E#6} in S#8) T#13[(var X#1)])])
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 T#13[S#2]))])
  )

where

   Delta1 = {T#12,A#9,T#4,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),A#11[(app (letrec {E#6} in S#8) T#13)]),
             (S#2,A#11[(app (letrec {E#6} in S#8) T#13)]),
             (A#11[(app (letrec {E#6} in S#8) T#13[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#13[S#2],(letrec {E#6} in [.])),
             ((var X#1),A#11[(app (letrec {E#6} in S#8) T#13[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in [.]),
           T#10  |->  [.],
           A#9   |->  A#11,
           T#4   |->  A#11[(app (letrec {E#6} in S#8) T#13)],
           T#12  |->  (app (letrec {E#6} in S#8) T#13),
           S#7   |->  T#13[S#2]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[S#2])])
    -ucp3->                       (letrec {E#5} in (letrec {X#1=S#2} in A#11[(app (letrec {E#6} in S#8) T#13[(var X#1)])]))
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[S#2])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 T#13[S#2]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (letrec {X#1=(app (letrec {E#6} in S#8) S#7)} in A#11[(var X#1)])
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {A#9,T#4,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),A#11[[.]]),
             ((app (letrec {E#6} in S#8) S#7),A#11[[.]]),
             (A#11[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#6} in S#8) S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in [.]),
           T#10  |->  [.],
           A#9   |->  A#11,
           T#4   |->  A#11[[.]],
           T#12  |->  [.],
           S#2   |->  (app (letrec {E#6} in S#8) S#7)}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -ucp3->                       (letrec {E#5} in (letrec {X#1=(app (letrec {E#6} in S#8) S#7)} in A#11[(var X#1)]))
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (letrec {X#1=A#12[(app (letrec {E#6} in S#8) S#7)]} in A#11[(var X#1)])
     )
    ,
     (letrec {E#5} in A#11[A#12[(letrec {E#6} in (app S#8 S#7))]])
  )

where

   Delta1 = {A#9,T#4,T#3,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),A#11),
             (A#12[(app (letrec {E#6} in S#8) S#7)],A#11),
             (A#11[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(app (letrec {E#6} in S#8) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),A#11[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in [.]),
           T#10  |->  [.],
           A#9   |->  A#11[A#12],
           T#4   |->  A#11,
           S#2   |->  A#12[(app (letrec {E#6} in S#8) S#7)]}

and instantiated rules:

                                  (letrec {E#5} in A#11[A#12[(app (letrec {E#6} in S#8) S#7)]])
    -ucp3->                       (letrec {E#5} in (letrec {X#1=A#12[(app (letrec {E#6} in S#8) S#7)]} in A#11[(var X#1)]))
    ................................................................................
                                  (letrec {E#5} in A#11[A#12[(app (letrec {E#6} in S#8) S#7)]])
    -SR,lapp2->                   (letrec {E#5} in A#11[A#12[(letrec {E#6} in (app S#8 S#7))]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (letrec
           X#1= S#2
        in
           A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(var X#1)])]
        )
     )
    ,
     (letrec {E#5} in A#11[(app A#12[(letrec {E#6} in (app S#8 S#7))] T#13[S#2])])
  )

where

   Delta1 = {A#9,T#4,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)]),
             (S#2,A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)]),
             (A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[[.]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in [.]),
           T#10  |->  [.],
           T#4   |->  A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[S#2])]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[S#2])])
    -ucp3->                       (letrec {E#5} in (letrec {X#1=S#2} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(var X#1)])]))
    ................................................................................
                                  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[S#2])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(app A#12[(letrec {E#6} in (app S#8 S#7))] T#13[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (letrec {X#1=S#2} in (app (letrec {E#6} in T#12[(var X#1)]) S#7))
     )
    ,
     (letrec {E#5} in (letrec {E#6} in (app T#12[S#2] S#7)))
  )

where

   Delta1 = {T#11,T#4,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(app (letrec {E#6} in T#12) S#7)),
             (S#2,(app (letrec {E#6} in T#12) S#7)),
             ((app (letrec {E#6} in T#12[(dummy3 )]) S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(app (letrec {E#6} in T#12[[.]]) S#7))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in [.]),
           T#10  |->  [.],
           A#9   |->  [.],
           T#4   |->  (app (letrec {E#6} in T#12) S#7),
           T#11  |->  (letrec {E#6} in T#12),
           S#8   |->  T#12[S#2]}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in T#12[S#2]) S#7))
    -ucp3->                       (letrec {E#5} in (letrec {X#1=S#2} in (app (letrec {E#6} in T#12[(var X#1)]) S#7)))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in T#12[S#2]) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app T#12[S#2] S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (letrec {X#1=S#2} in (app (letrec {X#13=T#12[(var X#1)];E#15} in S#8) S#7))
     )
    ,
     (letrec {E#5} in (letrec {X#13=T#12[S#2];E#15} in (app S#8 S#7)))
  )

where

   Delta1 = {T#11,T#4,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(app (letrec {X#13=T#12;E#15} in S#8) S#7)),
             (S#2,(app (letrec {X#13=T#12;E#15} in S#8) S#7)),
             ((app (letrec {X#13=T#12[(dummy3 )];E#15} in S#8) S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {X#13=T#12[S#2];E#15} in [.])),
             ((var X#1),(app (letrec {X#13=T#12[[.]];E#15} in S#8) S#7))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in [.]),
           T#10  |->  [.],
           A#9   |->  [.],
           T#4   |->  (app (letrec {X#13=T#12;E#15} in S#8) S#7),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#8),
           E#6   |->  {X#13=T#12[S#2];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {X#13=T#12[S#2];E#15} in S#8) S#7))
    -ucp3->                       (letrec {E#5} in (letrec {X#1=S#2} in (app (letrec {X#13=T#12[(var X#1)];E#15} in S#8) S#7)))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {X#13=T#12[S#2];E#15} in S#8) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {X#13=T#12[S#2];E#15} in (app S#8 S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec {E#5} in (letrec {X#1=(letrec {E#6} in S#8)} in (app (var X#1) S#7)))
    ,
     (letrec {E#5} in (letrec {E#6} in (app S#8 S#7)))
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(app [.] S#7)),
             ((letrec {E#6} in S#8),(app [.] S#7)),
             ((app (dummy3 ) S#7),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#6} in S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(app [.] S#7))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in [.]),
           T#10  |->  [.],
           A#9   |->  [.],
           T#4   |->  (app [.] S#7),
           T#11  |->  [.],
           S#2   |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in S#8) S#7))
    -ucp3->                       (letrec {E#5} in (letrec {X#1=(letrec {E#6} in S#8)} in (app (var X#1) S#7)))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in S#8) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app S#8 S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (letrec {X#1=S#2} in (app (letrec {E#6} in S#8) T#11[(var X#1)]))
     )
    ,
     (letrec {E#5} in (letrec {E#6} in (app S#8 T#11[S#2])))
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(app (letrec {E#6} in S#8) T#11)),
             (S#2,(app (letrec {E#6} in S#8) T#11)),
             ((app (letrec {E#6} in S#8) T#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[S#2],(letrec {E#6} in [.])),
             ((var X#1),(app (letrec {E#6} in S#8) T#11[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in [.]),
           T#10  |->  [.],
           A#9   |->  [.],
           T#4   |->  (app (letrec {E#6} in S#8) T#11),
           S#7   |->  T#11[S#2]}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[S#2]))
    -ucp3->                       (letrec {E#5} in (letrec {X#1=S#2} in (app (letrec {E#6} in S#8) T#11[(var X#1)])))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[S#2]))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app S#8 T#11[S#2])))
    

================================================================================
Critical Pair:

  (
     (letrec
        E#5
     in
        (letrec {X#1=A#9[(app (letrec {E#6} in S#8) S#7)]} in (var X#1))
     )
    ,
     (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),[.]),
             (A#9[(app (letrec {E#6} in S#8) S#7)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(app (letrec {E#6} in S#8) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#5} in [.]),
           T#10  |->  [.],
           T#4   |->  [.],
           S#2   |->  A#9[(app (letrec {E#6} in S#8) S#7)]}

and instantiated rules:

                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -ucp3->                       (letrec {E#5} in (letrec {X#1=A#9[(app (letrec {E#6} in S#8) S#7)]} in (var X#1)))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#11= T#10[(letrec {X#1=S#2} in T#4[(var X#1)])]
       ;E#13
     in
        A#9[(app (letrec {E#6} in S#8) S#7)]
     )
    ,
     (letrec {X#11=T#10[T#4[S#2]];E#13} in A#9[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),T#4[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#11=T#10;E#13} in A#9[(app (letrec {E#6} in S#8) S#7)]),
           E#5   |->  {X#11=T#10[T#4[S#2]];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[T#4[S#2]];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -ucp3->                       (letrec {X#11=T#10[(letrec {X#1=S#2} in T#4[(var X#1)])];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    ................................................................................
                                  (letrec {X#11=T#10[T#4[S#2]];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {X#11=T#10[T#4[S#2]];E#13} in A#9[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(var X#1)]) S#7)])
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[S#2] S#7))])
  )

where

   Delta1 = {T#13,T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#5} in A#11[(app (letrec {E#6} in T#14) S#7)])),
             (S#2,(letrec {E#5} in A#11[(app (letrec {E#6} in T#14) S#7)])),
             ((letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(dummy3 )]) S#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(letrec {E#5} in A#11[(app (letrec {E#6} in T#14[[.]]) S#7)]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14) S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {E#6} in T#14) S#7)],
           T#12  |->  (app (letrec {E#6} in T#14) S#7),
           T#13  |->  (letrec {E#6} in T#14),
           S#8   |->  T#14[S#2]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[S#2]) S#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[(var X#1)]) S#7)]))
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in T#14[S#2]) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app T#14[S#2] S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {E#5} in A#11[(app (letrec {X#15=T#14[(var X#1)];E#17} in S#8) S#7)])
     )
    ,
     (letrec {E#5} in A#11[(letrec {X#15=T#14[S#2];E#17} in (app S#8 S#7))])
  )

where

   Delta1 = {T#13,T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#5} in A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)])),
             (S#2,(letrec {E#5} in A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)])),
             ((letrec {E#5} in A#11[(app (letrec {X#15=T#14[(dummy3 )];E#17} in S#8) S#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {X#15=T#14[S#2];E#17} in [.])),
             ((var X#1),(letrec {E#5} in A#11[(app (letrec {X#15=T#14[[.]];E#17} in S#8) S#7)]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#5} in A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {X#15=T#14;E#17} in S#8) S#7)],
           T#12  |->  (app (letrec {X#15=T#14;E#17} in S#8) S#7),
           T#13  |->  (letrec {X#15=T#14;E#17} in S#8),
           E#6   |->  {X#15=T#14[S#2];E#17},
           E#16  |->  {E#17}}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[S#2];E#17} in S#8) S#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {E#5} in A#11[(app (letrec {X#15=T#14[(var X#1)];E#17} in S#8) S#7)]))
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {X#15=T#14[S#2];E#17} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {X#15=T#14[S#2];E#17} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#6} in S#8)
     in
        (letrec {E#5} in A#11[(app (var X#1) S#7)])
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#5} in A#11[(app [.] S#7)])),
             ((letrec {E#6} in S#8),(letrec {E#5} in A#11[(app [.] S#7)])),
             ((letrec {E#5} in A#11[(app (dummy3 ) S#7)]),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#6} in S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(letrec {E#5} in A#11[(app [.] S#7)]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#5} in A#11[(app [.] S#7)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app [.] S#7)],
           T#12  |->  (app [.] S#7),
           T#13  |->  [.],
           S#2   |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -ucp3->                       (letrec {X#1=(letrec {E#6} in S#8)} in (letrec {E#5} in A#11[(app (var X#1) S#7)]))
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(var X#1)])])
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 T#13[S#2]))])
  )

where

   Delta1 = {T#12,A#9,T#10,T#4,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13)])),
             (S#2,(letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13)])),
             ((letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#13[S#2],(letrec {E#6} in [.])),
             ((var X#1),(letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[[.]])]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13)]),
           A#9   |->  A#11,
           T#10  |->  A#11[(app (letrec {E#6} in S#8) T#13)],
           T#12  |->  (app (letrec {E#6} in S#8) T#13),
           S#7   |->  T#13[S#2]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[S#2])])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[(var X#1)])]))
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) T#13[S#2])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 T#13[S#2]))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (app (letrec {E#6} in S#8) S#7)
     in
        (letrec {E#5} in A#11[(var X#1)])
     )
    ,
     (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {A#9,T#10,T#4,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#5} in A#11[[.]])),
             ((app (letrec {E#6} in S#8) S#7),(letrec {E#5} in A#11[[.]])),
             ((letrec {E#5} in A#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#6} in S#8) S#7),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(letrec {E#5} in A#11[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#5} in A#11[[.]]),
           A#9   |->  A#11,
           T#10  |->  A#11[[.]],
           T#12  |->  [.],
           S#2   |->  (app (letrec {E#6} in S#8) S#7)}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -ucp3->                       (letrec {X#1=(app (letrec {E#6} in S#8) S#7)} in (letrec {E#5} in A#11[(var X#1)]))
    ................................................................................
                                  (letrec {E#5} in A#11[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#11[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#12[(app (letrec {E#6} in S#8) S#7)]
     in
        (letrec {E#5} in A#11[(var X#1)])
     )
    ,
     (letrec {E#5} in A#11[A#12[(letrec {E#6} in (app S#8 S#7))]])
  )

where

   Delta1 = {A#9,T#10,T#4,A#11}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#5} in A#11)),
             (A#12[(app (letrec {E#6} in S#8) S#7)],(letrec {E#5} in A#11)),
             ((letrec {E#5} in A#11[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (A#12[(app (letrec {E#6} in S#8) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(letrec {E#5} in A#11[[.]]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#5} in A#11),
           A#9   |->  A#11[A#12],
           T#10  |->  A#11,
           S#2   |->  A#12[(app (letrec {E#6} in S#8) S#7)]}

and instantiated rules:

                                  (letrec {E#5} in A#11[A#12[(app (letrec {E#6} in S#8) S#7)]])
    -ucp3->                       (letrec {X#1=A#12[(app (letrec {E#6} in S#8) S#7)]} in (letrec {E#5} in A#11[(var X#1)]))
    ................................................................................
                                  (letrec {E#5} in A#11[A#12[(app (letrec {E#6} in S#8) S#7)]])
    -SR,lapp2->                   (letrec {E#5} in A#11[A#12[(letrec {E#6} in (app S#8 S#7))]])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           E#5
        in
           A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(var X#1)])]
        )
     )
    ,
     (letrec {E#5} in A#11[(app A#12[(letrec {E#6} in (app S#8 S#7))] T#13[S#2])])
  )

where

   Delta1 = {A#9,T#10,T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)])),
             (S#2,(letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)])),
             ((letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[[.]])]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)]),
           T#10  |->  A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13)],
           A#9   |->  A#11[(app A#12 T#13[S#2])]}

and instantiated rules:

                                  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[S#2])])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[(var X#1)])]))
    ................................................................................
                                  (letrec {E#5} in A#11[(app A#12[(app (letrec {E#6} in S#8) S#7)] T#13[S#2])])
    -SR,lapp2->                   (letrec {E#5} in A#11[(app A#12[(letrec {E#6} in (app S#8 S#7))] T#13[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {E#5} in (app (letrec {E#6} in T#12[(var X#1)]) S#7))
     )
    ,
     (letrec {E#5} in (letrec {E#6} in (app T#12[S#2] S#7)))
  )

where

   Delta1 = {T#11,T#10,T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#5} in (app (letrec {E#6} in T#12) S#7))),
             (S#2,(letrec {E#5} in (app (letrec {E#6} in T#12) S#7))),
             ((letrec {E#5} in (app (letrec {E#6} in T#12[(dummy3 )]) S#7)),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(letrec {E#5} in (app (letrec {E#6} in T#12[[.]]) S#7)))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#5} in (app (letrec {E#6} in T#12) S#7)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {E#6} in T#12) S#7),
           T#11  |->  (letrec {E#6} in T#12),
           S#8   |->  T#12[S#2]}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in T#12[S#2]) S#7))
    -ucp3->                       (letrec {X#1=S#2} in (letrec {E#5} in (app (letrec {E#6} in T#12[(var X#1)]) S#7)))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in T#12[S#2]) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app T#12[S#2] S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {E#5} in (app (letrec {X#13=T#12[(var X#1)];E#15} in S#8) S#7))
     )
    ,
     (letrec {E#5} in (letrec {X#13=T#12[S#2];E#15} in (app S#8 S#7)))
  )

where

   Delta1 = {T#11,T#10,T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#5} in (app (letrec {X#13=T#12;E#15} in S#8) S#7))),
             (S#2,(letrec {E#5} in (app (letrec {X#13=T#12;E#15} in S#8) S#7))),
             ((letrec {E#5} in (app (letrec {X#13=T#12[(dummy3 )];E#15} in S#8) S#7)),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {X#13=T#12[S#2];E#15} in [.])),
             ((var X#1),(letrec {E#5} in (app (letrec {X#13=T#12[[.]];E#15} in S#8) S#7)))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#5} in (app (letrec {X#13=T#12;E#15} in S#8) S#7)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {X#13=T#12;E#15} in S#8) S#7),
           T#11  |->  (letrec {X#13=T#12;E#15} in S#8),
           E#6   |->  {X#13=T#12[S#2];E#15},
           E#14  |->  {E#15}}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {X#13=T#12[S#2];E#15} in S#8) S#7))
    -ucp3->                       (letrec {X#1=S#2} in (letrec {E#5} in (app (letrec {X#13=T#12[(var X#1)];E#15} in S#8) S#7)))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {X#13=T#12[S#2];E#15} in S#8) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {X#13=T#12[S#2];E#15} in (app S#8 S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec {X#1=(letrec {E#6} in S#8)} in (letrec {E#5} in (app (var X#1) S#7)))
    ,
     (letrec {E#5} in (letrec {E#6} in (app S#8 S#7)))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#5} in (app [.] S#7))),
             ((letrec {E#6} in S#8),(letrec {E#5} in (app [.] S#7))),
             ((letrec {E#5} in (app (dummy3 ) S#7)),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#6} in S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(letrec {E#5} in (app [.] S#7)))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#5} in (app [.] S#7)),
           A#9   |->  [.],
           T#10  |->  (app [.] S#7),
           T#11  |->  [.],
           S#2   |->  (letrec {E#6} in S#8)}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in S#8) S#7))
    -ucp3->                       (letrec {X#1=(letrec {E#6} in S#8)} in (letrec {E#5} in (app (var X#1) S#7)))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in S#8) S#7))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app S#8 S#7)))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(var X#1)]))
     )
    ,
     (letrec {E#5} in (letrec {E#6} in (app S#8 T#11[S#2])))
  )

where

   Delta1 = {T#10,T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#5} in (app (letrec {E#6} in S#8) T#11))),
             (S#2,(letrec {E#5} in (app (letrec {E#6} in S#8) T#11))),
             ((letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(dummy3 )])),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#11[S#2],(letrec {E#6} in [.])),
             ((var X#1),(letrec {E#5} in (app (letrec {E#6} in S#8) T#11[[.]])))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11)),
           A#9   |->  [.],
           T#10  |->  (app (letrec {E#6} in S#8) T#11),
           S#7   |->  T#11[S#2]}

and instantiated rules:

                                  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[S#2]))
    -ucp3->                       (letrec {X#1=S#2} in (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[(var X#1)])))
    ................................................................................
                                  (letrec {E#5} in (app (letrec {E#6} in S#8) T#11[S#2]))
    -SR,lapp2->                   (letrec {E#5} in (letrec {E#6} in (app S#8 T#11[S#2])))
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#9[(app (letrec {E#6} in S#8) S#7)]
     in
        (letrec {E#5} in (var X#1))
     )
    ,
     (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {E#5} in [.])),
             (A#9[(app (letrec {E#6} in S#8) S#7)],(letrec {E#5} in [.])),
             ((letrec {E#5} in (dummy3 )),(letrec {X#1=(dummy3 )} in [.])),
             (A#9[(app (letrec {E#6} in S#8) S#7)],(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(letrec {E#5} in [.]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#5} in [.]),
           T#10  |->  [.],
           S#2   |->  A#9[(app (letrec {E#6} in S#8) S#7)]}

and instantiated rules:

                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -ucp3->                       (letrec {X#1=A#9[(app (letrec {E#6} in S#8) S#7)]} in (letrec {E#5} in (var X#1)))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec {X#11=T#10[(var X#1)];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
     )
    ,
     (letrec {X#11=T#10[S#2];E#13} in A#9[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),(letrec {X#11=T#10;E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])),
             (S#2,(letrec {X#11=T#10;E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])),
             ((letrec {X#11=T#10[(dummy3 )];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),(letrec {X#11=T#10[[.]];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)]))}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#11=T#10;E#13} in A#9[(app (letrec {E#6} in S#8) S#7)]),
           E#5   |->  {X#11=T#10[S#2];E#13},
           E#12  |->  {E#13}}

and instantiated rules:

                                  (letrec {X#11=T#10[S#2];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#11=T#10[(var X#1)];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)]))
    ................................................................................
                                  (letrec {X#11=T#10[S#2];E#13} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {X#11=T#10[S#2];E#13} in A#9[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
     in
        (var X#1)
     )
    ,
     (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
  )

where

   Delta1 = {}
   Delta2 = {E#5,E#6}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)]),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#7,(letrec {E#6} in [.])),
             ((var X#1),[.])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp2-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    and constraints: E#5/= {}, E#6/= {}, (S#7,(letrec {E#6} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]] =?= (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}
      Delta1=  {}
      Delta2=  {E#5,E#6}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#7,(letrec {E#6} in [.])),((var X#1),T#4[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  [.],
           S#2  |->  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])}

and instantiated rules:

                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -ucp3->                       (letrec {X#1=(letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])} in (var X#1))
    ................................................................................
                                  (letrec {E#5} in A#9[(app (letrec {E#6} in S#8) S#7)])
    -SR,lapp2->                   (letrec {E#5} in A#9[(letrec {E#6} in (app S#8 S#7))])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        A#13[(letrec {X#1=(var X#5)} in (var X#1))]
     )
    ,
     (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[(var X#5)])
  )

where

   Delta1 = {A#10,T#12,T#3,A#13}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((var X#5),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#13[[.]]),
             ((var X#5),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[[.]]),
           A#10  |->  A#13,
           T#12  |->  A#13[[.]],
           T#14  |->  [.],
           T#4   |->  [.],
           S#2   |->  (var X#5)}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(var X#5)])
    -ucp3->                       (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(letrec {X#1=(var X#5)} in (var X#1))])
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        A#13[(letrec {X#1=(var X#5)} in A#15[(var X#1)])]
     )
    ,
     (letrec
        E#6
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#13[A#15[(var X#5)]]
     )
  )

where

   Delta1 = {A#14,T#4,A#10,T#12,T#3,A#13,A#15}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#15[[.]]),
             ((var X#5),A#15[[.]]),
             (A#15[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#15[[.]]),
             ((var X#5),A#13[A#15[[.]]]),
             ((var X#5),A#13[A#15[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13),
           A#10  |->  A#13[A#15],
           T#12  |->  A#13,
           A#14  |->  A#15,
           T#4   |->  A#15[[.]],
           T#16  |->  [.],
           S#2   |->  (var X#5)}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[A#15[(var X#5)]])
    -ucp3->                       (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(letrec {X#1=(var X#5)} in A#15[(var X#1)])])
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[A#15[(var X#5)]])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[A#15[(var X#5)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        A#13[(letrec {X#1=A#16[(var X#5)]} in A#15[(var X#1)])]
     )
    ,
     (letrec
        E#6
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#13[A#15[A#16[(var X#5)]]]
     )
  )

where

   Delta1 = {A#14,T#4,A#10,T#12,T#3,A#13,A#15}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#15),
             (A#16[(var X#5)],A#15),
             (A#15[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#16[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#15[[.]]),
             ((var X#5),A#13[A#15[A#16[[.]]]]),
             ((var X#5),A#13[A#15[A#16[[.]]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13),
           A#10  |->  A#13[A#15[A#16]],
           T#12  |->  A#13,
           A#14  |->  A#15[A#16],
           T#4   |->  A#15,
           S#2   |->  A#16[(var X#5)]}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[A#15[A#16[(var X#5)]]])
    -ucp3->                       (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(letrec {X#1=A#16[(var X#5)]} in A#15[(var X#1)])])
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[A#15[A#16[(var X#5)]]])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[A#15[A#16[(var X#5)]]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        A#13[(letrec {X#1=S#2} in A#15[(app A#16[(var X#5)] T#17[(var X#1)])])]
     )
    ,
     (letrec
        E#6
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#13[A#15[(app A#16[(var X#5)] T#17[S#2])]]
     )
  )

where

   Delta1 = {A#14,T#4,A#10,T#12,T#3,A#13}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#15[(app A#16[(var X#5)] T#17)]),
             (S#2,A#15[(app A#16[(var X#5)] T#17)]),
             (A#15[(app A#16[(var X#5)] T#17[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#15[(app A#16[(var X#5)] T#17[[.]])]),
             ((var X#5),A#13[A#15[(app A#16[[.]] T#17[S#2])]]),
             ((var X#5),A#13[A#15[(app A#16[[.]] T#17[S#2])]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13),
           A#10  |->  A#13[A#15[(app A#16 T#17[S#2])]],
           T#12  |->  A#13,
           T#4   |->  A#15[(app A#16[(var X#5)] T#17)],
           A#14  |->  A#15[(app A#16 T#17[S#2])]}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[A#15[(app A#16[(var X#5)] T#17[S#2])]])
    -ucp3->                       (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(letrec {X#1=S#2} in A#15[(app A#16[(var X#5)] T#17[(var X#1)])])])
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[A#15[(app A#16[(var X#5)] T#17[S#2])]])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[A#15[(app A#16[(var X#5)] T#17[S#2])]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        A#13[(letrec {X#1=A#14[(var X#5)]} in (var X#1))]
     )
    ,
     (letrec
        E#6
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#13[A#14[(var X#5)]]
     )
  )

where

   Delta1 = {A#10,T#12,T#3,A#13}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#14[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#13[A#14[[.]]]),
             ((var X#5),A#13[A#14[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13),
           A#10  |->  A#13[A#14],
           T#12  |->  A#13,
           T#4   |->  [.],
           S#2   |->  A#14[(var X#5)]}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[A#14[(var X#5)]])
    -ucp3->                       (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(letrec {X#1=A#14[(var X#5)]} in (var X#1))])
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[A#14[(var X#5)]])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[A#14[(var X#5)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        A#13[(app A#14[(var X#5)] T#15[(letrec {X#1=S#2} in T#4[(var X#1)])])]
     )
    ,
     (letrec
        E#6
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#13[(app A#14[(var X#5)] T#15[T#4[S#2]])]
     )
  )

where

   Delta1 = {A#10,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#13[(app A#14[[.]] T#15[T#4[S#2]])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[T#4[S#2]])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#5)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[T#4[S#2]])])
    -ucp3->                       (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(letrec {X#1=S#2} in T#4[(var X#1)])])])
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[T#4[S#2]])])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[(app A#14[(var X#5)] T#15[T#4[S#2]])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        (letrec {X#1=(var X#5)} in A#13[(var X#1)])
     )
    ,
     (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[(var X#5)])
  )

where

   Delta1 = {A#10,T#4,T#3,A#13}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#13[[.]]),
             ((var X#5),A#13[[.]]),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#5),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#13[[.]]),
             ((var X#5),A#13[[.]]),
             ((var X#5),A#13[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in [.]),
           T#12  |->  [.],
           A#10  |->  A#13,
           T#4   |->  A#13[[.]],
           T#14  |->  [.],
           S#2   |->  (var X#5)}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(var X#5)])
    -ucp3->                       (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in (letrec {X#1=(var X#5)} in A#13[(var X#1)]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        (letrec {X#1=A#14[(var X#5)]} in A#13[(var X#1)])
     )
    ,
     (letrec
        E#6
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#13[A#14[(var X#5)]]
     )
  )

where

   Delta1 = {A#10,T#4,T#3,A#13}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#13),
             (A#14[(var X#5)],A#13),
             (A#13[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#14[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#13[[.]]),
             ((var X#5),A#13[A#14[[.]]]),
             ((var X#5),A#13[A#14[[.]]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in [.]),
           T#12  |->  [.],
           A#10  |->  A#13[A#14],
           T#4   |->  A#13,
           S#2   |->  A#14[(var X#5)]}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[A#14[(var X#5)]])
    -ucp3->                       (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in (letrec {X#1=A#14[(var X#5)]} in A#13[(var X#1)]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[A#14[(var X#5)]])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[A#14[(var X#5)]])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        (letrec {X#1=S#2} in A#13[(app A#14[(var X#5)] T#15[(var X#1)])])
     )
    ,
     (letrec
        E#6
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#13[(app A#14[(var X#5)] T#15[S#2])]
     )
  )

where

   Delta1 = {A#10,T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#13[(app A#14[(var X#5)] T#15)]),
             (S#2,A#13[(app A#14[(var X#5)] T#15)]),
             (A#13[(app A#14[(var X#5)] T#15[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#13[(app A#14[(var X#5)] T#15[[.]])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[S#2])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[S#2])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in [.]),
           T#12  |->  [.],
           T#4   |->  A#13[(app A#14[(var X#5)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[S#2])]}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[S#2])])
    -ucp3->                       (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in (letrec {X#1=S#2} in A#13[(app A#14[(var X#5)] T#15[(var X#1)])]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[S#2])])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[(app A#14[(var X#5)] T#15[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        E#6
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        (letrec {X#1=A#10[(var X#5)]} in (var X#1))
     )
    ,
     (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#10[(var X#5)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#10[(var X#5)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in [.]),
           T#12  |->  [.],
           T#4   |->  [.],
           S#2   |->  A#10[(var X#5)]}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in (letrec {X#1=A#10[(var X#5)]} in (var X#1)))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#13= T#12[(letrec {X#1=S#2} in T#4[(var X#1)])]
       ;E#15
       ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#13= T#12[T#4[S#2]]
       ;E#15
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  (letrec {X#13=T#12;E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           E#6   |->  {X#13=T#12[T#4[S#2]];E#15},
           E#14  |->  {E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[T#4[S#2]];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#13=T#12[(letrec {X#1=S#2} in T#4[(var X#1)])];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#13=T#12[T#4[S#2]];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#13=T#12[T#4[S#2]];E#15;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {E#7} in T#19[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#8)]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app T#19[T#4[S#2]] S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[(app (letrec {E#7} in T#19) S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {E#7} in T#19) S#8)],
           T#17         |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[T#4[S#2]]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[T#4[S#2]]) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(app (letrec {E#7} in T#19[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[T#4[S#2]]) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app T#19[T#4[S#2]] S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {X#20=T#19[(letrec {X#1=S#2} in T#4[(var X#1)])];E#22} in S#9) S#8)]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {X#20=T#19[T#4[S#2]];E#22} in (app S#9 S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#20=T#19[T#4[S#2]];E#22} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)],
           T#17         |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[T#4[S#2]];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[T#4[S#2]];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(app (letrec {X#20=T#19[(letrec {X#1=S#2} in T#4[(var X#1)])];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[T#4[S#2]];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {X#20=T#19[T#4[S#2]];E#22} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {X#1=S#2} in (letrec {E#7} in T#19[(var X#1)])) S#8)]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app T#19[S#2] S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,T#17,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {E#7} in T#19)),
             (S#2,(letrec {E#7} in T#19)),
             ((letrec {E#7} in T#19[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {E#7} in T#19[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[(app [.] S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app [.] S#8)],
           T#17         |->  (app [.] S#8),
           T#18         |->  [.],
           T#4          |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[S#2]) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(app (letrec {X#1=S#2} in (letrec {E#7} in T#19[(var X#1)])) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[S#2]) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app T#19[S#2] S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {X#1=S#2} in (letrec {X#20=T#19[(var X#1)];E#22} in S#9)) S#8)]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,T#17,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#20=T#19;E#22} in S#9)),
             (S#2,(letrec {X#20=T#19;E#22} in S#9)),
             ((letrec {X#20=T#19[(dummy3 )];E#22} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#20=T#19[S#2];E#22} in [.])),
             ((var X#1),(letrec {X#20=T#19[[.]];E#22} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[(app [.] S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app [.] S#8)],
           T#17         |->  (app [.] S#8),
           T#18         |->  [.],
           T#4          |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[S#2];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(app (letrec {X#1=S#2} in (letrec {X#20=T#19[(var X#1)];E#22} in S#9)) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {X#1=(letrec {E#7} in S#9)} in (var X#1)) S#8)]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#17,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#7} in S#9),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[(app [.] S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app [.] S#8)],
           T#17         |->  (app [.] S#8),
           T#18         |->  [.],
           T#4          |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(app (letrec {X#1=(letrec {E#7} in S#9)} in (var X#1)) S#8)];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app (letrec {E#7} in S#9) T#18[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app S#9 T#18[T#4[S#2]]))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#17,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[T#4[S#2]],(letrec {E#7} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {E#7} in S#9) T#18)],
           T#17         |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[T#4[S#2]]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[T#4[S#2]])];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[T#4[S#2]])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 T#18[T#4[S#2]]))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=S#2} in (app (letrec {E#7} in T#19[(var X#1)]) S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app T#19[S#2] S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#4,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in T#19) S#8)),
             (S#2,(app (letrec {E#7} in T#19) S#8)),
             ((app (letrec {E#7} in T#19[(dummy3 )]) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in T#19[[.]]) S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[[.]];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[[.]],
           T#17         |->  [.],
           T#4          |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[S#2]) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=S#2} in (app (letrec {E#7} in T#19[(var X#1)]) S#8))];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[S#2]) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app T#19[S#2] S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=S#2} in (app (letrec {X#20=T#19[(var X#1)];E#22} in S#9) S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#4,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {X#20=T#19;E#22} in S#9) S#8)),
             (S#2,(app (letrec {X#20=T#19;E#22} in S#9) S#8)),
             ((app (letrec {X#20=T#19[(dummy3 )];E#22} in S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#20=T#19[S#2];E#22} in [.])),
             ((var X#1),(app (letrec {X#20=T#19[[.]];E#22} in S#9) S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[[.]];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[[.]],
           T#17         |->  [.],
           T#4          |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[S#2];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=S#2} in (app (letrec {X#20=T#19[(var X#1)];E#22} in S#9) S#8))];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=(letrec {E#7} in S#9)} in (app (var X#1) S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app [.] S#8)),
             ((letrec {E#7} in S#9),(app [.] S#8)),
             ((app (dummy3 ) S#8),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(app [.] S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[[.]];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[[.]],
           T#17         |->  [.],
           T#4          |->  (app [.] S#8),
           T#18         |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=(letrec {E#7} in S#9)} in (app (var X#1) S#8))];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=S#2} in (app (letrec {E#7} in S#9) T#18[(var X#1)]))]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app S#9 T#18[S#2]))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in S#9) T#18)),
             (S#2,(app (letrec {E#7} in S#9) T#18)),
             ((app (letrec {E#7} in S#9) T#18[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[S#2],(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in S#9) T#18[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[[.]];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[[.]],
           T#17         |->  [.],
           T#4          |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[S#2])];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=S#2} in (app (letrec {E#7} in S#9) T#18[(var X#1)]))];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[S#2])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 T#18[S#2]))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=(app (letrec {E#7} in S#9) S#8)} in (var X#1))]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((app (letrec {E#7} in S#9) S#8),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#7} in S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[[.]];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[[.]],
           T#17         |->  [.],
           T#4          |->  [.],
           S#2          |->  (app (letrec {E#7} in S#9) S#8)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=(app (letrec {E#7} in S#9) S#8)} in (var X#1))];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=S#2} in A#18[(app (letrec {E#7} in T#21[(var X#1)]) S#8)])]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[A#18[(letrec {E#7} in (app T#21[S#2] S#8))]]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#17,T#4,A#15,T#12,T#3,A#16,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[(app (letrec {E#7} in T#21) S#8)]),
             (S#2,A#18[(app (letrec {E#7} in T#21) S#8)]),
             (A#18[(app (letrec {E#7} in T#21[(dummy3 )]) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#18[(app (letrec {E#7} in T#21[[.]]) S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#18[[.2]]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16[A#18],
           T#12         |->  A#16,
           A#17         |->  A#18,
           T#4          |->  A#18[(app (letrec {E#7} in T#21) S#8)],
           T#19         |->  (app (letrec {E#7} in T#21) S#8),
           T#20         |->  (letrec {E#7} in T#21),
           S#9          |->  T#21[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[A#18[(app (letrec {E#7} in T#21[S#2]) S#8)]];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=S#2} in A#18[(app (letrec {E#7} in T#21[(var X#1)]) S#8)])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#18[(app (letrec {E#7} in T#21[S#2]) S#8)]];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[A#18[(letrec {E#7} in (app T#21[S#2] S#8))]];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec
                      X#1= S#2
                   in
                      A#18[(app (letrec {X#22=T#21[(var X#1)];E#24} in S#9) S#8)]
                   )]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[A#18[(letrec {X#22=T#21[S#2];E#24} in (app S#9 S#8))]]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#17,T#4,A#15,T#12,T#3,A#16,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)]),
             (S#2,A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)]),
             (A#18[(app (letrec {X#22=T#21[(dummy3 )];E#24} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#22=T#21[S#2];E#24} in [.])),
             ((var X#1),A#18[(app (letrec {X#22=T#21[[.]];E#24} in S#9) S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#18[[.2]]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16[A#18],
           T#12         |->  A#16,
           A#17         |->  A#18,
           T#4          |->  A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)],
           T#19         |->  (app (letrec {X#22=T#21;E#24} in S#9) S#8),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#9),
           E#7          |->  {X#22=T#21[S#2];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#5=A#16[A#18[(app (letrec {X#22=T#21[S#2];E#24} in S#9) S#8)]];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=S#2} in A#18[(app (letrec {X#22=T#21[(var X#1)];E#24} in S#9) S#8)])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#18[(app (letrec {X#22=T#21[S#2];E#24} in S#9) S#8)]];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[A#18[(letrec {X#22=T#21[S#2];E#24} in (app S#9 S#8))]];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=(letrec {E#7} in S#9)} in A#18[(app (var X#1) S#8)])]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[A#18[(letrec {E#7} in (app S#9 S#8))]]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#17,T#4,A#15,T#12,T#3,A#16,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[(app [.] S#8)]),
             ((letrec {E#7} in S#9),A#18[(app [.] S#8)]),
             (A#18[(app (dummy3 ) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#18[(app [.] S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#18[[.2]]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16[A#18],
           T#12         |->  A#16,
           A#17         |->  A#18,
           T#4          |->  A#18[(app [.] S#8)],
           T#19         |->  (app [.] S#8),
           T#20         |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#5=A#16[A#18[(app (letrec {E#7} in S#9) S#8)]];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=(letrec {E#7} in S#9)} in A#18[(app (var X#1) S#8)])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#18[(app (letrec {E#7} in S#9) S#8)]];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[A#18[(letrec {E#7} in (app S#9 S#8))]];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=S#2} in A#18[(app (letrec {E#7} in S#9) T#20[(var X#1)])])]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[A#18[(letrec {E#7} in (app S#9 T#20[S#2]))]]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#17,T#4,A#15,T#12,T#3,A#16,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[(app (letrec {E#7} in S#9) T#20)]),
             (S#2,A#18[(app (letrec {E#7} in S#9) T#20)]),
             (A#18[(app (letrec {E#7} in S#9) T#20[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#20[S#2],(letrec {E#7} in [.])),
             ((var X#1),A#18[(app (letrec {E#7} in S#9) T#20[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#18[[.2]]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16[A#18],
           T#12         |->  A#16,
           A#17         |->  A#18,
           T#4          |->  A#18[(app (letrec {E#7} in S#9) T#20)],
           T#19         |->  (app (letrec {E#7} in S#9) T#20),
           S#8          |->  T#20[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[A#18[(app (letrec {E#7} in S#9) T#20[S#2])]];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=S#2} in A#18[(app (letrec {E#7} in S#9) T#20[(var X#1)])])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#18[(app (letrec {E#7} in S#9) T#20[S#2])]];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[A#18[(letrec {E#7} in (app S#9 T#20[S#2]))]];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=(app (letrec {E#7} in S#9) S#8)} in A#18[(var X#1)])]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[A#18[(letrec {E#7} in (app S#9 S#8))]]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#17,T#4,A#15,T#12,T#3,A#16,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[[.]]),
             ((app (letrec {E#7} in S#9) S#8),A#18[[.]]),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#7} in S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#18[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#18[[.2]]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16[A#18],
           T#12         |->  A#16,
           A#17         |->  A#18,
           T#4          |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  (app (letrec {E#7} in S#9) S#8)}

and instantiated rules:

                                  (letrec {X#5=A#16[A#18[(app (letrec {E#7} in S#9) S#8)]];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=(app (letrec {E#7} in S#9) S#8)} in A#18[(var X#1)])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#18[(app (letrec {E#7} in S#9) S#8)]];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[A#18[(letrec {E#7} in (app S#9 S#8))]];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=A#19[(app (letrec {E#7} in S#9) S#8)]} in A#18[(var X#1)])]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[A#18[A#19[(letrec {E#7} in (app S#9 S#8))]]]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#17,T#4,A#15,T#12,T#3,A#16,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18),
             (A#19[(app (letrec {E#7} in S#9) S#8)],A#18),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(app (letrec {E#7} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#18[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#18[A#19[[.2]]]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16[A#18[A#19]],
           T#12         |->  A#16,
           A#17         |->  A#18[A#19],
           T#4          |->  A#18,
           S#2          |->  A#19[(app (letrec {E#7} in S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#5=A#16[A#18[A#19[(app (letrec {E#7} in S#9) S#8)]]];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=A#19[(app (letrec {E#7} in S#9) S#8)]} in A#18[(var X#1)])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#18[A#19[(app (letrec {E#7} in S#9) S#8)]]];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[A#18[A#19[(letrec {E#7} in (app S#9 S#8))]]];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec
                      X#1= S#2
                   in
                      A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(var X#1)])]
                   )]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[S#2])]]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#17,T#4,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)]),
             (S#2,A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)]),
             (A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#18[(app A#19[[.2]] T#20[S#2])]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16[A#18[(app A#19 T#20[S#2])]],
           T#12         |->  A#16,
           T#4          |->  A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)],
           A#17         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#5=A#16[A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[S#2])]];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=S#2} in A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(var X#1)])])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[S#2])]];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[S#2])]];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=S#2} in (app (letrec {E#7} in T#19[(var X#1)]) S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app T#19[S#2] S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#4,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in T#19) S#8)),
             (S#2,(app (letrec {E#7} in T#19) S#8)),
             ((app (letrec {E#7} in T#19[(dummy3 )]) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in T#19[[.]]) S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16[[.]],
           T#12         |->  A#16,
           A#17         |->  [.],
           T#4          |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[S#2]) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=S#2} in (app (letrec {E#7} in T#19[(var X#1)]) S#8))];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[S#2]) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app T#19[S#2] S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=S#2} in (app (letrec {X#20=T#19[(var X#1)];E#22} in S#9) S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#4,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {X#20=T#19;E#22} in S#9) S#8)),
             (S#2,(app (letrec {X#20=T#19;E#22} in S#9) S#8)),
             ((app (letrec {X#20=T#19[(dummy3 )];E#22} in S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#20=T#19[S#2];E#22} in [.])),
             ((var X#1),(app (letrec {X#20=T#19[[.]];E#22} in S#9) S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16[[.]],
           T#12         |->  A#16,
           A#17         |->  [.],
           T#4          |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[S#2];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=S#2} in (app (letrec {X#20=T#19[(var X#1)];E#22} in S#9) S#8))];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=(letrec {E#7} in S#9)} in (app (var X#1) S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app [.] S#8)),
             ((letrec {E#7} in S#9),(app [.] S#8)),
             ((app (dummy3 ) S#8),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(app [.] S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16[[.]],
           T#12         |->  A#16,
           A#17         |->  [.],
           T#4          |->  (app [.] S#8),
           T#18         |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=(letrec {E#7} in S#9)} in (app (var X#1) S#8))];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=S#2} in (app (letrec {E#7} in S#9) T#18[(var X#1)]))]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app S#9 T#18[S#2]))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in S#9) T#18)),
             (S#2,(app (letrec {E#7} in S#9) T#18)),
             ((app (letrec {E#7} in S#9) T#18[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[S#2],(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in S#9) T#18[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16[[.]],
           T#12         |->  A#16,
           A#17         |->  [.],
           T#4          |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[S#2])];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=S#2} in (app (letrec {E#7} in S#9) T#18[(var X#1)]))];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[S#2])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 T#18[S#2]))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(letrec {X#1=A#17[(app (letrec {E#7} in S#9) S#8)]} in (var X#1))]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[A#17[(letrec {E#7} in (app S#9 S#8))]]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#17[(app (letrec {E#7} in S#9) S#8)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#17[(app (letrec {E#7} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16;E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#17[[.2]]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16[A#17],
           T#12         |->  A#16,
           T#4          |->  [.],
           S#2          |->  A#17[(app (letrec {E#7} in S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#5=A#16[A#17[(app (letrec {E#7} in S#9) S#8)]];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(letrec {X#1=A#17[(app (letrec {E#7} in S#9) S#8)]} in (var X#1))];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#17[(app (letrec {E#7} in S#9) S#8)]];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[A#17[(letrec {E#7} in (app S#9 S#8))]];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(app A#17[(letrec {E#7} in (app S#9 S#8))] T#18[T#4[S#2]])]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[T#4[S#2]])]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[T#4[S#2]])];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[T#4[S#2]])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(app A#17[(letrec {E#7} in (app S#9 S#8))] T#18[T#4[S#2]])];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {E#7} in T#17[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#8)
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=(letrec {E#7} in (app T#17[T#4[S#2]] S#8));E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#16,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(app (letrec {E#7} in T#17) S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in T#17) S#8),
           T#16         |->  (letrec {E#7} in T#17),
           S#9          |->  T#17[T#4[S#2]]}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in T#17[T#4[S#2]]) S#8);E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(app (letrec {E#7} in T#17[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in T#17[T#4[S#2]]) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app T#17[T#4[S#2]] S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {X#18=T#17[(letrec {X#1=S#2} in T#4[(var X#1)])];E#20} in S#9) S#8)
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {X#18=T#17[T#4[S#2]];E#20} in (app S#9 S#8))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#16,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#18=T#17[T#4[S#2]];E#20} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(app (letrec {X#18=T#17;E#20} in S#9) S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {X#18=T#17;E#20} in S#9) S#8),
           T#16         |->  (letrec {X#18=T#17;E#20} in S#9),
           E#7          |->  {X#18=T#17[T#4[S#2]];E#20},
           E#19         |->  {E#20}}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {X#18=T#17[T#4[S#2]];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(app (letrec {X#18=T#17[(letrec {X#1=S#2} in T#4[(var X#1)])];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {X#18=T#17[T#4[S#2]];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {X#18=T#17[T#4[S#2]];E#20} in (app S#9 S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {X#1=S#2} in (letrec {E#7} in T#17[(var X#1)])) S#8)
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=(letrec {E#7} in (app T#17[S#2] S#8));E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#4,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {E#7} in T#17)),
             (S#2,(letrec {E#7} in T#17)),
             ((letrec {E#7} in T#17[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {E#7} in T#17[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(app [.] S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#16         |->  [.],
           T#4          |->  (letrec {E#7} in T#17),
           S#9          |->  T#17[S#2]}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in T#17[S#2]) S#8);E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(app (letrec {X#1=S#2} in (letrec {E#7} in T#17[(var X#1)])) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in T#17[S#2]) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app T#17[S#2] S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {X#1=S#2} in (letrec {X#18=T#17[(var X#1)];E#20} in S#9)) S#8)
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {X#18=T#17[S#2];E#20} in (app S#9 S#8))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#18=T#17;E#20} in S#9)),
             (S#2,(letrec {X#18=T#17;E#20} in S#9)),
             ((letrec {X#18=T#17[(dummy3 )];E#20} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#18=T#17[S#2];E#20} in [.])),
             ((var X#1),(letrec {X#18=T#17[[.]];E#20} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(app [.] S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#16         |->  [.],
           T#4          |->  (letrec {X#18=T#17;E#20} in S#9),
           E#7          |->  {X#18=T#17[S#2];E#20},
           E#19         |->  {E#20}}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {X#18=T#17[S#2];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(app (letrec {X#1=S#2} in (letrec {X#18=T#17[(var X#1)];E#20} in S#9)) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {X#18=T#17[S#2];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {X#18=T#17[S#2];E#20} in (app S#9 S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {X#1=(letrec {E#7} in S#9)} in (var X#1)) S#8)
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=(letrec {E#7} in (app S#9 S#8));E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#7} in S#9),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(app [.] S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#16         |->  [.],
           T#4          |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in S#9) S#8);E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(app (letrec {X#1=(letrec {E#7} in S#9)} in (var X#1)) S#8);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in S#9) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app S#9 S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (app (letrec {E#7} in S#9) T#16[(letrec {X#1=S#2} in T#4[(var X#1)])])
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=(letrec {E#7} in (app S#9 T#16[T#4[S#2]]));E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#16[T#4[S#2]],(letrec {E#7} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=(app (letrec {E#7} in S#9) T#16);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in S#9) T#16),
           S#8          |->  T#16[T#4[S#2]]}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in S#9) T#16[T#4[S#2]]);E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(app (letrec {E#7} in S#9) T#16[(letrec {X#1=S#2} in T#4[(var X#1)])]);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in S#9) T#16[T#4[S#2]]);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app S#9 T#16[T#4[S#2]]));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=S#2} in A#16[(app (letrec {E#7} in T#19[(var X#1)]) S#8)])
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app T#19[S#2] S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#4,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#16[(app (letrec {E#7} in T#19) S#8)]),
             (S#2,A#16[(app (letrec {E#7} in T#19) S#8)]),
             (A#16[(app (letrec {E#7} in T#19[(dummy3 )]) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#16[(app (letrec {E#7} in T#19[[.]]) S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  [.],
           A#15         |->  A#16,
           T#4          |->  A#16[(app (letrec {E#7} in T#19) S#8)],
           T#17         |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[S#2]) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in A#16[(app (letrec {E#7} in T#19[(var X#1)]) S#8)]);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[S#2]) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app T#19[S#2] S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec
                X#1= S#2
             in
                A#16[(app (letrec {X#20=T#19[(var X#1)];E#22} in S#9) S#8)]
             )
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#4,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)]),
             (S#2,A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)]),
             (A#16[(app (letrec {X#20=T#19[(dummy3 )];E#22} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#20=T#19[S#2];E#22} in [.])),
             ((var X#1),A#16[(app (letrec {X#20=T#19[[.]];E#22} in S#9) S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  [.],
           A#15         |->  A#16,
           T#4          |->  A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)],
           T#17         |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[S#2];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in A#16[(app (letrec {X#20=T#19[(var X#1)];E#22} in S#9) S#8)]);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=(letrec {E#7} in S#9)} in A#16[(app (var X#1) S#8)])
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#17,A#15,T#4,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#16[(app [.] S#8)]),
             ((letrec {E#7} in S#9),A#16[(app [.] S#8)]),
             (A#16[(app (dummy3 ) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#16[(app [.] S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  [.],
           A#15         |->  A#16,
           T#4          |->  A#16[(app [.] S#8)],
           T#17         |->  (app [.] S#8),
           T#18         |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=(letrec {E#7} in S#9)} in A#16[(app (var X#1) S#8)]);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=S#2} in A#16[(app (letrec {E#7} in S#9) T#18[(var X#1)])])
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app S#9 T#18[S#2]))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#17,A#15,T#4,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#16[(app (letrec {E#7} in S#9) T#18)]),
             (S#2,A#16[(app (letrec {E#7} in S#9) T#18)]),
             (A#16[(app (letrec {E#7} in S#9) T#18[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[S#2],(letrec {E#7} in [.])),
             ((var X#1),A#16[(app (letrec {E#7} in S#9) T#18[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  [.],
           A#15         |->  A#16,
           T#4          |->  A#16[(app (letrec {E#7} in S#9) T#18)],
           T#17         |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[S#2])];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in A#16[(app (letrec {E#7} in S#9) T#18[(var X#1)])]);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[S#2])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 T#18[S#2]))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=(app (letrec {E#7} in S#9) S#8)} in A#16[(var X#1)])
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {A#15,T#4,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#16[[.]]),
             ((app (letrec {E#7} in S#9) S#8),A#16[[.]]),
             (A#16[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#7} in S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#16[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  [.],
           A#15         |->  A#16,
           T#4          |->  A#16[[.]],
           T#17         |->  [.],
           S#2          |->  (app (letrec {E#7} in S#9) S#8)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=(app (letrec {E#7} in S#9) S#8)} in A#16[(var X#1)]);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=A#17[(app (letrec {E#7} in S#9) S#8)]} in A#16[(var X#1)])
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[A#17[(letrec {E#7} in (app S#9 S#8))]]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#16),
             (A#17[(app (letrec {E#7} in S#9) S#8)],A#16),
             (A#16[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#17[(app (letrec {E#7} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#16[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#17[[.2]]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  [.],
           A#15         |->  A#16[A#17],
           T#4          |->  A#16,
           S#2          |->  A#17[(app (letrec {E#7} in S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#5=A#16[A#17[(app (letrec {E#7} in S#9) S#8)]];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=A#17[(app (letrec {E#7} in S#9) S#8)]} in A#16[(var X#1)]);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[A#17[(app (letrec {E#7} in S#9) S#8)]];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[A#17[(letrec {E#7} in (app S#9 S#8))]];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec
                X#1= S#2
             in
                A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(var X#1)])]
             )
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#16[(app A#17[(letrec {E#7} in (app S#9 S#8))] T#18[S#2])]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)]),
             (S#2,A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)]),
             (A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[S#2])]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  [.],
           T#4          |->  A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[S#2])]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[S#2])];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(var X#1)])]);E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[S#2])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(app A#17[(letrec {E#7} in (app S#9 S#8))] T#18[S#2])];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=S#2} in (app (letrec {E#7} in T#17[(var X#1)]) S#8))
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=(letrec {E#7} in (app T#17[S#2] S#8));E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#16,T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in T#17) S#8)),
             (S#2,(app (letrec {E#7} in T#17) S#8)),
             ((app (letrec {E#7} in T#17[(dummy3 )]) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in T#17[[.]]) S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  [.],
           A#15         |->  [.],
           T#4          |->  (app (letrec {E#7} in T#17) S#8),
           T#16         |->  (letrec {E#7} in T#17),
           S#9          |->  T#17[S#2]}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in T#17[S#2]) S#8);E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in (app (letrec {E#7} in T#17[(var X#1)]) S#8));E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in T#17[S#2]) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app T#17[S#2] S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=S#2} in (app (letrec {X#18=T#17[(var X#1)];E#20} in S#9) S#8))
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= (letrec {X#18=T#17[S#2];E#20} in (app S#9 S#8))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#16,T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {X#18=T#17;E#20} in S#9) S#8)),
             (S#2,(app (letrec {X#18=T#17;E#20} in S#9) S#8)),
             ((app (letrec {X#18=T#17[(dummy3 )];E#20} in S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#18=T#17[S#2];E#20} in [.])),
             ((var X#1),(app (letrec {X#18=T#17[[.]];E#20} in S#9) S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  [.],
           A#15         |->  [.],
           T#4          |->  (app (letrec {X#18=T#17;E#20} in S#9) S#8),
           T#16         |->  (letrec {X#18=T#17;E#20} in S#9),
           E#7          |->  {X#18=T#17[S#2];E#20},
           E#19         |->  {E#20}}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {X#18=T#17[S#2];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in (app (letrec {X#18=T#17[(var X#1)];E#20} in S#9) S#8));E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {X#18=T#17[S#2];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {X#18=T#17[S#2];E#20} in (app S#9 S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=(letrec {E#7} in S#9)} in (app (var X#1) S#8))
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=(letrec {E#7} in (app S#9 S#8));E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app [.] S#8)),
             ((letrec {E#7} in S#9),(app [.] S#8)),
             ((app (dummy3 ) S#8),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(app [.] S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  [.],
           A#15         |->  [.],
           T#4          |->  (app [.] S#8),
           T#16         |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in S#9) S#8);E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=(letrec {E#7} in S#9)} in (app (var X#1) S#8));E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in S#9) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app S#9 S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=S#2} in (app (letrec {E#7} in S#9) T#16[(var X#1)]))
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=(letrec {E#7} in (app S#9 T#16[S#2]));E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in S#9) T#16)),
             (S#2,(app (letrec {E#7} in S#9) T#16)),
             ((app (letrec {E#7} in S#9) T#16[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#16[S#2],(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in S#9) T#16[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  [.],
           A#15         |->  [.],
           T#4          |->  (app (letrec {E#7} in S#9) T#16),
           S#8          |->  T#16[S#2]}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in S#9) T#16[S#2]);E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in (app (letrec {E#7} in S#9) T#16[(var X#1)]));E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in S#9) T#16[S#2]);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app S#9 T#16[S#2]));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=A#15[(app (letrec {E#7} in S#9) S#8)]} in (var X#1))
       ;E#6
     in
        A#10[(var X#5)]
     )
    ,
     (letrec {X#5=A#15[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#15[(app (letrec {E#7} in S#9) S#8)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(app (letrec {E#7} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#15[(app (letrec {E#7} in S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#5=A#15[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=A#15[(app (letrec {E#7} in S#9) S#8)]} in (var X#1));E#6} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#15[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#15[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(letrec {X#1=(var X#16)} in (var X#1))]
       ;E#6
       ;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(var X#16)]
       ;E#6
       ;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((var X#16),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#16),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#18[[.]];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(var X#16)];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#5=A#18[(var X#16)];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#18[(letrec {X#1=(var X#16)} in (var X#1))];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(var X#16)];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#18[(var X#16)];E#6;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(letrec {X#1=(var X#16)} in A#20[(var X#1)])]
       ;E#6
       ;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[A#20[(var X#16)]]
       ;E#6
       ;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[[.]]),
             ((var X#16),A#20[[.]]),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#16),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#20[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#18;E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#20[(var X#16)]];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]},
           A#15         |->  A#18[A#20],
           T#12         |->  A#18,
           A#19         |->  A#20,
           T#4          |->  A#20[[.]],
           T#21         |->  [.],
           S#2          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#5=A#18[A#20[(var X#16)]];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#18[(letrec {X#1=(var X#16)} in A#20[(var X#1)])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[A#20[(var X#16)]];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#18[A#20[(var X#16)]];E#6;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(letrec {X#1=A#21[(var X#16)]} in A#20[(var X#1)])]
       ;E#6
       ;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[A#20[A#21[(var X#16)]]]
       ;E#6
       ;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20),
             (A#21[(var X#16)],A#20),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#21[(var X#16)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#20[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#18;E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#20[A#21[(var X#16)]]];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]},
           A#15         |->  A#18[A#20[A#21]],
           T#12         |->  A#18,
           A#19         |->  A#20[A#21],
           T#4          |->  A#20,
           S#2          |->  A#21[(var X#16)]}

and instantiated rules:

                                  (letrec {X#5=A#18[A#20[A#21[(var X#16)]]];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#18[(letrec {X#1=A#21[(var X#16)]} in A#20[(var X#1)])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[A#20[A#21[(var X#16)]]];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#18[A#20[A#21[(var X#16)]]];E#6;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(letrec {X#1=S#2} in A#20[(app A#21[(var X#16)] T#22[(var X#1)])])]
       ;E#6
       ;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]]
       ;E#6
       ;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[(app A#21[(var X#16)] T#22)]),
             (S#2,A#20[(app A#21[(var X#16)] T#22)]),
             (A#20[(app A#21[(var X#16)] T#22[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#20[(app A#21[(var X#16)] T#22[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#18;E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]},
           A#15         |->  A#18[A#20[(app A#21 T#22[S#2])]],
           T#12         |->  A#18,
           T#4          |->  A#20[(app A#21[(var X#16)] T#22)],
           A#19         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#5=A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#18[(letrec {X#1=S#2} in A#20[(app A#21[(var X#16)] T#22[(var X#1)])])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#18[A#20[(app A#21[(var X#16)] T#22[S#2])]];E#6;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(letrec {X#1=A#19[(var X#16)]} in (var X#1))]
       ;E#6
       ;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[A#19[(var X#16)]]
       ;E#6
       ;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#19[(var X#16)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(var X#16)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#18;E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#19[(var X#16)]];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]},
           A#15         |->  A#18[A#19],
           T#12         |->  A#18,
           T#4          |->  [.],
           S#2          |->  A#19[(var X#16)]}

and instantiated rules:

                                  (letrec {X#5=A#18[A#19[(var X#16)]];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#18[(letrec {X#1=A#19[(var X#16)]} in (var X#1))];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[A#19[(var X#16)]];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#18[A#19[(var X#16)]];E#6;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#6
       ;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])]
       ;E#6
       ;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[T#4[S#2]])];E#6;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=(var X#16)} in A#18[(var X#1)])
       ;E#6
       ;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(var X#16)]
       ;E#6
       ;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[[.]]),
             ((var X#16),A#18[[.]]),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#16),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#18[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(var X#16)];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  [.],
           A#15         |->  A#18,
           T#4          |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  (var X#16)}

and instantiated rules:

                                  (letrec {X#5=A#18[(var X#16)];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=(var X#16)} in A#18[(var X#1)]);E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(var X#16)];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#18[(var X#16)];E#6;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=A#19[(var X#16)]} in A#18[(var X#1)])
       ;E#6
       ;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[A#19[(var X#16)]]
       ;E#6
       ;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18),
             (A#19[(var X#16)],A#18),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(var X#16)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#18[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[A#19[(var X#16)]];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  [.],
           A#15         |->  A#18[A#19],
           T#4          |->  A#18,
           S#2          |->  A#19[(var X#16)]}

and instantiated rules:

                                  (letrec {X#5=A#18[A#19[(var X#16)]];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=A#19[(var X#16)]} in A#18[(var X#1)]);E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[A#19[(var X#16)]];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#18[A#19[(var X#16)]];E#6;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=S#2} in A#18[(app A#19[(var X#16)] T#20[(var X#1)])])
       ;E#6
       ;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[S#2])]
       ;E#6
       ;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[(app A#19[(var X#16)] T#20)]),
             (S#2,A#18[(app A#19[(var X#16)] T#20)]),
             (A#18[(app A#19[(var X#16)] T#20[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#18[(app A#19[(var X#16)] T#20[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[S#2])];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  [.],
           T#4          |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[S#2])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=S#2} in A#18[(app A#19[(var X#16)] T#20[(var X#1)])]);E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[S#2])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[S#2])];E#6;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#5= (letrec {X#1=A#15[(var X#16)]} in (var X#1))
       ;E#6
       ;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#5= A#15[(var X#16)]
       ;E#6
       ;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#15[(var X#16)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(var X#16)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#5=[.];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#15[(var X#16)];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#15[(var X#16)]}

and instantiated rules:

                                  (letrec {X#5=A#15[(var X#16)];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#5=(letrec {X#1=A#15[(var X#16)]} in (var X#1));E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#5=A#15[(var X#16)];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#15[(var X#16)];E#6;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {X#1=(var X#17)} in (var X#1))]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(var X#17)]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((var X#17),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20[[.]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]},
           A#15         |->  A#20,
           T#12         |->  A#20[[.]],
           T#21         |->  [.],
           T#4          |->  [.],
           S#2          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#16=A#20[(var X#17)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#20[(letrec {X#1=(var X#17)} in (var X#1))];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(var X#17)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#20[(var X#17)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {X#1=(var X#17)} in A#22[(var X#1)])]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[A#22[(var X#17)]]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#21,T#4,A#15,T#12,T#3,A#20,A#22}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#22[[.]]),
             ((var X#17),A#22[[.]]),
             (A#22[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#22[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20;E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#22[(var X#17)]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]},
           A#15         |->  A#20[A#22],
           T#12         |->  A#20,
           A#21         |->  A#22,
           T#4          |->  A#22[[.]],
           T#23         |->  [.],
           S#2          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#16=A#20[A#22[(var X#17)]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#20[(letrec {X#1=(var X#17)} in A#22[(var X#1)])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[A#22[(var X#17)]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#20[A#22[(var X#17)]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {X#1=A#23[(var X#17)]} in A#22[(var X#1)])]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[A#22[A#23[(var X#17)]]]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#21,T#4,A#15,T#12,T#3,A#20,A#22}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#22),
             (A#23[(var X#17)],A#22),
             (A#22[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#23[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#22[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20;E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#22[A#23[(var X#17)]]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]},
           A#15         |->  A#20[A#22[A#23]],
           T#12         |->  A#20,
           A#21         |->  A#22[A#23],
           T#4          |->  A#22,
           S#2          |->  A#23[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#22[A#23[(var X#17)]]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#20[(letrec {X#1=A#23[(var X#17)]} in A#22[(var X#1)])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[A#22[A#23[(var X#17)]]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#20[A#22[A#23[(var X#17)]]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {X#1=S#2} in A#22[(app A#23[(var X#17)] T#24[(var X#1)])])]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#21,T#4,A#15,T#12,T#3,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#22[(app A#23[(var X#17)] T#24)]),
             (S#2,A#22[(app A#23[(var X#17)] T#24)]),
             (A#22[(app A#23[(var X#17)] T#24[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#22[(app A#23[(var X#17)] T#24[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20;E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]},
           A#15         |->  A#20[A#22[(app A#23 T#24[S#2])]],
           T#12         |->  A#20,
           T#4          |->  A#22[(app A#23[(var X#17)] T#24)],
           A#21         |->  A#22[(app A#23 T#24[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#20[(letrec {X#1=S#2} in A#22[(app A#23[(var X#17)] T#24[(var X#1)])])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#20[A#22[(app A#23[(var X#17)] T#24[S#2])]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(letrec {X#1=A#21[(var X#17)]} in (var X#1))]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[A#21[(var X#17)]]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#21[(var X#17)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#21[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20;E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#21[(var X#17)]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]},
           A#15         |->  A#20[A#21],
           T#12         |->  A#20,
           T#4          |->  [.],
           S#2          |->  A#21[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#21[(var X#17)]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#20[(letrec {X#1=A#21[(var X#17)]} in (var X#1))];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[A#21[(var X#17)]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#20[A#21[(var X#17)]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[T#4[S#2]])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=(var X#17)} in A#20[(var X#1)])
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(var X#17)]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[[.]]),
             ((var X#17),A#20[[.]]),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((var X#17),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#20[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  [.],
           A#15         |->  A#20,
           T#4          |->  A#20[[.]],
           T#21         |->  [.],
           S#2          |->  (var X#17)}

and instantiated rules:

                                  (letrec {X#16=A#20[(var X#17)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=(var X#17)} in A#20[(var X#1)]);E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(var X#17)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#20[(var X#17)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=A#21[(var X#17)]} in A#20[(var X#1)])
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[A#21[(var X#17)]]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20),
             (A#21[(var X#17)],A#20),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#21[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#20[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[A#21[(var X#17)]];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  [.],
           A#15         |->  A#20[A#21],
           T#4          |->  A#20,
           S#2          |->  A#21[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#20[A#21[(var X#17)]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=A#21[(var X#17)]} in A#20[(var X#1)]);E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[A#21[(var X#17)]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#20[A#21[(var X#17)]];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=S#2} in A#20[(app A#21[(var X#17)] T#22[(var X#1)])])
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[S#2])]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[(app A#21[(var X#17)] T#22)]),
             (S#2,A#20[(app A#21[(var X#17)] T#22)]),
             (A#20[(app A#21[(var X#17)] T#22[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#20[(app A#21[(var X#17)] T#22[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  [.],
           T#4          |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=S#2} in A#20[(app A#21[(var X#17)] T#22[(var X#1)])]);E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=A#15[(var X#17)]} in (var X#1))
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#15[(var X#17)]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#15[(var X#17)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(var X#17)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#15[(var X#17)];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#15[(var X#17)]}

and instantiated rules:

                                  (letrec {X#16=A#15[(var X#17)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=A#15[(var X#17)]} in (var X#1));E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#15[(var X#17)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#15[(var X#17)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {E#7} in T#21[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app T#21[T#4[S#2]] S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[(app (letrec {E#7} in T#21) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {E#7} in T#21) S#8)],
           T#19         |->  (app (letrec {E#7} in T#21) S#8),
           T#20         |->  (letrec {E#7} in T#21),
           S#9          |->  T#21[T#4[S#2]]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[T#4[S#2]]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(app (letrec {E#7} in T#21[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[T#4[S#2]]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app T#21[T#4[S#2]] S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {X#22=T#21[(letrec {X#1=S#2} in T#4[(var X#1)])];E#24} in S#9) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#22=T#21[T#4[S#2]];E#24} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#22=T#21[T#4[S#2]];E#24} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)],
           T#19         |->  (app (letrec {X#22=T#21;E#24} in S#9) S#8),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#9),
           E#7          |->  {X#22=T#21[T#4[S#2]];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[T#4[S#2]];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(app (letrec {X#22=T#21[(letrec {X#1=S#2} in T#4[(var X#1)])];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[T#4[S#2]];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {X#22=T#21[T#4[S#2]];E#24} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {X#1=S#2} in (letrec {E#7} in T#21[(var X#1)])) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app T#21[S#2] S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,T#19,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {E#7} in T#21)),
             (S#2,(letrec {E#7} in T#21)),
             ((letrec {E#7} in T#21[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {E#7} in T#21[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[(app [.] S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app [.] S#8)],
           T#19         |->  (app [.] S#8),
           T#20         |->  [.],
           T#4          |->  (letrec {E#7} in T#21),
           S#9          |->  T#21[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[S#2]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(app (letrec {X#1=S#2} in (letrec {E#7} in T#21[(var X#1)])) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[S#2]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app T#21[S#2] S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {X#1=S#2} in (letrec {X#22=T#21[(var X#1)];E#24} in S#9)) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#22=T#21[S#2];E#24} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,T#19,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#22=T#21;E#24} in S#9)),
             (S#2,(letrec {X#22=T#21;E#24} in S#9)),
             ((letrec {X#22=T#21[(dummy3 )];E#24} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#22=T#21[S#2];E#24} in [.])),
             ((var X#1),(letrec {X#22=T#21[[.]];E#24} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[(app [.] S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app [.] S#8)],
           T#19         |->  (app [.] S#8),
           T#20         |->  [.],
           T#4          |->  (letrec {X#22=T#21;E#24} in S#9),
           E#7          |->  {X#22=T#21[S#2];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[S#2];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(app (letrec {X#1=S#2} in (letrec {X#22=T#21[(var X#1)];E#24} in S#9)) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[S#2];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {X#22=T#21[S#2];E#24} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {X#1=(letrec {E#7} in S#9)} in (var X#1)) S#8)]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#7} in S#9),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[(app [.] S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app [.] S#8)],
           T#19         |->  (app [.] S#8),
           T#20         |->  [.],
           T#4          |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(app (letrec {X#1=(letrec {E#7} in S#9)} in (var X#1)) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app (letrec {E#7} in S#9) T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 T#20[T#4[S#2]]))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#20[T#4[S#2]],(letrec {E#7} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {E#7} in S#9) T#20)],
           T#19         |->  (app (letrec {E#7} in S#9) T#20),
           S#8          |->  T#20[T#4[S#2]]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[T#4[S#2]])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[T#4[S#2]])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 T#20[T#4[S#2]]))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=S#2} in (app (letrec {E#7} in T#21[(var X#1)]) S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app T#21[S#2] S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#4,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in T#21) S#8)),
             (S#2,(app (letrec {E#7} in T#21) S#8)),
             ((app (letrec {E#7} in T#21[(dummy3 )]) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in T#21[[.]]) S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[[.]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           T#4          |->  (app (letrec {E#7} in T#21) S#8),
           T#20         |->  (letrec {E#7} in T#21),
           S#9          |->  T#21[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[S#2]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=S#2} in (app (letrec {E#7} in T#21[(var X#1)]) S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[S#2]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app T#21[S#2] S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=S#2} in (app (letrec {X#22=T#21[(var X#1)];E#24} in S#9) S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#22=T#21[S#2];E#24} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#4,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {X#22=T#21;E#24} in S#9) S#8)),
             (S#2,(app (letrec {X#22=T#21;E#24} in S#9) S#8)),
             ((app (letrec {X#22=T#21[(dummy3 )];E#24} in S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#22=T#21[S#2];E#24} in [.])),
             ((var X#1),(app (letrec {X#22=T#21[[.]];E#24} in S#9) S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[[.]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           T#4          |->  (app (letrec {X#22=T#21;E#24} in S#9) S#8),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#9),
           E#7          |->  {X#22=T#21[S#2];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[S#2];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=S#2} in (app (letrec {X#22=T#21[(var X#1)];E#24} in S#9) S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[S#2];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {X#22=T#21[S#2];E#24} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=(letrec {E#7} in S#9)} in (app (var X#1) S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app [.] S#8)),
             ((letrec {E#7} in S#9),(app [.] S#8)),
             ((app (dummy3 ) S#8),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(app [.] S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[[.]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           T#4          |->  (app [.] S#8),
           T#20         |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=(letrec {E#7} in S#9)} in (app (var X#1) S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=S#2} in (app (letrec {E#7} in S#9) T#20[(var X#1)]))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 T#20[S#2]))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in S#9) T#20)),
             (S#2,(app (letrec {E#7} in S#9) T#20)),
             ((app (letrec {E#7} in S#9) T#20[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#20[S#2],(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in S#9) T#20[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[[.]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           T#4          |->  (app (letrec {E#7} in S#9) T#20),
           S#8          |->  T#20[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[S#2])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=S#2} in (app (letrec {E#7} in S#9) T#20[(var X#1)]))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[S#2])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 T#20[S#2]))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=(app (letrec {E#7} in S#9) S#8)} in (var X#1))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((app (letrec {E#7} in S#9) S#8),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#7} in S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[[.]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           T#4          |->  [.],
           S#2          |->  (app (letrec {E#7} in S#9) S#8)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=(app (letrec {E#7} in S#9) S#8)} in (var X#1))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=S#2} in A#20[(app (letrec {E#7} in T#23[(var X#1)]) S#8)])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#20[(letrec {E#7} in (app T#23[S#2] S#8))]]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#22,T#21,A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[(app (letrec {E#7} in T#23) S#8)]),
             (S#2,A#20[(app (letrec {E#7} in T#23) S#8)]),
             (A#20[(app (letrec {E#7} in T#23[(dummy3 )]) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#20[(app (letrec {E#7} in T#23[[.]]) S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#20[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#20],
           T#12         |->  A#18,
           A#19         |->  A#20,
           T#4          |->  A#20[(app (letrec {E#7} in T#23) S#8)],
           T#21         |->  (app (letrec {E#7} in T#23) S#8),
           T#22         |->  (letrec {E#7} in T#23),
           S#9          |->  T#23[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[(app (letrec {E#7} in T#23[S#2]) S#8)]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=S#2} in A#20[(app (letrec {E#7} in T#23[(var X#1)]) S#8)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[(app (letrec {E#7} in T#23[S#2]) S#8)]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[A#20[(letrec {E#7} in (app T#23[S#2] S#8))]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec
                       X#1= S#2
                    in
                       A#20[(app (letrec {X#24=T#23[(var X#1)];E#26} in S#9) S#8)]
                    )]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#20[(letrec {X#24=T#23[S#2];E#26} in (app S#9 S#8))]]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#22,T#21,A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[(app (letrec {X#24=T#23;E#26} in S#9) S#8)]),
             (S#2,A#20[(app (letrec {X#24=T#23;E#26} in S#9) S#8)]),
             (A#20[(app (letrec {X#24=T#23[(dummy3 )];E#26} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#24=T#23[S#2];E#26} in [.])),
             ((var X#1),A#20[(app (letrec {X#24=T#23[[.]];E#26} in S#9) S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#20[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#20],
           T#12         |->  A#18,
           A#19         |->  A#20,
           T#4          |->  A#20[(app (letrec {X#24=T#23;E#26} in S#9) S#8)],
           T#21         |->  (app (letrec {X#24=T#23;E#26} in S#9) S#8),
           T#22         |->  (letrec {X#24=T#23;E#26} in S#9),
           E#7          |->  {X#24=T#23[S#2];E#26},
           E#25         |->  {E#26}}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[(app (letrec {X#24=T#23[S#2];E#26} in S#9) S#8)]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=S#2} in A#20[(app (letrec {X#24=T#23[(var X#1)];E#26} in S#9) S#8)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[(app (letrec {X#24=T#23[S#2];E#26} in S#9) S#8)]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[A#20[(letrec {X#24=T#23[S#2];E#26} in (app S#9 S#8))]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=(letrec {E#7} in S#9)} in A#20[(app (var X#1) S#8)])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#20[(letrec {E#7} in (app S#9 S#8))]]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#21,A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[(app [.] S#8)]),
             ((letrec {E#7} in S#9),A#20[(app [.] S#8)]),
             (A#20[(app (dummy3 ) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#20[(app [.] S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#20[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#20],
           T#12         |->  A#18,
           A#19         |->  A#20,
           T#4          |->  A#20[(app [.] S#8)],
           T#21         |->  (app [.] S#8),
           T#22         |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[(app (letrec {E#7} in S#9) S#8)]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=(letrec {E#7} in S#9)} in A#20[(app (var X#1) S#8)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[(app (letrec {E#7} in S#9) S#8)]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[A#20[(letrec {E#7} in (app S#9 S#8))]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=S#2} in A#20[(app (letrec {E#7} in S#9) T#22[(var X#1)])])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#20[(letrec {E#7} in (app S#9 T#22[S#2]))]]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#21,A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[(app (letrec {E#7} in S#9) T#22)]),
             (S#2,A#20[(app (letrec {E#7} in S#9) T#22)]),
             (A#20[(app (letrec {E#7} in S#9) T#22[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#22[S#2],(letrec {E#7} in [.])),
             ((var X#1),A#20[(app (letrec {E#7} in S#9) T#22[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#20[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#20],
           T#12         |->  A#18,
           A#19         |->  A#20,
           T#4          |->  A#20[(app (letrec {E#7} in S#9) T#22)],
           T#21         |->  (app (letrec {E#7} in S#9) T#22),
           S#8          |->  T#22[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[(app (letrec {E#7} in S#9) T#22[S#2])]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=S#2} in A#20[(app (letrec {E#7} in S#9) T#22[(var X#1)])])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[(app (letrec {E#7} in S#9) T#22[S#2])]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[A#20[(letrec {E#7} in (app S#9 T#22[S#2]))]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=(app (letrec {E#7} in S#9) S#8)} in A#20[(var X#1)])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#20[(letrec {E#7} in (app S#9 S#8))]]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[[.]]),
             ((app (letrec {E#7} in S#9) S#8),A#20[[.]]),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#7} in S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#20[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#20[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#20],
           T#12         |->  A#18,
           A#19         |->  A#20,
           T#4          |->  A#20[[.]],
           T#21         |->  [.],
           S#2          |->  (app (letrec {E#7} in S#9) S#8)}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[(app (letrec {E#7} in S#9) S#8)]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=(app (letrec {E#7} in S#9) S#8)} in A#20[(var X#1)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[(app (letrec {E#7} in S#9) S#8)]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[A#20[(letrec {E#7} in (app S#9 S#8))]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=A#21[(app (letrec {E#7} in S#9) S#8)]} in A#20[(var X#1)])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#20[A#21[(letrec {E#7} in (app S#9 S#8))]]]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18,A#20}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20),
             (A#21[(app (letrec {E#7} in S#9) S#8)],A#20),
             (A#20[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#21[(app (letrec {E#7} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#20[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#20[A#21[[.2]]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#20[A#21]],
           T#12         |->  A#18,
           A#19         |->  A#20[A#21],
           T#4          |->  A#20,
           S#2          |->  A#21[(app (letrec {E#7} in S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[A#21[(app (letrec {E#7} in S#9) S#8)]]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=A#21[(app (letrec {E#7} in S#9) S#8)]} in A#20[(var X#1)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[A#21[(app (letrec {E#7} in S#9) S#8)]]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[A#20[A#21[(letrec {E#7} in (app S#9 S#8))]]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec
                       X#1= S#2
                    in
                       A#20[(app A#21[(app (letrec {E#7} in S#9) S#8)] T#22[(var X#1)])]
                    )]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#20[(app A#21[(letrec {E#7} in (app S#9 S#8))] T#22[S#2])]]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#19,T#4,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#20[(app A#21[(app (letrec {E#7} in S#9) S#8)] T#22)]),
             (S#2,A#20[(app A#21[(app (letrec {E#7} in S#9) S#8)] T#22)]),
             (A#20[(app A#21[(app (letrec {E#7} in S#9) S#8)] T#22[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#20[(app A#21[(app (letrec {E#7} in S#9) S#8)] T#22[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#20[(app A#21[[.2]] T#22[S#2])]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#20[(app A#21 T#22[S#2])]],
           T#12         |->  A#18,
           T#4          |->  A#20[(app A#21[(app (letrec {E#7} in S#9) S#8)] T#22)],
           A#19         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#20[(app A#21[(app (letrec {E#7} in S#9) S#8)] T#22[S#2])]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=S#2} in A#20[(app A#21[(app (letrec {E#7} in S#9) S#8)] T#22[(var X#1)])])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#20[(app A#21[(app (letrec {E#7} in S#9) S#8)] T#22[S#2])]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[A#20[(app A#21[(letrec {E#7} in (app S#9 S#8))] T#22[S#2])]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=S#2} in (app (letrec {E#7} in T#21[(var X#1)]) S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app T#21[S#2] S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#4,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in T#21) S#8)),
             (S#2,(app (letrec {E#7} in T#21) S#8)),
             ((app (letrec {E#7} in T#21[(dummy3 )]) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in T#21[[.]]) S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[[.]],
           T#12         |->  A#18,
           A#19         |->  [.],
           T#4          |->  (app (letrec {E#7} in T#21) S#8),
           T#20         |->  (letrec {E#7} in T#21),
           S#9          |->  T#21[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[S#2]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=S#2} in (app (letrec {E#7} in T#21[(var X#1)]) S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[S#2]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app T#21[S#2] S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=S#2} in (app (letrec {X#22=T#21[(var X#1)];E#24} in S#9) S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#22=T#21[S#2];E#24} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#4,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {X#22=T#21;E#24} in S#9) S#8)),
             (S#2,(app (letrec {X#22=T#21;E#24} in S#9) S#8)),
             ((app (letrec {X#22=T#21[(dummy3 )];E#24} in S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#22=T#21[S#2];E#24} in [.])),
             ((var X#1),(app (letrec {X#22=T#21[[.]];E#24} in S#9) S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[[.]],
           T#12         |->  A#18,
           A#19         |->  [.],
           T#4          |->  (app (letrec {X#22=T#21;E#24} in S#9) S#8),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#9),
           E#7          |->  {X#22=T#21[S#2];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[S#2];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=S#2} in (app (letrec {X#22=T#21[(var X#1)];E#24} in S#9) S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[S#2];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {X#22=T#21[S#2];E#24} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=(letrec {E#7} in S#9)} in (app (var X#1) S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app [.] S#8)),
             ((letrec {E#7} in S#9),(app [.] S#8)),
             ((app (dummy3 ) S#8),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(app [.] S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[[.]],
           T#12         |->  A#18,
           A#19         |->  [.],
           T#4          |->  (app [.] S#8),
           T#20         |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=(letrec {E#7} in S#9)} in (app (var X#1) S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=S#2} in (app (letrec {E#7} in S#9) T#20[(var X#1)]))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 T#20[S#2]))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in S#9) T#20)),
             (S#2,(app (letrec {E#7} in S#9) T#20)),
             ((app (letrec {E#7} in S#9) T#20[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#20[S#2],(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in S#9) T#20[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[[.]],
           T#12         |->  A#18,
           A#19         |->  [.],
           T#4          |->  (app (letrec {E#7} in S#9) T#20),
           S#8          |->  T#20[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[S#2])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=S#2} in (app (letrec {E#7} in S#9) T#20[(var X#1)]))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[S#2])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 T#20[S#2]))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(letrec {X#1=A#19[(app (letrec {E#7} in S#9) S#8)]} in (var X#1))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#19[(letrec {E#7} in (app S#9 S#8))]]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#19[(app (letrec {E#7} in S#9) S#8)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(app (letrec {E#7} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18;E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#19[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#19],
           T#12         |->  A#18,
           T#4          |->  [.],
           S#2          |->  A#19[(app (letrec {E#7} in S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#19[(app (letrec {E#7} in S#9) S#8)]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(letrec {X#1=A#19[(app (letrec {E#7} in S#9) S#8)]} in (var X#1))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#19[(app (letrec {E#7} in S#9) S#8)]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[A#19[(letrec {E#7} in (app S#9 S#8))]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[T#4[S#2]])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[T#4[S#2]])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[T#4[S#2]])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[T#4[S#2]])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(letrec {X#1=S#2} in T#4[(var X#1)])])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[T#4[S#2]])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[T#4[S#2]])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {E#7} in T#19[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app T#19[T#4[S#2]] S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=(app (letrec {E#7} in T#19) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[T#4[S#2]]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in T#19[T#4[S#2]]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(app (letrec {E#7} in T#19[(letrec {X#1=S#2} in T#4[(var X#1)])]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in T#19[T#4[S#2]]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app T#19[T#4[S#2]] S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {X#20=T#19[(letrec {X#1=S#2} in T#4[(var X#1)])];E#22} in S#9) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#20=T#19[T#4[S#2]];E#22} in (app S#9 S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#20=T#19[T#4[S#2]];E#22} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=(app (letrec {X#20=T#19;E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[T#4[S#2]];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {X#20=T#19[T#4[S#2]];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(app (letrec {X#20=T#19[(letrec {X#1=S#2} in T#4[(var X#1)])];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {X#20=T#19[T#4[S#2]];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {X#20=T#19[T#4[S#2]];E#22} in (app S#9 S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {X#1=S#2} in (letrec {E#7} in T#19[(var X#1)])) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app T#19[S#2] S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {E#7} in T#19)),
             (S#2,(letrec {E#7} in T#19)),
             ((letrec {E#7} in T#19[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {E#7} in T#19[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=(app [.] S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#18         |->  [.],
           T#4          |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[S#2]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in T#19[S#2]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(app (letrec {X#1=S#2} in (letrec {E#7} in T#19[(var X#1)])) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in T#19[S#2]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app T#19[S#2] S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {X#1=S#2} in (letrec {X#20=T#19[(var X#1)];E#22} in S#9)) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#20=T#19;E#22} in S#9)),
             (S#2,(letrec {X#20=T#19;E#22} in S#9)),
             ((letrec {X#20=T#19[(dummy3 )];E#22} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#20=T#19[S#2];E#22} in [.])),
             ((var X#1),(letrec {X#20=T#19[[.]];E#22} in S#9)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=(app [.] S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#18         |->  [.],
           T#4          |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[S#2];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(app (letrec {X#1=S#2} in (letrec {X#20=T#19[(var X#1)];E#22} in S#9)) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {X#1=(letrec {E#7} in S#9)} in (var X#1)) S#8)
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app S#9 S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#7} in S#9),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=(app [.] S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#18         |->  [.],
           T#4          |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(app (letrec {X#1=(letrec {E#7} in S#9)} in (var X#1)) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app S#9 S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (app (letrec {E#7} in S#9) T#18[(letrec {X#1=S#2} in T#4[(var X#1)])])
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app S#9 T#18[T#4[S#2]]))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),T#4),
             (S#2,T#4),
             (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[T#4[S#2]],(letrec {E#7} in [.])),
             ((var X#1),T#4[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=(app (letrec {E#7} in S#9) T#18);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[T#4[S#2]]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in S#9) T#18[T#4[S#2]]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(app (letrec {E#7} in S#9) T#18[(letrec {X#1=S#2} in T#4[(var X#1)])]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in S#9) T#18[T#4[S#2]]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app S#9 T#18[T#4[S#2]]));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=S#2} in A#18[(app (letrec {E#7} in T#21[(var X#1)]) S#8)])
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app T#21[S#2] S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#4,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[(app (letrec {E#7} in T#21) S#8)]),
             (S#2,A#18[(app (letrec {E#7} in T#21) S#8)]),
             (A#18[(app (letrec {E#7} in T#21[(dummy3 )]) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#18[(app (letrec {E#7} in T#21[[.]]) S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  A#18,
           T#4          |->  A#18[(app (letrec {E#7} in T#21) S#8)],
           T#19         |->  (app (letrec {E#7} in T#21) S#8),
           T#20         |->  (letrec {E#7} in T#21),
           S#9          |->  T#21[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[S#2]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=S#2} in A#18[(app (letrec {E#7} in T#21[(var X#1)]) S#8)]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[S#2]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app T#21[S#2] S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec
                 X#1= S#2
              in
                 A#18[(app (letrec {X#22=T#21[(var X#1)];E#24} in S#9) S#8)]
              )
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#22=T#21[S#2];E#24} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#4,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)]),
             (S#2,A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)]),
             (A#18[(app (letrec {X#22=T#21[(dummy3 )];E#24} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#22=T#21[S#2];E#24} in [.])),
             ((var X#1),A#18[(app (letrec {X#22=T#21[[.]];E#24} in S#9) S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  A#18,
           T#4          |->  A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)],
           T#19         |->  (app (letrec {X#22=T#21;E#24} in S#9) S#8),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#9),
           E#7          |->  {X#22=T#21[S#2];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[S#2];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=S#2} in A#18[(app (letrec {X#22=T#21[(var X#1)];E#24} in S#9) S#8)]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[S#2];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {X#22=T#21[S#2];E#24} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=(letrec {E#7} in S#9)} in A#18[(app (var X#1) S#8)])
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#4,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[(app [.] S#8)]),
             ((letrec {E#7} in S#9),A#18[(app [.] S#8)]),
             (A#18[(app (dummy3 ) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#18[(app [.] S#8)]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  A#18,
           T#4          |->  A#18[(app [.] S#8)],
           T#19         |->  (app [.] S#8),
           T#20         |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=(letrec {E#7} in S#9)} in A#18[(app (var X#1) S#8)]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=S#2} in A#18[(app (letrec {E#7} in S#9) T#20[(var X#1)])])
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 T#20[S#2]))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#4,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[(app (letrec {E#7} in S#9) T#20)]),
             (S#2,A#18[(app (letrec {E#7} in S#9) T#20)]),
             (A#18[(app (letrec {E#7} in S#9) T#20[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#20[S#2],(letrec {E#7} in [.])),
             ((var X#1),A#18[(app (letrec {E#7} in S#9) T#20[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  A#18,
           T#4          |->  A#18[(app (letrec {E#7} in S#9) T#20)],
           T#19         |->  (app (letrec {E#7} in S#9) T#20),
           S#8          |->  T#20[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[S#2])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=S#2} in A#18[(app (letrec {E#7} in S#9) T#20[(var X#1)])]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[S#2])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 T#20[S#2]))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=(app (letrec {E#7} in S#9) S#8)} in A#18[(var X#1)])
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[[.]]),
             ((app (letrec {E#7} in S#9) S#8),A#18[[.]]),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#7} in S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#18[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  A#18,
           T#4          |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  (app (letrec {E#7} in S#9) S#8)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=(app (letrec {E#7} in S#9) S#8)} in A#18[(var X#1)]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=A#19[(app (letrec {E#7} in S#9) S#8)]} in A#18[(var X#1)])
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[A#19[(letrec {E#7} in (app S#9 S#8))]]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18),
             (A#19[(app (letrec {E#7} in S#9) S#8)],A#18),
             (A#18[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(app (letrec {E#7} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#18[[.]]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#19[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  A#18[A#19],
           T#4          |->  A#18,
           S#2          |->  A#19[(app (letrec {E#7} in S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#19[(app (letrec {E#7} in S#9) S#8)]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=A#19[(app (letrec {E#7} in S#9) S#8)]} in A#18[(var X#1)]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[A#19[(app (letrec {E#7} in S#9) S#8)]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[A#19[(letrec {E#7} in (app S#9 S#8))]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec
                 X#1= S#2
              in
                 A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(var X#1)])]
              )
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[S#2])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)]),
             (S#2,A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)]),
             (A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(dummy3 )])],(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[[.]])]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[S#2])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           T#4          |->  A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[S#2])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=S#2} in A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(var X#1)])]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[S#2])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[S#2])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=S#2} in (app (letrec {E#7} in T#19[(var X#1)]) S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app T#19[S#2] S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in T#19) S#8)),
             (S#2,(app (letrec {E#7} in T#19) S#8)),
             ((app (letrec {E#7} in T#19[(dummy3 )]) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in T#19[[.]]) S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  [.],
           T#4          |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[S#2]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in T#19[S#2]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=S#2} in (app (letrec {E#7} in T#19[(var X#1)]) S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in T#19[S#2]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app T#19[S#2] S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=S#2} in (app (letrec {X#20=T#19[(var X#1)];E#22} in S#9) S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {X#20=T#19;E#22} in S#9) S#8)),
             (S#2,(app (letrec {X#20=T#19;E#22} in S#9) S#8)),
             ((app (letrec {X#20=T#19[(dummy3 )];E#22} in S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#20=T#19[S#2];E#22} in [.])),
             ((var X#1),(app (letrec {X#20=T#19[[.]];E#22} in S#9) S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  [.],
           T#4          |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[S#2];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=S#2} in (app (letrec {X#20=T#19[(var X#1)];E#22} in S#9) S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=(letrec {E#7} in S#9)} in (app (var X#1) S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app S#9 S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app [.] S#8)),
             ((letrec {E#7} in S#9),(app [.] S#8)),
             ((app (dummy3 ) S#8),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(app [.] S#8)),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  [.],
           T#4          |->  (app [.] S#8),
           T#18         |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=(letrec {E#7} in S#9)} in (app (var X#1) S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app S#9 S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=S#2} in (app (letrec {E#7} in S#9) T#18[(var X#1)]))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app S#9 T#18[S#2]))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4,T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(app (letrec {E#7} in S#9) T#18)),
             (S#2,(app (letrec {E#7} in S#9) T#18)),
             ((app (letrec {E#7} in S#9) T#18[(dummy3 )]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[S#2],(letrec {E#7} in [.])),
             ((var X#1),(app (letrec {E#7} in S#9) T#18[[.]])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           A#15         |->  [.],
           T#4          |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[S#2]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in S#9) T#18[S#2]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=S#2} in (app (letrec {E#7} in S#9) T#18[(var X#1)]));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in S#9) T#18[S#2]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app S#9 T#18[S#2]));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#16= (letrec {X#1=A#15[(app (letrec {E#7} in S#9) S#8)]} in (var X#1))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
    ,
     (letrec
        X#16= A#15[(letrec {E#7} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#3}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             (A#15[(app (letrec {E#7} in S#9) S#8)],[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(app (letrec {E#7} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  (letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#15[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           T#4          |->  [.],
           S#2          |->  A#15[(app (letrec {E#7} in S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#16=A#15[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#16=(letrec {X#1=A#15[(app (letrec {E#7} in S#9) S#8)]} in (var X#1));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    ................................................................................
                                  (letrec {X#16=A#15[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#15[(letrec {E#7} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           E#6
          ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
        in
           A#13[(app A#14[(var X#5)] T#15[(var X#1)])]
        )
     )
    ,
     (letrec
        E#6
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#13[(app A#14[(var X#5)] T#15[S#2])]
     )
  )

where

   Delta1 = {A#10,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)])),
             (S#2,(letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)])),
             ((letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(dummy3 )])]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[[.]])])),
             ((var X#5),A#13[(app A#14[[.]] T#15[S#2])]),
             ((var X#5),A#13[(app A#14[[.]] T#15[S#2])])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15)]),
           T#12  |->  A#13[(app A#14[(var X#5)] T#15)],
           A#10  |->  A#13[(app A#14 T#15[S#2])]}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[S#2])])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[(var X#1)])]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#13[(app A#14[(var X#5)] T#15[S#2])])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#13[(app A#14[(var X#5)] T#15[S#2])])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#13= T#12[(var X#1)]
          ;E#15
          ;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#13= T#12[S#2]
       ;E#15
       ;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#13=T#12;E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#13=T#12;E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])),
             ((letrec {X#13=T#12[(dummy3 )];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#13=T#12[[.]];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3   |->  [.],
           T#4   |->  (letrec {X#13=T#12;E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           E#6   |->  {X#13=T#12[S#2];E#15},
           E#14  |->  {E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]}}

and instantiated rules:

                                  (letrec {X#13=T#12[S#2];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#13=T#12[(var X#1)];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#13=T#12[S#2];E#15;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#13=T#12[S#2];E#15;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= A#16[(app (letrec {E#7} in T#19[(var X#1)]) S#8)]
          ;E#6
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app T#19[S#2] S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=A#16[(app (letrec {E#7} in T#19) S#8)];E#6} in A#10[(var X#5)])),
             (S#2,(letrec {X#5=A#16[(app (letrec {E#7} in T#19) S#8)];E#6} in A#10[(var X#5)])),
             ((letrec {X#5=A#16[(app (letrec {E#7} in T#19[(dummy3 )]) S#8)];E#6} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#5=A#16[(app (letrec {E#7} in T#19[[.]]) S#8)];E#6} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=A#16[(app (letrec {E#7} in T#19) S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {E#7} in T#19) S#8)],
           T#17         |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[S#2]) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=A#16[(app (letrec {E#7} in T#19[(var X#1)]) S#8)];E#6} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in T#19[S#2]) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app T#19[S#2] S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= A#16[(app (letrec {X#20=T#19[(var X#1)];E#22} in S#9) S#8)]
          ;E#6
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#5= A#16[(letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])),
             (S#2,(letrec {X#5=A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])),
             ((letrec {X#5=A#16[(app (letrec {X#20=T#19[(dummy3 )];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#20=T#19[S#2];E#22} in [.])),
             ((var X#1),(letrec {X#5=A#16[(app (letrec {X#20=T#19[[.]];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {X#20=T#19;E#22} in S#9) S#8)],
           T#17         |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[S#2];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=A#16[(app (letrec {X#20=T#19[(var X#1)];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#7} in S#9)
     in
        (letrec {X#5=A#16[(app (var X#1) S#8)];E#6} in A#10[(var X#5)])
     )
    ,
     (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=A#16[(app [.] S#8)];E#6} in A#10[(var X#5)])),
             ((letrec {E#7} in S#9),(letrec {X#5=A#16[(app [.] S#8)];E#6} in A#10[(var X#5)])),
             ((letrec {X#5=A#16[(app (dummy3 ) S#8)];E#6} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#5=A#16[(app [.] S#8)];E#6} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=A#16[(app [.] S#8)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app [.] S#8)],
           T#17         |->  (app [.] S#8),
           T#18         |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=(letrec {E#7} in S#9)} in (letrec {X#5=A#16[(app (var X#1) S#8)];E#6} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= A#16[(app (letrec {E#7} in S#9) T#18[(var X#1)])]
          ;E#6
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#5= A#16[(letrec {E#7} in (app S#9 T#18[S#2]))]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#17,A#15,T#12,T#4,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18)];E#6} in A#10[(var X#5)])),
             (S#2,(letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18)];E#6} in A#10[(var X#5)])),
             ((letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[(dummy3 )])];E#6} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[S#2],(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[[.]])];E#6} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[(app (letrec {E#7} in S#9) T#18)],
           T#17         |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[S#2]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[S#2])];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[(var X#1)])];E#6} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) T#18[S#2])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 T#18[S#2]))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (app (letrec {E#7} in S#9) S#8)
     in
        (letrec {X#5=A#16[(var X#1)];E#6} in A#10[(var X#5)])
     )
    ,
     (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {A#15,T#12,T#4,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=A#16[[.]];E#6} in A#10[(var X#5)])),
             ((app (letrec {E#7} in S#9) S#8),(letrec {X#5=A#16[[.]];E#6} in A#10[(var X#5)])),
             ((letrec {X#5=A#16[(dummy3 )];E#6} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#7} in S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#5=A#16[[.]];E#6} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=A#16[[.]];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16,
           T#12         |->  A#16[[.]],
           T#17         |->  [.],
           S#2          |->  (app (letrec {E#7} in S#9) S#8)}

and instantiated rules:

                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=(app (letrec {E#7} in S#9) S#8)} in (letrec {X#5=A#16[(var X#1)];E#6} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#16[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#17[(app (letrec {E#7} in S#9) S#8)]
     in
        (letrec {X#5=A#16[(var X#1)];E#6} in A#10[(var X#5)])
     )
    ,
     (letrec
        X#5= A#16[A#17[(letrec {E#7} in (app S#9 S#8))]]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4,A#16}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=A#16;E#6} in A#10[(var X#5)])),
             (A#17[(app (letrec {E#7} in S#9) S#8)],(letrec {X#5=A#16;E#6} in A#10[(var X#5)])),
             ((letrec {X#5=A#16[(dummy3 )];E#6} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (A#17[(app (letrec {E#7} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#5=A#16[[.]];E#6} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=A#16;E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[A#17[[.2]]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  A#16[A#17],
           T#12         |->  A#16,
           S#2          |->  A#17[(app (letrec {E#7} in S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#5=A#16[A#17[(app (letrec {E#7} in S#9) S#8)]];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=A#17[(app (letrec {E#7} in S#9) S#8)]} in (letrec {X#5=A#16[(var X#1)];E#6} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#16[A#17[(app (letrec {E#7} in S#9) S#8)]];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[A#17[(letrec {E#7} in (app S#9 S#8))]];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(var X#1)])]
          ;E#6
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#5= A#16[(app A#17[(letrec {E#7} in (app S#9 S#8))] T#18[S#2])]
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)];E#6} in A#10[(var X#5)])),
             (S#2,(letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)];E#6} in A#10[(var X#5)])),
             ((letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(dummy3 )])];E#6} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[[.]])];E#6} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#16[(app A#17[[.2]] T#18[S#2])]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18)],
           A#15         |->  A#16[(app A#17 T#18[S#2])]}

and instantiated rules:

                                  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[S#2])];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[(var X#1)])];E#6} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#16[(app A#17[(app (letrec {E#7} in S#9) S#8)] T#18[S#2])];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#16[(app A#17[(letrec {E#7} in (app S#9 S#8))] T#18[S#2])];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (app (letrec {E#7} in T#17[(var X#1)]) S#8)
          ;E#6
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec {X#5=(letrec {E#7} in (app T#17[S#2] S#8));E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#16,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=(app (letrec {E#7} in T#17) S#8);E#6} in A#10[(var X#5)])),
             (S#2,(letrec {X#5=(app (letrec {E#7} in T#17) S#8);E#6} in A#10[(var X#5)])),
             ((letrec {X#5=(app (letrec {E#7} in T#17[(dummy3 )]) S#8);E#6} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#5=(app (letrec {E#7} in T#17[[.]]) S#8);E#6} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(app (letrec {E#7} in T#17) S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in T#17) S#8),
           T#16         |->  (letrec {E#7} in T#17),
           S#9          |->  T#17[S#2]}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in T#17[S#2]) S#8);E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(app (letrec {E#7} in T#17[(var X#1)]) S#8);E#6} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in T#17[S#2]) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app T#17[S#2] S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (app (letrec {X#18=T#17[(var X#1)];E#20} in S#9) S#8)
          ;E#6
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#5= (letrec {X#18=T#17[S#2];E#20} in (app S#9 S#8))
       ;E#6
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#16,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=(app (letrec {X#18=T#17;E#20} in S#9) S#8);E#6} in A#10[(var X#5)])),
             (S#2,(letrec {X#5=(app (letrec {X#18=T#17;E#20} in S#9) S#8);E#6} in A#10[(var X#5)])),
             ((letrec {X#5=(app (letrec {X#18=T#17[(dummy3 )];E#20} in S#9) S#8);E#6} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#18=T#17[S#2];E#20} in [.])),
             ((var X#1),(letrec {X#5=(app (letrec {X#18=T#17[[.]];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(app (letrec {X#18=T#17;E#20} in S#9) S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {X#18=T#17;E#20} in S#9) S#8),
           T#16         |->  (letrec {X#18=T#17;E#20} in S#9),
           E#7          |->  {X#18=T#17[S#2];E#20},
           E#19         |->  {E#20}}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {X#18=T#17[S#2];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(app (letrec {X#18=T#17[(var X#1)];E#20} in S#9) S#8);E#6} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=(app (letrec {X#18=T#17[S#2];E#20} in S#9) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {X#18=T#17[S#2];E#20} in (app S#9 S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#7} in S#9)
     in
        (letrec {X#5=(app (var X#1) S#8);E#6} in A#10[(var X#5)])
     )
    ,
     (letrec {X#5=(letrec {E#7} in (app S#9 S#8));E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=(app [.] S#8);E#6} in A#10[(var X#5)])),
             ((letrec {E#7} in S#9),(letrec {X#5=(app [.] S#8);E#6} in A#10[(var X#5)])),
             ((letrec {X#5=(app (dummy3 ) S#8);E#6} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#5=(app [.] S#8);E#6} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(app [.] S#8);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#16         |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in S#9) S#8);E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=(letrec {E#7} in S#9)} in (letrec {X#5=(app (var X#1) S#8);E#6} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in S#9) S#8);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app S#9 S#8));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= (app (letrec {E#7} in S#9) T#16[(var X#1)])
          ;E#6
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec {X#5=(letrec {E#7} in (app S#9 T#16[S#2]));E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=(app (letrec {E#7} in S#9) T#16);E#6} in A#10[(var X#5)])),
             (S#2,(letrec {X#5=(app (letrec {E#7} in S#9) T#16);E#6} in A#10[(var X#5)])),
             ((letrec {X#5=(app (letrec {E#7} in S#9) T#16[(dummy3 )]);E#6} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#16[S#2],(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#5=(app (letrec {E#7} in S#9) T#16[[.]]);E#6} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=(app (letrec {E#7} in S#9) T#16);E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=[.2]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in S#9) T#16),
           S#8          |->  T#16[S#2]}

and instantiated rules:

                                  (letrec {X#5=(app (letrec {E#7} in S#9) T#16[S#2]);E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=(app (letrec {E#7} in S#9) T#16[(var X#1)]);E#6} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=(app (letrec {E#7} in S#9) T#16[S#2]);E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=(letrec {E#7} in (app S#9 T#16[S#2]));E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#15[(app (letrec {E#7} in S#9) S#8)]
     in
        (letrec {X#5=(var X#1);E#6} in A#10[(var X#5)])
     )
    ,
     (letrec {X#5=A#15[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
  )

where

   Delta1 = {T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=[.];E#6} in A#10[(var X#5)])),
             (A#15[(app (letrec {E#7} in S#9) S#8)],(letrec {X#5=[.];E#6} in A#10[(var X#5)])),
             ((letrec {X#5=(dummy3 );E#6} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(app (letrec {E#7} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#5=[.];E#6} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=[.];E#6} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#15[[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6},
           T#12         |->  [.],
           S#2          |->  A#15[(app (letrec {E#7} in S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#5=A#15[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=A#15[(app (letrec {E#7} in S#9) S#8)]} in (letrec {X#5=(var X#1);E#6} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#15[(app (letrec {E#7} in S#9) S#8)];E#6} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#15[(letrec {E#7} in (app S#9 S#8))];E#6} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#5= A#18[(app A#19[(var X#16)] T#20[(var X#1)])]
          ;E#6
          ;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#5= A#18[(app A#19[(var X#16)] T#20[S#2])]
       ;E#6
       ;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])),
             ((letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(dummy3 )])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#5=A#18[(app A#19[(var X#16)] T#20[[.]])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20)];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {[.1]=A#18[(app A#19[(var X#16)] T#20[S#2])];EE#17[X#16,[.2]]},
           X#13         |->  X#5,
           E#14         |->  {E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  A#18[(app A#19[(var X#16)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[S#2])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[(var X#1)])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[S#2])];E#6;EE#17[X#16,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#5=A#18[(app A#19[(var X#16)] T#20[S#2])];E#6;EE#17[X#16,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#16= A#20[(app A#21[(var X#17)] T#22[(var X#1)])]
          ;E#6
          ;EE#18[X#5,(var X#16)]
          ;EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#16= A#20[(app A#21[(var X#17)] T#22[S#2])]
       ;E#6
       ;EE#18[X#5,(var X#16)]
       ;EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])),
             ((letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(dummy3 )])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#16=A#20[(app A#21[(var X#17)] T#22[[.]])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22)];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];EE#18[[.1],(var X#16)];EE#19[X#17,[.2]]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]},
           T#12         |->  A#20[(app A#21[(var X#17)] T#22)],
           A#15         |->  A#20[(app A#21 T#22[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[(var X#1)])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#20[(app A#21[(var X#17)] T#22[S#2])];E#6;EE#18[X#5,(var X#16)];EE#19[X#17,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#16= A#18[(app (letrec {E#7} in T#21[(var X#1)]) S#8)]
          ;E#6
          ;EE#17[X#5,(var X#16)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app T#21[S#2] S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=A#18[(app (letrec {E#7} in T#21) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#16=A#18[(app (letrec {E#7} in T#21) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=A#18[(app (letrec {E#7} in T#21[(dummy3 )]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#16=A#18[(app (letrec {E#7} in T#21[[.]]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#18[(app (letrec {E#7} in T#21) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {E#7} in T#21) S#8)],
           T#19         |->  (app (letrec {E#7} in T#21) S#8),
           T#20         |->  (letrec {E#7} in T#21),
           S#9          |->  T#21[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[S#2]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#16=A#18[(app (letrec {E#7} in T#21[(var X#1)]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in T#21[S#2]) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app T#21[S#2] S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#16= A#18[(app (letrec {X#22=T#21[(var X#1)];E#24} in S#9) S#8)]
          ;E#6
          ;EE#17[X#5,(var X#16)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#16= A#18[(letrec {X#22=T#21[S#2];E#24} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#20,T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#16=A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=A#18[(app (letrec {X#22=T#21[(dummy3 )];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#22=T#21[S#2];E#24} in [.])),
             ((var X#1),(letrec {X#16=A#18[(app (letrec {X#22=T#21[[.]];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {X#22=T#21;E#24} in S#9) S#8)],
           T#19         |->  (app (letrec {X#22=T#21;E#24} in S#9) S#8),
           T#20         |->  (letrec {X#22=T#21;E#24} in S#9),
           E#7          |->  {X#22=T#21[S#2];E#24},
           E#23         |->  {E#24}}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[S#2];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#16=A#18[(app (letrec {X#22=T#21[(var X#1)];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {X#22=T#21[S#2];E#24} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {X#22=T#21[S#2];E#24} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#7} in S#9)
     in
        (letrec
           X#16= A#18[(app (var X#1) S#8)]
          ;E#6
          ;EE#17[X#5,(var X#16)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=A#18[(app [.] S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {E#7} in S#9),(letrec {X#16=A#18[(app [.] S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=A#18[(app (dummy3 ) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#16=A#18[(app [.] S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#18[(app [.] S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app [.] S#8)],
           T#19         |->  (app [.] S#8),
           T#20         |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=(letrec {E#7} in S#9)} in (letrec {X#16=A#18[(app (var X#1) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#16= A#18[(app (letrec {E#7} in S#9) T#20[(var X#1)])]
          ;E#6
          ;EE#17[X#5,(var X#16)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 T#20[S#2]))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#19,A#15,T#12,T#4,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[(dummy3 )])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#20[S#2],(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[[.]])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[(app (letrec {E#7} in S#9) T#20)],
           T#19         |->  (app (letrec {E#7} in S#9) T#20),
           S#8          |->  T#20[S#2]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[S#2])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[(var X#1)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) T#20[S#2])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 T#20[S#2]))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (app (letrec {E#7} in S#9) S#8)
     in
        (letrec {X#16=A#18[(var X#1)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
     )
    ,
     (letrec
        X#16= A#18[(letrec {E#7} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=A#18[[.]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((app (letrec {E#7} in S#9) S#8),(letrec {X#16=A#18[[.]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=A#18[(dummy3 )];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             ((app (letrec {E#7} in S#9) S#8),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#16=A#18[[.]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#18[[.]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18,
           T#12         |->  A#18[[.]],
           T#19         |->  [.],
           S#2          |->  (app (letrec {E#7} in S#9) S#8)}

and instantiated rules:

                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=(app (letrec {E#7} in S#9) S#8)} in (letrec {X#16=A#18[(var X#1)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#18[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(letrec {E#7} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#19[(app (letrec {E#7} in S#9) S#8)]
     in
        (letrec {X#16=A#18[(var X#1)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
     )
    ,
     (letrec
        X#16= A#18[A#19[(letrec {E#7} in (app S#9 S#8))]]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4,A#18}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=A#18;E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             (A#19[(app (letrec {E#7} in S#9) S#8)],(letrec {X#16=A#18;E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=A#18[(dummy3 )];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (A#19[(app (letrec {E#7} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#16=A#18[[.]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#18;E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[A#19[[.2]]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  A#18[A#19],
           T#12         |->  A#18,
           S#2          |->  A#19[(app (letrec {E#7} in S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#16=A#18[A#19[(app (letrec {E#7} in S#9) S#8)]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=A#19[(app (letrec {E#7} in S#9) S#8)]} in (letrec {X#16=A#18[(var X#1)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#18[A#19[(app (letrec {E#7} in S#9) S#8)]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[A#19[(letrec {E#7} in (app S#9 S#8))]];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#16= A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(var X#1)])]
          ;E#6
          ;EE#17[X#5,(var X#16)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#16= A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[S#2])]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {A#15,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(dummy3 )])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[[.]])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#18[(app A#19[[.2]] T#20[S#2])];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20)],
           A#15         |->  A#18[(app A#19 T#20[S#2])]}

and instantiated rules:

                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[S#2])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[(var X#1)])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#18[(app A#19[(app (letrec {E#7} in S#9) S#8)] T#20[S#2])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#18[(app A#19[(letrec {E#7} in (app S#9 S#8))] T#20[S#2])];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#16= (app (letrec {E#7} in T#19[(var X#1)]) S#8)
          ;E#6
          ;EE#17[X#5,(var X#16)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app T#19[S#2] S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=(app (letrec {E#7} in T#19) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#16=(app (letrec {E#7} in T#19) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=(app (letrec {E#7} in T#19[(dummy3 )]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#16=(app (letrec {E#7} in T#19[[.]]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=(app (letrec {E#7} in T#19) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in T#19) S#8),
           T#18         |->  (letrec {E#7} in T#19),
           S#9          |->  T#19[S#2]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in T#19[S#2]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#16=(app (letrec {E#7} in T#19[(var X#1)]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in T#19[S#2]) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app T#19[S#2] S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#16= (app (letrec {X#20=T#19[(var X#1)];E#22} in S#9) S#8)
          ;E#6
          ;EE#17[X#5,(var X#16)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#16= (letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#18,T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=(app (letrec {X#20=T#19;E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#16=(app (letrec {X#20=T#19;E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=(app (letrec {X#20=T#19[(dummy3 )];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {X#20=T#19[S#2];E#22} in [.])),
             ((var X#1),(letrec {X#16=(app (letrec {X#20=T#19[[.]];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=(app (letrec {X#20=T#19;E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {X#20=T#19;E#22} in S#9) S#8),
           T#18         |->  (letrec {X#20=T#19;E#22} in S#9),
           E#7          |->  {X#20=T#19[S#2];E#22},
           E#21         |->  {E#22}}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#16=(app (letrec {X#20=T#19[(var X#1)];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=(app (letrec {X#20=T#19[S#2];E#22} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {X#20=T#19[S#2];E#22} in (app S#9 S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#7} in S#9)
     in
        (letrec {X#16=(app (var X#1) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app S#9 S#8))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=(app [.] S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {E#7} in S#9),(letrec {X#16=(app [.] S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=(app (dummy3 ) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#7} in S#9),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#16=(app [.] S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=(app [.] S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app [.] S#8),
           T#18         |->  [.],
           S#2          |->  (letrec {E#7} in S#9)}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=(letrec {E#7} in S#9)} in (letrec {X#16=(app (var X#1) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in S#9) S#8);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app S#9 S#8));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= S#2
     in
        (letrec
           X#16= (app (letrec {E#7} in S#9) T#18[(var X#1)])
          ;E#6
          ;EE#17[X#5,(var X#16)]
        in
           A#10[(var X#5)]
        )
     )
    ,
     (letrec
        X#16= (letrec {E#7} in (app S#9 T#18[S#2]))
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#12,T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=(app (letrec {E#7} in S#9) T#18);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             (S#2,(letrec {X#16=(app (letrec {E#7} in S#9) T#18);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=(app (letrec {E#7} in S#9) T#18[(dummy3 )]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#2,(letrec {X#1=(dummy3 )} in [.])),
             (T#18[S#2],(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#16=(app (letrec {E#7} in S#9) T#18[[.]]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=(app (letrec {E#7} in S#9) T#18);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=[.2];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           A#15         |->  [.],
           T#12         |->  (app (letrec {E#7} in S#9) T#18),
           S#8          |->  T#18[S#2]}

and instantiated rules:

                                  (letrec {X#16=(app (letrec {E#7} in S#9) T#18[S#2]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=S#2} in (letrec {X#16=(app (letrec {E#7} in S#9) T#18[(var X#1)]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=(app (letrec {E#7} in S#9) T#18[S#2]);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=(letrec {E#7} in (app S#9 T#18[S#2]));E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= A#15[(app (letrec {E#7} in S#9) S#8)]
     in
        (letrec {X#16=(var X#1);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
     )
    ,
     (letrec
        X#16= A#15[(letrec {E#7} in (app S#9 S#8))]
       ;E#6
       ;EE#17[X#5,(var X#16)]
     in
        A#10[(var X#5)]
     )
  )

where

   Delta1 = {T#4}
   Delta2 = {E#7}
   Delta3 = {((var X#1),(letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             (A#15[(app (letrec {E#7} in S#9) S#8)],(letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((letrec {X#16=(dummy3 );E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (A#15[(app (letrec {E#7} in S#9) S#8)],(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),(letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3          |->  [.],
           T#4          |->  (letrec {X#16=[.];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]),
           EE#11[.1,.2] |-> {X#16=A#15[[.2]];EE#17[[.1],(var X#16)]},
           X#13         |->  X#16,
           E#14         |->  {E#6;EE#17[X#5,(var X#16)]},
           T#12         |->  [.],
           S#2          |->  A#15[(app (letrec {E#7} in S#9) S#8)]}

and instantiated rules:

                                  (letrec {X#16=A#15[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=A#15[(app (letrec {E#7} in S#9) S#8)]} in (letrec {X#16=(var X#1);E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)]))
    ................................................................................
                                  (letrec {X#16=A#15[(app (letrec {E#7} in S#9) S#8)];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {X#16=A#15[(letrec {E#7} in (app S#9 S#8))];E#6;EE#17[X#5,(var X#16)]} in A#10[(var X#5)])
    

================================================================================
Critical Pair:

  (
     (letrec
        X#1= (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
     in
        (var X#1)
     )
    ,
     (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
  )

where

   Delta1 = {}
   Delta2 = {E#7}
   Delta3 = {((var X#1),[.]),
             ((letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),[.]),
             ((dummy3 ),(letrec {X#1=(dummy3 )} in [.])),
             ((letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)]),(letrec {X#1=(dummy3 )} in [.])),
             (S#8,(letrec {E#7} in [.])),
             ((var X#1),[.]),
             ((var X#5),A#10[[.]]),
             ((var X#5),A#10[[.]])}
   Delta4=  {}

from overlapping -ucp3-> . -SR,lapp3-> with input rules:

                                  T#3[T#4[S#2]]
    -ucp3->                       T#3[(letrec {X#1=S#2} in T#4[(var X#1)])]
    and constraints: ((var X#1),T#4), (S#2,T#4), (T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])), (S#2,(letrec {X#1=(dummy3 )} in [.]))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    and constraints: E#7/= {}, (S#8,(letrec {E#7} in [.]))

and letrec unification problem:

      Gamma ={
        T#3[T#4[S#2]]
        =?=
        (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}
      Delta1=  {}
      Delta2=  {E#7}
      Delta3=  {((var X#1),T#4),(S#2,T#4),(T#4[(dummy3 )],(letrec {X#1=(dummy3 )} in [.])),(S#2,(letrec {X#1=(dummy3 )} in [.])),(S#8,(letrec {E#7} in [.])),((var X#1),T#4[[.]]),((var X#5),A#10[[.]]),((var X#5),A#10[[.]])}


and found solution:

    Sol = {T#3  |->  [.],
           T#4  |->  [.],
           S#2  |->  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])}

and instantiated rules:

                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -ucp3->                       (letrec {X#1=(letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])} in (var X#1))
    ................................................................................
                                  (letrec {E#6;EE#11[X#5,(app (letrec {E#7} in S#9) S#8)]} in A#10[(var X#5)])
    -SR,lapp3->                   (letrec {E#6;EE#11[X#5,(letrec {E#7} in (app S#9 S#8))]} in A#10[(var X#5)])
    


=========================================================
Statistics: 
---------------------------------------------------------
                                                  #critical pairs
==llet-in1==> . ==SR,lbeta1==>                    : 3
==llet-in1==> . ==SR,lbeta2==>                    : 5
==llet-in1==> . ==SR,lbeta3==>                    : 13
==llet-in1==> . ==SR,cp-in1==>                    : 4
==llet-in1==> . ==SR,cp-in2==>                    : 5
==llet-in1==> . ==SR,cp-e1==>                     : 13
==llet-in1==> . ==SR,cp-e2==>                     : 14
==llet-in1==> . ==SR,llet-in1==>                  : 5
==llet-in1==> . ==SR,llet-e1==>                   : 7
==llet-in1==> . ==SR,llet-e2==>                   : 12
==llet-in1==> . ==SR,lapp1==>                     : 9
==llet-in1==> . ==SR,lapp2==>                     : 11
==llet-in1==> . ==SR,lapp3==>                     : 25
==llet-e1==> . ==SR,lbeta1==>                     : 3
==llet-e1==> . ==SR,lbeta2==>                     : 5
==llet-e1==> . ==SR,lbeta3==>                     : 17
==llet-e1==> . ==SR,cp-in1==>                     : 4
==llet-e1==> . ==SR,cp-in2==>                     : 14
==llet-e1==> . ==SR,cp-e1==>                      : 22
==llet-e1==> . ==SR,cp-e2==>                      : 36
==llet-e1==> . ==SR,llet-in1==>                   : 5
==llet-e1==> . ==SR,llet-e1==>                    : 7
==llet-e1==> . ==SR,llet-e2==>                    : 21
==llet-e1==> . ==SR,lapp1==>                      : 9
==llet-e1==> . ==SR,lapp2==>                      : 11
==llet-e1==> . ==SR,lapp3==>                      : 29
==cp-e1==> . ==SR,lbeta1==>                       : 3
==cp-e1==> . ==SR,lbeta2==>                       : 5
==cp-e1==> . ==SR,lbeta3==>                       : 27
==cp-e1==> . ==SR,cp-in1==>                       : 6
==cp-e1==> . ==SR,cp-in2==>                       : 6
==cp-e1==> . ==SR,cp-e1==>                        : 30
==cp-e1==> . ==SR,cp-e2==>                        : 30
==cp-e1==> . ==SR,llet-in1==>                     : 5
==cp-e1==> . ==SR,llet-e1==>                      : 8
==cp-e1==> . ==SR,llet-e2==>                      : 16
==cp-e1==> . ==SR,lapp1==>                        : 9
==cp-e1==> . ==SR,lapp2==>                        : 11
==cp-e1==> . ==SR,lapp3==>                        : 39
==cp-in1==> . ==SR,lbeta1==>                      : 3
==cp-in1==> . ==SR,lbeta2==>                      : 11
==cp-in1==> . ==SR,lbeta3==>                      : 11
==cp-in1==> . ==SR,cp-in1==>                      : 4
==cp-in1==> . ==SR,cp-in2==>                      : 4
==cp-in1==> . ==SR,cp-e1==>                       : 12
==cp-in1==> . ==SR,cp-e2==>                       : 12
==cp-in1==> . ==SR,llet-in1==>                    : 6
==cp-in1==> . ==SR,llet-e1==>                     : 6
==cp-in1==> . ==SR,llet-e2==>                     : 10
==cp-in1==> . ==SR,lapp1==>                       : 9
==cp-in1==> . ==SR,lapp2==>                       : 17
==cp-in1==> . ==SR,lapp3==>                       : 23
==lbeta1==> . ==SR,lbeta1==>                      : 3
==lbeta1==> . ==SR,lbeta2==>                      : 5
==lbeta1==> . ==SR,lbeta3==>                      : 11
==lbeta1==> . ==SR,cp-in1==>                      : 3
==lbeta1==> . ==SR,cp-in2==>                      : 2
==lbeta1==> . ==SR,cp-e1==>                       : 10
==lbeta1==> . ==SR,cp-e2==>                       : 10
==lbeta1==> . ==SR,llet-in1==>                    : 5
==lbeta1==> . ==SR,llet-e1==>                     : 6
==lbeta1==> . ==SR,llet-e2==>                     : 9
==lbeta1==> . ==SR,lapp1==>                       : 9
==lbeta1==> . ==SR,lapp2==>                       : 11
==lbeta1==> . ==SR,lapp3==>                       : 23
==lapp1==> . ==SR,lbeta1==>                       : 3
==lapp1==> . ==SR,lbeta2==>                       : 6
==lapp1==> . ==SR,lbeta3==>                       : 11
==lapp1==> . ==SR,cp-in1==>                       : 3
==lapp1==> . ==SR,cp-in2==>                       : 3
==lapp1==> . ==SR,cp-e1==>                        : 11
==lapp1==> . ==SR,cp-e2==>                        : 11
==lapp1==> . ==SR,llet-in1==>                     : 4
==lapp1==> . ==SR,llet-e1==>                      : 6
==lapp1==> . ==SR,llet-e2==>                      : 10
==lapp1==> . ==SR,lapp1==>                        : 9
==lapp1==> . ==SR,lapp2==>                        : 12
==lapp1==> . ==SR,lapp3==>                        : 23
==cpx-in1==> . ==SR,lbeta1==>                     : 3
==cpx-in1==> . ==SR,lbeta2==>                     : 9
==cpx-in1==> . ==SR,lbeta3==>                     : 16
==cpx-in1==> . ==SR,cp-in1==>                     : 6
==cpx-in1==> . ==SR,cp-in2==>                     : 10
==cpx-in1==> . ==SR,cp-e1==>                      : 16
==cpx-in1==> . ==SR,cp-e2==>                      : 20
==cpx-in1==> . ==SR,llet-in1==>                   : 6
==cpx-in1==> . ==SR,llet-e1==>                    : 9
==cpx-in1==> . ==SR,llet-e2==>                    : 17
==cpx-in1==> . ==SR,lapp1==>                      : 9
==cpx-in1==> . ==SR,lapp2==>                      : 17
==cpx-in1==> . ==SR,lapp3==>                      : 28
==cpx-e1==> . ==SR,lbeta1==>                      : 3
==cpx-e1==> . ==SR,lbeta2==>                      : 5
==cpx-e1==> . ==SR,lbeta3==>                      : 59
==cpx-e1==> . ==SR,cp-in1==>                      : 4
==cpx-e1==> . ==SR,cp-in2==>                      : 16
==cpx-e1==> . ==SR,cp-e1==>                       : 58
==cpx-e1==> . ==SR,cp-e2==>                       : 102
==cpx-e1==> . ==SR,llet-in1==>                    : 5
==cpx-e1==> . ==SR,llet-e1==>                     : 8
==cpx-e1==> . ==SR,llet-e2==>                     : 56
==cpx-e1==> . ==SR,lapp1==>                       : 9
==cpx-e1==> . ==SR,lapp2==>                       : 11
==cpx-e1==> . ==SR,lapp3==>                       : 83
==xch1==> . ==SR,lbeta1==>                        : 3
==xch1==> . ==SR,lbeta2==>                        : 5
==xch1==> . ==SR,lbeta3==>                        : 19
==xch1==> . ==SR,cp-in1==>                        : 4
==xch1==> . ==SR,cp-in2==>                        : 14
==xch1==> . ==SR,cp-e1==>                         : 20
==xch1==> . ==SR,cp-e2==>                         : 30
==xch1==> . ==SR,llet-in1==>                      : 5
==xch1==> . ==SR,llet-e1==>                       : 7
==xch1==> . ==SR,llet-e2==>                       : 21
==xch1==> . ==SR,lapp1==>                         : 9
==xch1==> . ==SR,lapp2==>                         : 11
==xch1==> . ==SR,lapp3==>                         : 31
==gc1==> . ==SR,lbeta1==>                         : 8
==gc1==> . ==SR,lbeta2==>                         : 10
==gc1==> . ==SR,lbeta3==>                         : 30
==gc1==> . ==SR,cp-in1==>                         : 7
==gc1==> . ==SR,cp-in2==>                         : 11
==gc1==> . ==SR,cp-e1==>                          : 35
==gc1==> . ==SR,cp-e2==>                          : 39
==gc1==> . ==SR,llet-in1==>                       : 5
==gc1==> . ==SR,llet-e1==>                        : 9
==gc1==> . ==SR,llet-e2==>                        : 25
==gc1==> . ==SR,lapp1==>                          : 12
==gc1==> . ==SR,lapp2==>                          : 14
==gc1==> . ==SR,lapp3==>                          : 38
==gc2==> . ==SR,lbeta1==>                         : 3
==gc2==> . ==SR,lbeta2==>                         : 5
==gc2==> . ==SR,lbeta3==>                         : 11
==gc2==> . ==SR,cp-in1==>                         : 3
==gc2==> . ==SR,cp-in2==>                         : 3
==gc2==> . ==SR,cp-e1==>                          : 11
==gc2==> . ==SR,cp-e2==>                          : 11
==gc2==> . ==SR,llet-in1==>                       : 5
==gc2==> . ==SR,llet-e1==>                        : 6
==gc2==> . ==SR,llet-e2==>                        : 10
==gc2==> . ==SR,lapp1==>                          : 9
==gc2==> . ==SR,lapp2==>                          : 11
==gc2==> . ==SR,lapp3==>                          : 23
==ucp1==> . ==SR,lbeta1==>                        : 3
==ucp1==> . ==SR,lbeta2==>                        : 12
==ucp1==> . ==SR,lbeta3==>                        : 14
==ucp1==> . ==SR,cp-in1==>                        : 6
==ucp1==> . ==SR,cp-in2==>                        : 6
==ucp1==> . ==SR,cp-e1==>                         : 14
==ucp1==> . ==SR,cp-e2==>                         : 14
==ucp1==> . ==SR,llet-in1==>                      : 7
==ucp1==> . ==SR,llet-e1==>                       : 9
==ucp1==> . ==SR,llet-e2==>                       : 13
==ucp1==> . ==SR,lapp1==>                         : 9
==ucp1==> . ==SR,lapp2==>                         : 22
==ucp1==> . ==SR,lapp3==>                         : 26
==ucp2==> . ==SR,lbeta1==>                        : 3
==ucp2==> . ==SR,lbeta2==>                        : 5
==ucp2==> . ==SR,lbeta3==>                        : 35
==ucp2==> . ==SR,cp-in1==>                        : 4
==ucp2==> . ==SR,cp-in2==>                        : 8
==ucp2==> . ==SR,cp-e1==>                         : 40
==ucp2==> . ==SR,cp-e2==>                         : 44
==ucp2==> . ==SR,llet-in1==>                      : 5
==ucp2==> . ==SR,llet-e1==>                       : 9
==ucp2==> . ==SR,llet-e2==>                       : 29
==ucp2==> . ==SR,lapp1==>                         : 9
==ucp2==> . ==SR,lapp2==>                         : 11
==ucp2==> . ==SR,lapp3==>                         : 55
==ucp3==> . ==SR,lbeta1==>                        : 24
==ucp3==> . ==SR,lbeta2==>                        : 35
==ucp3==> . ==SR,lbeta3==>                        : 100
==ucp3==> . ==SR,cp-in1==>                        : 16
==ucp3==> . ==SR,cp-in2==>                        : 20
==ucp3==> . ==SR,cp-e1==>                         : 118
==ucp3==> . ==SR,cp-e2==>                         : 122
==ucp3==> . ==SR,llet-in1==>                      : 11
==ucp3==> . ==SR,llet-e1==>                       : 22
==ucp3==> . ==SR,llet-e2==>                       : 66
==ucp3==> . ==SR,lapp1==>                         : 42
==ucp3==> . ==SR,lapp2==>                         : 57
==ucp3==> . ==SR,lapp3==>                         : 144

---------------------------------------------------------
Overlaps per transformation
                                                  #critical pairs
cp-e1                                             : 195
cp-in1                                            : 128
cpx-e1                                            : 419
cpx-in1                                           : 166
gc1                                               : 243
gc2                                               : 111
lapp1                                             : 112
lbeta1                                            : 107
llet-e1                                           : 183
llet-in1                                          : 126
ucp1                                              : 155
ucp2                                              : 257
ucp3                                              : 777
xch1                                              : 179

---------------------------------------------------------
=========================================================
 Total number of critical pairs:                  3158
=========================================================